SlideShare a Scribd company logo
, ,f,,f+[i':l*t
rP ql r'
..rl:.1?"i
:::'lJt,l.;

?fdJ:,

              #ii,f,i*
+ rllt{^

tii::
              ',;:,"8:;i,.':,i:..:t.-,
              tt ,ACr, -i., r'+ l)
              ir l:'J,?i
                       ;ic'l;;k:'"'|
              r ; :i^"i:          :,
                      "1.:,:'nL,'
              ,,;,;:,,;;i:ii'11,.,
              ;fiij'.:;lf ' ;;i1;1

              {#ffit'rt:i
              iiii,ii#ilii::;ii
              ltir,'.ri
              '
                                Ii::i; ;,
                             St.l
                  . r i " - ' . t a l
              .r,i;";iTij|,:s.;;r- - l
               j:ti1;;|i;
                         i5;:;',:
              iiiiii'ilJr 'i*ir:.


              ffiffiffi
GOAI PROGRAMMING
                              AIPNOACETO
               ACGREGAMPRODUCTIOH
                                PI,AI{NING
                       I A CA,SESIIIDY




                    A Thesls submltted.

               In Parttal    lrlfilnent   of the
          Reqrrlrementsfor the Degree of



                  }IASMR OF TECIINOIOGY




                             BY

                    YOGESHSA:GNA
,i'd
                        r0 TiIs

       DEPART}MVT MECHANICAI
                OF         M{G]NEERING
           ?
       rNDrAlIrNsTrrutB oF TEcHIIOIocy,
                                     DEIHI
                            1982
This is to certily           that
I'lrr Yogesh Sarcenaworked. for his
i{. Tecirr proS ec t r'Goal prog ransdng

Approaci:. to Aegregate productlon
Planning     :         A ease strdyrr r:nd.er
rV sup ervi sion in           the i,iechanic aL
Engineering Depar tiuento Ind.ian
Ins titute       o f Technologyr Del jrl e
                 I further      certify   that
tn-ls proJ ect has no t been taken
up before        for     the award. of any
degr€er



                                ,i




                             ( DF.' I,i. SIIIGH)
                                 .
                             Deptt. of i'ieeh. Engg.
                             I.I.TrDellti.
g 9-$J E N.p
                  A C_$_N. br_,L D_
                         0




             I aJngrcattry            ind.ebt€d. to Dr. N.Singh
my pro j ect supervl sor and. express ry
g rati tud.e for his               af fec tionate     and encourag tng
guld,anceo During                  the year in wlrieh I worked.

uncler hiln I forrnd. hls invaluable                      adl.Lce of
g reat he1P.

              Thanlrs are also d.ue to I4r. G'DrSardanae
Gen, r"ianas                      K .Ganpathy r i'ianager, l'lalru-
          "l;pt?;
facturing              for provioj-ng roe inva^]-uable
                   Senrices,
                                               '
h elp and. suggestions .
             I aJ so acls"Ioi^IJ e '*[ th t]rank s the he]p
                               e€
extended by llr.               Sond|rl l Indlts trial         nngineer

and. other          staff      of llj-nd.rrstan Bro'nrnBovffr.
              Thanks are al-so due tc the s taf f o f

C o n r p u t e rC e n t r e , I . I . T .   Delhlr




I . I. TrDelhl
                                                 =)*'l-f<^^

            19E2.                               (YoGESHSAlGliA)
LB_S T R A C_T


               In this    thesls    an attempt has been mad.eto
analy s e the Agg reg ate Proclrrction p] annlng o f
Hindustan Brown govd, Far idabad, op tirnally.
            The denand of the noicr s w:tth d.ifferent            specificatlons
ve re no t the c ons tant          during   the planning    horizon   of on e
year io€r        1982-83? Consisting of three plaruring period.s.
            To meet wltir       the fl-uc fuations   in demand.e
Ag g regate Plannlng         mo,iel was formirlated., which concerr-
trate s on d.etermining lrhich comblnatton of the d.eclsion
variables       J.il<e prodirction     Taie, inventoryl      backord.ering
over   tiile     etc.    should be r-rtilis ed. in order to optimally
acUus t tlre demand fluc tuation s wi th-tn the con sl"raln ts
i f BnX.
            The AggregaLe planrring moder-was formulated. in
the form of goal s wi thr dlf f erent prloritieso                The
problen     was then solved           by uslng r'Coraputerlsed.technique
o f S .i'i. Lee to solve      the CoaJ- Prog ramnrlng ProbL errls The
                                                                rr,
decis icn variabl es were obtained for all                 the planning
p eriods.
C O N T E N T-S

                                                             Page
 1r      INTRODUCTION
 1.1     Oeneral                                                  t
                                                             fl
 1 oz    $eg reg at e prod.uctlon p1 annlng i                 L
         General Form
                                                              tl
 1 o3    lirqlest   structure of Aggregate
         Prod.uctlon plannlne
 1.4     I'Iul tl s tag e AgSreg ate pl annlng Sys tem        5
 1r
 I rO    Intpor tance of 'loal prog raJxalng                  G
 1.6     The Goal Prograuxning Concept                       a
 1o7    0 bJ ec tive    Func tion   ln Goa-l p rog ra$ming    3
 1.8    Rankire    & weighr.Lng of i'iul tlpl e g oal s       3
 2.      IJTEiiATUiiE nnVIS^I                                11
 3o     GOAL PnOGRAi'Ii'IIliG A I,',.,A,[E,.1ATICAL
                            AS                   ICOI        L
3.1     General i'iath einatical ;,iocieI                    LI
 3o2    Step s o f the Siuplex        method of Goal         L2-
        Prog rarunlng
3.3     Computer based Solution of Goal                      L6
        Prog raminlng
3o4     Flow Di aeraul
4.      PROCIE;.ISTA'IE.i.fiI{
                            T                                3L
4.1     General                                              3L
4o2     Data Oollection       Tabl_es                        3G
5o      GOAL PRG RAi,li,iN,IG}-IJrd,ir.JLArIOl,I             ql
6.      SOLUTIUI]
                 At,iDO iiEjitS                              55
7.      S UGGESTIuI'jS
                     FOn FIJliIiG.,t yjr,,rrK                58
Bo      REFEREJ]CBS                                         53
9.      APPENDIX
CHAPTER I
                           -



                          rNT,Rg.pucTIoN



     1 .1       GH'IEF4,.L
                        :

                i'lost manag
                           ers want to plan and, control          operatlons
     at     the broades t revelthro ugh some rrrnd. of aggreg ate
     pl'annlng    that by passes detalls of indlrridual prod.ucts
     and detailed        schedrrllng of facillties       and. personirelo
     i'ianagemer:t would. tr.eal $r:ith baslc relevant
                                                        d,ecisions
     of progra.uaud.nggtne use of resourC€sr
                                                      Thls ts &ccon_
    -pllshed by reviewirrg proJ ected.
                                            enpl0yment levels and
     by setting actlvity      rates trat can be varied. wlth rn
     a Blven errploynent level b7 varytng hours ruorked,
    ( worklng    overtirne or rrnd.ertiiie) r

           Once ilres e basic d.ecislons have been mad.e
                                                        for
    the upconlng perlod, detalled. sched.rrltng ean proceed.
    a t a lorser level      rvi thln   the cons traln ts o f the bro ad.
    pIan.      Finally    last   rnlnute ciranges tn actlvtty     levels
    need to be uade with          the realisatlon    of thelr    posslble
    ef fects    on ttre cos t of clnnghg       prod.uctton level,
    and on lnventory        costs lf     they are a part of the
    sJ,:S
        temo                                         




-
1oZ         AC.CRECATF
                       g
                                                                    s
               The Aggregate prod.uctl0n plan'ing      problen ln
   lts   most generar form ear be stated.
                                          as forlows.

         Given a set of forecasts of
                                     d.emand,,
                                            what shorrl.
  be for each period

               a)    Itre size of work forcel l{t
               b)    Ihe rate of prpductlon, pt
               c)    The QuantltY shlpped, Str

          The resrrrtrng lnventory per month
                                             can be deter_
  nlned. as f; = It-1 + pt - St.

          The problen ls 'sua{y resolved
                                            analytlcarly by
  mlnlntzlng the e :rpected to tar
                                   cost over a g i.ven Flann-
-lng horrzon consrsting
                           of soc* or arl of the fouowfus
  cost coqponents:

          a)        Ihe Cost of regular payroll     and,over tlne
          b)        The cost of chanelng the productl0n
                                                        rate
                    from one perlod. to the next
          c)        The cost of carrfing   jnventory
          d)        Cost of shortag es resul tlng frour
                                                        not
                    meettrg the d.ennand.

          The solutron to ttre problem
                                       ls greatly srncpll_
-fled' lf average d.emand
                          over the prannlng horlzon is
 expeeteti. to be constant.
The compl-exlty ln the Aggregate production

Plannlng     problen   arlses    fr"on the fact   that tn most
situations     d.enrand.
                      fer   perlod. ls not ccmstant but are
subJ ec t to subs tantlal       ff-uc baablon and the ques tlon
atLs es as to how the se func tions          should. b e absorb€d..
Assunlng     that   there are no problems ln receivjng          a
constant     supply of raw materials         and. labour at a fixed.
wage rate,     the problem ouy be seen by eonsld.erlng
thr ee Pure al ternative        ways o f r e spondlng to such
fluc fuations o

a)      A lnci'ease in orders ls met by hirirrg            anC a
        d.ecrease 1n orders ls accotapll sned b1'.layoff s.


b)      i.iain tenance of constant work force,           adJus ting
        productlon     r ate to orders by working ovelrtlme
        and wrder t1 ure ac c or dlng ly .


c)      i,ialntenanee of a constant work force and constant
        pTo duc tlon   rate r allow-tng lnventories        and order
        b acl0og s to fluc t,aate .


d)      l,iajn tenance of c snstant     wor k force    and mee the
                                                              t
        fluetuation      i.:n demalid.through planned bacKlogs
        o r by sub con trac tlng     exce s s d.e
                                                marrd,
                                                    r

        In generalr     none of the so-called. pure a-lternattvesl
dlscus s ed w111 prove be s t, but rather          some courblnation
o f ttrem. ord,er flue ttratl0ns
                                   showed. g eneral be
                                          In         l
  absorbed, partly bD' inventorxr parily
                                           by overtlme,
  and partJ.y by fririne and, Iayof,f,s
                                        and the opttuun
  eqphasls of these factors                 lnlll    depend.
                                                           upon the costs
  ln any parttcular           factoryr

  1.3       u
            PRosrFS
                  :

            The structure        of   t'e     Aggregate plannfrg            problen
 is     represented. by tlre slngle
                                                stag e sys tem trer         the
 plan'lng     horlzon      ls only one period a'ead.r
                                                 the state
 of the system at ttre e'd. of perlod.
                                       1s d,efined. by wo,
 Pe and ror the Asgregate work force
                                        slzel productlon
or ac tlvibl'    rate      and. jnventory           leve1,    respectlvely.
'rhe end'lng
                state      c qrd.lttons    beeoure the 1nltlal condtttons
for     the upcourlng perrod.          'rle
                                            have a forecast of the
requlrements         for
                      the upconlng perlod.s through soge
proc €ss o    Deelsions are nad,e that set the slze of the
work force      and' prod.uetron rate               for   the up-cond.ng perlod..
The d,eclsions       ma,ie uray call- for            hlrlng   or layj_rrg off
personnelt      thus expand.lng or contracttng                  ttre effcctlve
capacity     of the productJ.ua system,                   The uork force
slzel     together    lrrth   the d,ec1slon on actlvrty              rate    durc-ns
the pertodl     tlren d.eterrnrnes the requlred. arrcunt of
5




       overtimel lnventory levels or back ordering
                                                   r whether
       or not a shlft nust be added
                                    or deleted. and other
       posstble changes tn operating
                                     procedur€o

       1o4
                                                           :

                Ftg . shows a mrrl tl s tag
                                            e agg reg a te pLanntng
       sys teun vhere the horlzon
                                      has been expand.ed, th for _
                                                             w"l    e
       cas ts for eac' perl0d.o u*"
                                          obJec tive 1s to nake the
       declsions eoncernlng the work
                                             force slze and. productton
      ra te for the upconing p erlo d., In clolng
                                                   so r however
      we consid,er the sequenee of proJ
                                          ected decisions ln
      relation  to forecas ts and their cos i
                                               effectso    The
      declsion for the upcorntng perl0d,
                                           ls to be arf,ected. by
      the futr*e perl0d. forecasts
                                     a:d. the declsl0n process
      nnrs consld'er the cost effects
           t
                                             of the sequence of d,eclslons.
      Tir e conn ec tlng rtnks b e tween
                                          the s everal  s tag es ar e
      the w, pr and. r values that
                                         a^re at the end. of one
     perlod and the beglnnlrrg
                                     of the nextr    The feedback loop
     frour the d'ecision process
                                      ru4ylnvolve some lterative
     procedure to obtaln a
                                solutl0no      The seguentlal nature
     o f the declsions should. be
                                       kep t 1n mlnd.. All d.eclsions
     are rlght 01' wrong only ln terrns
                                              of the sequence of
     declstons over a perlod. of tlne.




h€
1o5
                                                              :

                  Organizattonal
                            obJectlves vary
                                                aecord.ing to
   the elraracteristicse
                           typesr FhtlosoptXr
                                                 of &anageuentl
   so partierrlar  environuenta-l (o ndlttons
                                                 of the organr_
   aat10n'    There ts no slngle raelversal
                                               goal fo.. a,.
  org anrzatl0ns.    rn boayr , cf,rnand.c
                                           business envlronment,
  fl*ns Flace g reat
                       emptrasls on soclal
                                             responslblll ttes
  social contrlbutlons,                                         e
                           publlc relatlons
                                              r lndustrlal
  and 1abor relatlonsl
                          €tcr

             rf    we grant
                        that roanagerent has
                                               m.[tlple   conffls_
  tlng obJ eetives to
                        achi€ver the d.eclslon
                                                 crlterta
  should arso be nru' trdlnensl0nal0    ,rh1s
                                              tupr_les that
 when a decislon lnvoLves
                              nultlple goa_1sr the_quantltatlve
 tecl:nlque used. should.
                           be eapable of hand*ne
                                                      muLtlple
 dectsj-on criterlao
                        The llnear programudrg
                                                   teehnlque
has a llelted    value for problems
                                      hvolvlng    rruLttple
t oal sr

            The primary        dlfflcurty     i.rrth llnear       progsamm{ng
ts not its         inablllty     to refrect     connplexreallty.
                                                                         Rather,
lts   dlfficuJ-ty      lles    rn the unldlmensl0nallby
                                               of the
obJ ective    Jnctionl
                     vrhleh requtres cost
                                          or proflt fuifor-
matl0n that 1s often
                      alnost lnposslble to
                                            obtalnr  To
.: ,!

                                                                           1




    overcone       the urld,lnenstonallty
                                                  of the obJ ecttve
    f*rrctton      requlred.    ln   the llnear
                                      prograrrrnilng, efforts
   have been natr"eto convert
                               varl0us goals, costs,
                                                          or
   value neasure lnto one
                           crlterton,   nanely utlllty.

            However exact neasurernent
                                          of uttllty    ls no t a
   slropl e mattere  f'Ience1 d.ec1s10n naklng
                                                  throug h llnear
  programmtng vla a uullw
                                 fraretl0n is onry feaslble
  ln a theorettcal     serseo

           Goal progra^urrd.ngts
                                 a mod.ification and. extensl0n
 of L'P' ' The goal progra-mrnlns
                                     approach ls a technlque
 tha t t s capable of handlr'g
                                  deelslon probleros that
 dealtvlth   a slngle goal wtth nrrltlple
                                              subgoals., as
 well asi problerus wlt'
                           multJ.ple 80a1s wlth n*ltlpte
 sub goalso


              irle can solve     the se prdblerns us jng Lrp r
                                                               ^rbth
 j{ul tlple
                obJ ee tives o     For t'rts r w€ nay ln trod.uce
                                                                  o ther
 than the obJ ective           fr:nctlon, as rod.el constralnts.
The l.p-        rccel r equires
                             ttrat the cptlnum solutton
 nrrst satlsf!  all constralrrts.    Furttrermore, lt ls
assumed here that equal
                            lnportarrce 1s attached. to
                                                          varlous
obJ ecttves r However in
                            reall wr such assurnp  t10n are
obsurdo trtrst of arl,
                          it ls quite posslbre that
                                                         arl
tl:e constratnts of the problem
                                     can not be satisfied..
such a problera 1s called. rlnfeasiblerro
                                                            secondly
  all    eonstralnts         do not have equal lcportanc€o            there-
  fore     goal progranrnlng vhech renpves al.r.
                                                 such dlffteul-
  tles     ls    us ed. to solve such probleins.

  1.o           ru&_QOAt            q)i,tgEF.T
                       lR0GRAtl},IryG        :

                The concept of goal progyarnr4ingwas first             lntro-
 d'uced by A' Charnes & l'^lol{oCooper as a tool                 to resoLve
 lnj'easible        linear    prograrnrd:rg problefis o     Ttrls technlque
 has been rrrther           reflned. by yorJ lri     & s rl,lrlee and.
 o thers r        Goal progran,ulng wnd.chis s pecial           extenslon
 of llnear         programrulng, ls capable of solvlng            declslon
p robl ens with        a slngle       g oal or uul tlpl e g oal s o   The
goals      set by tlre ttanagenent are often achlevable only
at      the erpense of other goals.              zurfher-no!€    these
g oal s are ln couunensurable i o€. they cannot be measured.

on the same unlt             scsl€r     Thus there 1s a need. fcr
establishlng         a hlerarcly        of tnportance    aupng these
confllctlng         goal s so that low ord.er goals a.re consld.ered.
only afLer         the hrgher orders prlorlty           goals are
satisfied         or have reached. the point         beyond wlrlch no
furtlrer        lqprovement j.s deslrableo          Hence the problen
can be solved. by goal pfogrenryr{ng tif the                uuaagement
can provide         the ordtnal       ranklng of the goals tn tenms
si
*?.
rt
.1.




         of thetr   tuportance & arl relattonshlp
                                                        of the rcd.elr
          Econonl'caily spealclngr
                                    the msnager faces the problen
          of the allocatlon of scrace
                                           resourc€so ft ls not
          always posslble to achleve
                                         ttre wery goar f*lly to
          the extent d.esrred.by i'anagement.
                                                   Thus, wrth or
         wl thout Plogramnlng the manag
                              ,             er attaches a c er taln prtor _
       -1ty to the achreveinent
                                   of a partlcurar goal. the true
         value of goar- progrannrins
                                      ir, there-or.€1 the sorutron
        of proble'Sl lnvolrnlng !rutttp1e,
                                                confltet,,'g goals
        acco'ulng to tlre i'ianag r s pr10r1ty
                                 er            s truc tur.e.

        1.?
                                                            :
                  rr: goal programmrpg rnstead.
                                                   of try1ne to haxrorise
         or nlnlnlae the obJec tive crlterlcm
                                                    dlreetly as ln
         rlnear progranndng, 1t trles to
                                               nlnfudze the d.errrattons
         anong the goaLs and wl th ln Lhe g
                                                lven sets of constralnts.
        rhe devlatlonar vartable is
                                          Tepresented. two
                                                        ln
        dimsrsl0ns 1n the obJecttve functl0n,
                                                      a posttlve and.
        a negatlve deviatlon fr"om each
                                            subgoal and/or con_
        s trainto    Then the obJ ectlve functlon becones
                                                               trre ninl-
      -wLza*ton of these d,evlatlonsl
                                           based,on the relatlve
       lnpor tance or prlorlty     as srgned. to then.

      1 .8
                                                       0AIS :

               in order to achleve the ord.lnal
                                                soLutlon-that
lsr     to achle ve the goals aecord.lng to thelr                lryortaneel
        (-) Begatlve    and Sr        posltlve        devlatlons   about the goal
        must be ranlced accord.Jng to the r,prerytiver'                      priority
        factorso       In thls     way the low-ord.er goals are consl-
        dered only after         higher- ord.er goals are achleved as

        deslred.       The I'Preerrytlvet' priority  factors have
        the relationship         of     pJ
        the multlplicatlon            of De however large lt          may be,
       cartuot rnakepJ+1 greater             thran or equal to pJ.

                  The next step to be consldered tn the goal
       prog ramrnlng i s the welg h-tng c.if devlatlonal               variable s at
       the same priorlty         leve.lr         rf   any goal involveb        many
       deviational      variables        and lre want to glve prlorlty              to
       one over the other,            thl.s can be achieved. by assigning
       dj.ff er ent l.Ielghts     to tl:e s e deviational          variabl-es at the
       sarne prlorlty     leveI.        At the sarneprlorlty           levelr      the
       subgoal which acguires             manrfuouui
                                                  dlfferenttal          qeight w111
       be satlsfled      first     & then lt          wLLl go t o the next.         Ihe
       crlteria     for ,leterinlnlng        the different         veights    of the
       devlatlonaL      varlable       could be the rnlnl rnlzatton of
       opportwtiW       cos t or regret.              Therefore, d.evlatlonal varl-
       ables on the s ame priorlty               level    must be coulrrensurable,
       although     deviatlons        that   are on the dlfferent            prlority
       levels     need no t be conrnensurable.




 i;
,.1-
#




&'
:" -:TT



                        cHAPTE&
                              rr




              The Productlon      plannlng problen
                                                       ts concerned.
    vt th sp eclfylng    the optlmar quantlttes
                                                 to be prod.uced.
    1n or.der to rneet
                        d.enrand,
                                for a speclfled. planntng
   'orlaon'    t'lary nod'else each
                                    of vblch has lts pros
   cons, have been d.                                       and.
                        evel0ped to help
                                           to solve trrls
   probl em.


             'Productd'on
                            nlan'lng     1s of a hlerarchical
                                                              naturee
  since   each level    of    the organl zatLon jr[erar.;*tlc1_
-p8 tes   rrr t he plan'lng     process wlth d.lfferent
                                                            braphaslsr
  scoPer and planning
                              hortz6n.     Those operattrng at the
 strategtc      level are prlnarlly
                                          concerned. v,*ft the
                                                                 10ng_
  r''nge plans of the
                             org anLzatl0n as a
                                                  whoJe. This
  requlres    sl'nrl taneous consld.eratlon
                                                of the dlfferent
 func tional policles
                              and tirelr coordlnatlon
                                                          so that tLre
 f trnt s frarc tlonal
                          s trateg ies b e consls
                                                  tent r*rth each
 otherr     As we go from the top
                                         level to t|re tactlcal
and opela tlonal levels
                                r planntng horlzon     d.ecrease
and ttre degree of
                         uncertatntby Ceereases.
                                                        However, the
d ep en d'ence b e bween
                          the frnc t10na1 ac
                                               t1v:Ltl e s t s
byplcaly     coordlnated. more
                                     at the tactical
                                                        level than




                                                                              ;
                                                                              Ir
lz
                                                                                            -'   L ,   ,tsi   ''- {',




                                                                                        :




          at    the operatlonal         levelr      Thls also hints       at the hlerar-
    - chlcal            lnfornatlon     problems associatal           u:tth prod.ucfi,on
      plannlng  slncb pl-ans at any glven l_evel
                                                 are based.
      on the inforunatlon before
                                  the factl and trren upd.ated.
?     accordlng to the lnformatl0n
                                     feed.-back after the f aet.

                    productlon        plannlng     nooels t       ]      lntroduced.
      in       the Li teratrere trffer           ln thelr   oriertation,       scope,
      co n ten ts & n ethodology.                Ilowever e lre can cras s ify
      thes e models ln            two r.raln categor.i es ; deserlp tlve
                                                                                    &
     normative.

     Dggglpttve             i,rod
                                ef,S 3

                   Descrlptlve         nodels alm pf descrlblng the process
     by whlch procluctlon              plans     are determlned ln practice.
     The rnaln examples of               such rnodels are!

    1):


                   t lo]
                  rntrod.uced br Bownan ( 1gfu) and extend.ed
  by Kumren ther ( 1969) thls
                           ,      nod.el assunes that manager
  behave efflci entry an average,
                                     but suf fer frora 1n-
- cons ls tency and. blas
                          es to recent events o Lrnear
    FRE8 regresslon             ls used. to d.evelop decislon              ruJ.es
    for        actual     productlon     ancl vork force oeclstons           uttlizlng
r   ':.' i ..r
                                                                                                - l.*;i
                                                                                                          1




     lnd.epend.ent vartables                  such as pas t sq,les and.
                                                                        logged
    produetlon,                 tnventoryr     ard. work forceo lhts nod.e1
    ls      very        f'exlble     ln belne not restrlcted.
                                                                       to a partt-
    cular         frrnctl0nal        beharrour        of ttre cost elernents
    1nvo1ved..


                   t,
                   A Serl0us d.rawbackof the proeed're
                            I
                                                       ls
   tire essentially   subJective selectfq  of the form of
   the ruler    rt very easily can be sereete.
                                                ln co*ectlyo

   i.1)           ljre-s                                                   ):
          Ti:e marn id.ea of thl s model is
                                             to proeeed in
   sequence s tartlng from a prespecifled.
                                             acceptable
  range of inventoryr and set
                                  accordtngly the llne_shlft
  levels of ruork forceo rhen ad.Just
                                         these according
   to      the rar'rge of lnventory                 d.eviatlon frorn lts    pernlsdlble
  r8'.g e r        r J' devlatl0ns           occur too frequentlyl         then the
  acc ep tabl e Level inven tory rang
                                      es ar e subJ ec t to ad.J t-
                                                              us
- ilentr


  r11)                                          :

              cExtensrve work has been c a*ied.
                        ]                          out rn
 thls fleld' uslng dlfferent statlstlcal
                                            and.mathenatlcal
 approaehes lncludlng vronte
                             carl0r saryll,,g, and.conputer
 anal0gu€o rn t, he nodell introd.uced.
                                         by vlrgln ( 1966),
tFre slurrlatton          starts     wlth a productlon         plan basirti
on past         e{perlence        of the flrn,      and, then cLrangessre
ln troduced. 1n enployment levele                   ov€rtlne1        lnventorles ,
sub -contractjng           r and so forttrl      untll    a loca]         opexst:lg
cos t mlrrlmunr ls          achiwed.r      0 ther    slnrrlatlon         nocleJ.sln
bhl.s regard. axe developed by Enshoff and Sisson ( 1g?0)r
and by tlayior           ( 19?1) r using both discrete,              and contlnuous
events         sinnrlation.       An lryortant       feature of slurulstion
ls     that     stoehasttc      d.ernand
                                       pattern        can be lncorporilted
ln     the uodel o        Thls p erml ts the analysls           of the forecast
error     on strategy          developme:t.

              No_rILE
                    tlv.e_ liosl el s :
                                                                     a




              Tire corunon focus 1n normative rrcCels ls on wirat
prod.uctlon         planners      should dor        i,lodels of thjs category
are f:r ther        clas sl fied. into    class€sr

(1.)          Aggregate PLannirg irpdels;              Ilrelr   --

              - - comrnonobj ec tlve      ls   to d,eteruilne the optlmal
production         quarttlty      to produee anci r,rork force leve]             to
us e ln aggregate for               a cordng ts plannlng horlLcut.

              j.iod,els ln thls     class are elther        exact or lreurlstlc.
T!




            E{Acr }rQgJ$ :

            tarrsportatl0n      I'{ethod foruulatlon
                                                       of tsowraan
   ( 10s61
            L 1 l proposed. the dis trlbutl0n
                                                      rnod.el 0f
  llnear    progra-ur'ring
                           fo:: Asgreg ate planning
                                                       , Th[s mod.el
  f ocus s ed' on tJ:e obJ ee
                              ttve of ass lgnlng units
                                                           of
  produc tive capact ty,
                             s o that procluction plus
                                                           s tora€ e
  cos ts were ,u''.luc-sed.
                             and, sales d.ernand. l'as met with iJl
  the cons tralnts     of avaiJ.abL e capaci ty.
                                                     Thls nrodel
 d.oes not aceornrt for prod.uctlon
                                          ehange cos tsr Such
 as hirlng & layoff of personnell
                                           and. there is no
 co s t p enal ty for baekor,J.erlng
                                       or 10 s t sal es .

        The slrnplex iuethod. of
                                 llnear        prograoro,lng urakes
 1t possible to inclu3.e prod"uction
                                             level     change costs
 and inventory     shortag e costs in ihe
                                          r.,roclel. Iianssnan
 and' lless a+r         d.ever-oped slrrplex *rodel
                                  a                 usr'g work
 force   an. prod.uctl0n rate     as lnclependrentdee1s10n
varlables     ancl in  terus of the coiliponents
                                                 of the cos t
moderr      arl   cost frure tdons are consrclered,
                                                   rlnear.

         One of the basic wealaress
                                       of llnear prograurmlng
3pproaches ( ana rcst oQrer
                              aggregate planriing technlqees)
is the assL'nrption of d,eterud.nls
                                    tic demand.o Another
short-contrrg of tlre llnear
                              progranunlrrg urod,el ls
                                                       the




                                                                       I
                                                                       t

                                                                       il
regutrenent of llnear                 cost frrctloDso      iloweverl ttr.e po-
  sslbiLiby     of piece rrrlse ltnear{.ty lnrproves the vatre}ty.

            Holtr        l,iodtellanl     and. S1rcn t lLl         gave tLre
 well    lceown mod.el ln whlch they mlntnlze                  a      qua{ratlc
 cost    f:nctlon        and come up with a llnear            decision        rure
  that   solves      for     op tlrnal Agereg ate prod.uction           rate    and.
 work force         size for        al-l the perlod.s over tLre plannlng
 horlzon.      L.i).R.        has nany advant&g€s o           First     the nod.el
 ls   optlmld-W           and the two decislon rules,              once d.erlvede
 are slniple        to apply.           In ad.dltion the rcd.el 1s dynamig
 and representattve              of     the unrltlstage klnd. of sys temo
 But quadrattc            cost   structure      nay have severe llmltation
 and. probably       d.oes not ad.equately represent                  the cost
 s truc tur e o f any or€ ani zatlon .

          tsergstron and sulth E 2 7                      extended. the capabl-
- li tie s of the L. D .3 . mod.el 1n two new dlr ec tlons . Be-
-c&u.s€ of the a€gregate natrrre of L.D.R. tE tt                         1s
 not posslble        to solve dlrectly              for   the optlnrnrmprod.uctlon
 ra t es for   lnd.ilrldual           produc ts .   The d,evelopnren and.
                                                                   t
 applicatlon        of     thre l.DR rnod.el-
                                            suggests that it             1s now
 operatlonalLy           feaslble       to remove the requlrement of
 an adgregate productlon                 dluenslon ln plannlng mod.elso
Further-toorer glven ttrre availr,b1llty
                                          of rev€nue curres
  for each product in each tlme
                                   perlod. the MDRnrcd.el
  can d.eterrntne optlnal prod.uctionl
                                        sales1 rnventoryr
  and work force levels so
                             as to raaxLrd-ze proflt over
  a specified. tlme horlzon.

         il nnpence Burbridge
                  &            CZf presented.a uulti;ole
 goal llneal programrnlng
                           moclel consld.ering comrrcrrly
 occurlng goals of tlre firin
                              1n coord.lnatlng prodrrction
 and 1ogis tic planning . Tlre solsflon
                                         technique for l,'-Ls
 tnodel I^ILll- ]:c a cci-rl-Jute':rze:I
                                       .rr1 bi.i1 c coj:cLir,:   il;r.o.,l-oj._r.'r
 c f the revisecl simplex methoC.


          Good.man a f
                  C    presented. goal prog"u*.,[rre
                                                     approach
 to soLving non-lrnear agtregate
                                   plannlng iocr.els. rf
 actual   cos ts ( i{iri'g   ct firing   cost, overtime & lclebl,ne,
rnventory   &' shortag e cos t) can not L. satisfactorlly
                                           e
repres entad quafu'atically,     then the solution b eeornes
u}cre conplex.    One approachr to i:andllng these inoie
                                                             corr-
pl ex moclels i s to atLet:pt
                               fon:u:latlon o f arr apl)roxirnating
l_lnea"r mod.el to the       originaL    non llnear   cost teruis
an d' to apply  souie vari ate o f the s iunplex
                                                 metirod.. Thi s
approaclr offers the re*' advantage
                                        of at least provid,tng
an optlual   solutton   to the mocler usecl and. ls b
                                                       a^d.ed.
upon the goal progra.nnrtng in thls peperr


             Tang and Adulbhan r B ]        proposes a 11near prog -
   rarunlng formul-atlon     of Aggregate prod.uction planning
   problem 1n the context        of heaqy     uianufactrrying lnd.ustry.
   A bastc rrroclel is first     rLevelopeci to rnd,nlrrd-ze
                                                           the
   total    cost of prod.uction which 1s assumed. be piece-
                                                to
  wise linear.         Tire basic updel is then transforre.d.
  into     a llnear   progra^m.:alng
                                   inoCel to seek an optlmal
  solutlon     for    a serj-es of plannlng periods wtthln           the
  pl annlng horlzon.


          Jaaskalainess, v t 6)     h a s p r o p o s e d .a g o a l
  prograrunlng inodel for the sclied.ullng of produc tlon,

  eatployment and. j-nventorj-es      to s atl sf}r lcno.'nrn
                                                            d.emand.
  re qulrernent over a finl te tlme horlzon.            Thi s mod.el
  sets tnree separaue and inconpl_etegoals, the Level of
  productlonr einployment and. lnventories r

            Thornasand HiJ-1 Lg I       forunrlated a nmlti-obJ ectlve
 pr.od.uctlon plannlng      modeJ as a goaf progran which
  c apt taliz es on tire s treng tirs of g oa1 progranmlng in 1n,-
- corporatln8    mul tiple behavloral and, economlc consld.erations
 in to the analysl s r      Thls flceurr paper lncludes        the
 aspectsr     lgnored. by Goo,iuran a I
                                   C          and.Jaakelalnenf         61 .
Ja.raesPo Ignlzlo     t, 5 f   tras atterpted'      to provld'e

           loo}<, at the relatlvelJ          nev field      of goal
a brief
                 under a preemptlve priorlry             structure'
programmlng
                              goal prograd-ng       raodel presented'
As such, the general
                                   realistlc      and' rather n:fr'ural
ls vlewed as a practlcall
                                                       world
representatlon        of a wtd,e varj-ety of nany real

probl ens r

          ileuristlcs    Models 3

                               paralnetrlc     plarrrdrry    nod'el b)'
(a)        The Procluctlon
          J one s ( 19?5) .TtrLs model as sume the exis tence
                                               s
                                                        work force
           of tvro basic declsion rules addrosSlng
                                                    each of
           and. productlon levels respeetivelyl
                                                 suin of rates
           whlch 1s expressed' a*s a welghted
                                             durlng the plannins
           required. to meet frtr8 e sal es
           horizon.


 (b)       A Swltch rule       proposed. by Elmaleh and' Ellon            019?4)'

           Theyspeclfytlrreeinventorylevels,arrd.tirree
                                               by various
           prod.uctlon 1eveIs, to be obtalned'
                                                over a hlstori-
            combjnatlons of control parameters
                                                      for w$orl
          -ca1 dernand series, and chooslng the set
                                          to dlscrete       levels,   such
            production    ls linlted

                  as food' and. chemica-ls '
(c)     Search Declslon Rulesl

                                                                -
        taub erb,     extend.ed. tJ1e computer slnoulatton metho

        d.ology to lts      qlti.urate ggl eralib,v by d.eveloplng

        technlqugs calIed. Search Decislon Rules LlO J'
                                                       l'11-1
        Iie defined. C1g1 as a frarction of (i'ttt Ptt      I

        0 t)   and. then ldentified.        the values within

        CtOt bY the folIowlng           veetors:



                      Declslon Veotors = Pt, Wt

                      Stag e Veetor = Ht-1, It-lI

                      Paraneter Vector = C o s t C o e f f i c l e n t s
                      at timee t

                               for    d'eclslon vectors       trrat
 SDR searcires d.lrectly
 red.uce CIOT.      Couiputer search routi-nes atterrpt to
                        s tag es sinirl tarreously g enera ting       trial
 q&x op tlniz e all

 d.ecisions per lieratlon.           The search procedure terruinates

 when successlve tterations           resr:J-t in sna-ll reduc tlon

 in Cf0T'
ii!-




                                0ITAPTFR
                                       rrr
                       .                                                    ''


                 cOrq,.t         4g-4 liATHEl,la_TIcAt USIE
                     .p&w54l0'fiNc                 I09IL
                                       ',
       3o1       G4{ER4'.I,                 :
                                      ]'{oDE}
                        },tAIrEuj[TI.Cg,

                   The goa.l prograrnrnlng tlas ortgtnally                              pDoposed.

       by Chanres & Cooper for                         a linear     mod.elo lllhlch has

       been further             d.eveloped W unny othersr                            A preferled

       sol.utton        ts one whlch nlnlnt                   zes the d.errlatlons from

       the   set goa1s,             Ihus a sturple llnear                   goal prograrnmlrg

       problem         fb.rnulatton          ls       shor,nr belou:
                                       r                         -+
       i'linlnlze          Z =         2              p'J      (q+q-             )
                                       Jt = 1
                                n
                                                                        +
       SubJect to               z            arJ t     xr
                                                         JA
                                                              + d,l - q - = b 1 f O f       i=lrooolll


                                J=1
                                                  +
                           *J    ,d;        ,di


       wnere                    E xq.                    =0


                   xJ = Dectslon                  varlables       to be found

                   K       = Number of prlorlty
                   n       =    Nunber of declslon                  varlables

                   m =          Nunrber of goals
                   b1 = GoaI set by ttre deelslon                           maker

                   pJ, = The Breenptlve                         wergbts suclr that pJ I
In    addl tlon    to s e ttlng     g o aJ. for
                                                     s       the obJ ec tlves 1
the decision        maker must also be able to glve an or-
d,lnal    ranking     to the obJ ectives.           The ranking     ean
also     be fotmd. out by paired             colnparison nrethod whlch
provid,es       some check on the consi-stency ln the value

J udg ement of the decision            makerr       In tf s nethod
the d.eclslon maker ls            asked to compare the goals two

at a same tlme and. indicate                 r*'htch goal is   the upre

inportant        ln the palr.        Thls procedure is appllecl to

all    combjnations of goal pairs.                 Thls analysls

results     ln a complete ordlnal              ranking of the goals

ln    terms of their         lnPortancer
                                                                    t




           The goal prograunlng ut1-llses tbe siunplex nethod
o f solving       the linear      prog ramrnlrrg probl en.       !{or,rever

s everal    modifications         are required and that ls

why the slmplex rnethod. of goal progranralng is often
ref erred, to as the t'modifled               slmplex methodorr


3 o2       srEts ,0LIlE-F.r]/IplF,ic                           ;
                                         9L,cOlI,,3n09n4'l.t',is'i9
                                   lF3j{Oe

S-J:
            Set up the |nltial          table     flora goal progra.nning

fornulation.          We assume that           the lnttlal     solutlon

1 s at orr€ j3e         Therefore      all     the neg ative    deviational

variables        in tlre mod.el constralnt           nrmst enter the
so].utlon base lnltiallJ.
                                        Preare      a table as shown below:


        c1

                   Variabl e   RI{S                      +
                                        d,   oorl   di       oorl   X1 oor




                                bi           CU


  'J - cJ          PS

                   'D4
                   P3
                  P2
                  P1



 Fill      up ttrl s tabre 1r € r all
                                        .i J&b+ .

 The cJ colum wtlr contaln
                                the coeffleient of d.evlational
 varlabre because thes
                         e vartables only enter
                                                  the
 s oJ.utlon firs to fn the
                            (ZJ _ Cj ) matrlxr
                                               l1s t ttre
prl0rlty    level ln the variabre
                                    columrr fbon l0west at
the Gop to the hlghest
                           at the bottomr Calcr.&ate
                                                       the Z1
values a'c1 record. it
                        into the RHScorruorl carc*late
the ZJ - C3 Values for eacb columr and.record. lt                       ln the
approprlate        colu.umo

S tep 2 :        4e.tsrgml.ne _bhe ne.v SnteJ:l,pg Vali,ablg:

          Flrxl the highest          prlorlty      Level that has not
been attalned         coryletely      by exaurlning the ZJ values          ln
the nHS columro            After    d.eternlnlng     this,   f1nd. out the
hlghest     zJ -cJ entry        columrr     rle variable      of this
colurn    wILl     enter    the solutlon        bas e ln tlre n ext i teration .

          In cas e of tie,          cLreck the next lower prlority
Level- and s el ec t the colun:I that has the g reater
valueo      If    at thls      stage, the tle carrrot be lbr.oken,
choose one on an arbitrary                basis'    The other columr will
be chosen in subsequent lterations.                    rhis is Imor,ar
as key colttur.

Step 3 3         ])elg rrxfn e- tbg_!egvlps_yari-+19
                                 ,,
                 Solutl_on- b_a,$S

          Dirt:ide     the values of Rits by the coefftcients
ln   the key colrurr r         Thls wlll- g lve     the nelr ruIS val-ue s o
Select    the ro,J whlch has the aininun              non-o€gatlve     value.
The variabre        tJs that       row wiJ-r- be replaeed. by bhe varl-
abre ln the key eolumr in the next lterationo                      rf
there         exts ts a tle,
                        f,Lnd the ro*r that has the
  variable  with the higher prlority     faetor.   rn this
  way tire higher order goals
                                nilt be attained. first
  and thereby red,uces the nrrmber
                                     of iterationso

  Step 4 :           Delgrn+ins tl€ nelr
                                         .sglu!ro!:

                 First     find. tJre ner.r?Jis and. co_€fficients
                                                                         of thre
 key row by d.ivid.lng old values
                                      by the plvot element
 i r €o the erernent at tl.e lnrersec
                                       tion of the key row
 and key colunr.     Then fina the new var-ues for all
 o:irer rol/s qr usi::g the c:j-c-r-,._ai.-o;.t
                                            :j..,oce,.._;Je :
                                                          c.f

 ( ui-.i t't:e - ( Intersectlonal element of that now x i,leu
      "r
 vaLue ill the Key row iJr the sarire
                                      coluriur)) . lrlow courplete
 tire tacle         by find.jns      ZJ and Zj _ Cj vali:es for        ilre
 p rio ri V       rors o

Siep       O :


                Analyse     tne goal attain:rent      revel    of eacjr goal
b1- checki'g             ;ire zJ value for   eacrr pr"lority    Tou.     rf
rhe zJ values              are all   zero, u.nis is    tJre optimal    soLutlonr
Ihenr      lf
            there are posi_tive Zj _ Cj va]ues
                                               in the rowl
d.eternrlne whether there ar.e neg
                                   ative ZJ _ CJ values
a t a hlgher         prlorl    ty leveL   r', the sarfle eolunnrr
"26',




            I f there i s n egative
                                    ZJ{J value at a higher
   prlorlbf    level for the poslttve
                                      ZJ _ CJ value fu the
   row o f tntere str the solutlon
                                    is optlnal.    F1nally1 tf
   there exlsts a positlve
                              ZJ{.J value at a certaln
  prlority   1evel and. there ls no neg
                                        ative ZJ r CJ value
  -at' a hlgher pfloriw   level ln the sai^,e cor-urnn,tiris is
  no t an optlmal solutio'o
                               Hence return to step 2
                                                          and,
  con tlnue.

          Flg ot.deptcts ttre slnpl ex
                                       solutton proc edure for
  g oal progra"umr:Lngproblems ',' the form of
                                                Jf-ow ci:art,
 3.3
          @                                                     :
                                                          {
          In ord.er for
                      goal prograrnrntng to
                                            be a usefUl
 managenent sclence technlque
                               for d.ecision analysis,
                                                          a
 compuLer-based,solutlon
                          1s an e ss ential reguireuren
                                                       t.
           Lee t 13 ] presented. a
                                        colxputer-based solution
 procedure of Goal Progranmj.ng 'rrhich
                                              can be used. to
 solve the problem after
                                sultable mod.ificationsr
 The l-l sttng o f the prog
                              rauup is shourn in Appelndtx
                                                               ro
r t dlscusses the data input
                                    for the con-outer so1ut10n,
 the lnput proc ess the proe
                       r           es s for careuratlng the
resultsl    and, flnally   ure proced.ure for prrnt
                                                       out of
the re sul ts o The d.ata
                             lnput ls dl scus s ed. bel0w
                                                          and.
the corylete llst       of data lnput is shown
                                                   in Append.ix II,
z-lk




 1.              ;*-= ?r.o hl eul g.ar4;

                                                     card and. defines               the
    ::-;":: ;:il":':: H:.
 numb'f                                              varlables         and. nurnber
 o f pt i r,'/1= 3s as slrown belov:
            / a:              i{Rows       1-IVA.R     NPRT

 2.         ;-e          S:qn Carg:

                .':-? s scond card descrlb es the direction
                                                                                 of con-
 s tralr t ?,*,
              o


                            " both directions
            ,t     .H

                                                   al'e possibleot'
           ,' !-'           ,, Iess th3.rrr',

           tt iU            r'ExactJ.y Egual
                                             .r,
           tr
                 /) tt      r,Sreater tltap.r,


0n e or. i t/,,i!- :evlational-        varlable s Af a cons tan t rrnrs
                                                                      t
app ear l./' 7.-e obi eetive           flrctionr  If nelther d,evlationC
var Lab I rt Q ?" ar s in        the obJ ective      frnc tlon,       it       1s
pos sLttl,, E'nzz both deviational               varlables     nay end. up
ln    tho tru-T and. the - cons tralnt
              -s                                     d; . d1       =        0
wLLl fittl, be neto

3.        1I:
          ,l,l rtse c ards are
             t                 pre fac ed. by a n ae' c
                                                        ard wlth
trO&l-rf puuChedo
!,,i


x




                          All   other    gard.s are punehed. ln the
                                                                    folr.owing
         rn=rrY]gro



         f ernlation                  Rov jn whlch         Pr iorlty       Welght
                                      ieqlation
                                      a_Dpeared

        ir -trlj




        t-l


                         These carc.s sp eclf!        the technclog ical    cterricients
       oi          ine choice vciables.             loer ( a1J) r and are prrnched.
       i -         tre   folloivlns     rcrrr€r o   The fir s t card ls punched.
       vi --:: the word. ,')A.I-qrr, onlyr



       .3. .- ix wlfl ch
         o                                  Colunnn ln uhl ch
        aij   app eared
                                                                       Value of aU
                                            aif appeared.
2?r=i




5.         The .3iFlt-Han$-S i4e:g args

            The flrst      eard. is punched with     trre word trRIGHTtr
onlyr      Rest card.s are punched with the values of
Right     hand side of al-J- the equatlons r


           Angir sl s o f the_9ornprrler 0! tpgli

            The Computer soLutlon of goal prograrn provides

the     folloiring    output;

Computer print          out of lnput dara ( the rlght       hand slde,
the substj. brtion         rates,   and the obJec tive     frnctlon) ,
the fixa-l      sirrplex    solutlon      table ( lncLudlng Zj - CJ matrix

an d. evalua tlon       o f ob j ective   fr:nc tion) , slack analysls ,
varlable       analysisr     and the analysis      of the obJective.

The lmpor tant        ones are elaborated bel-ow:

            T:Ii 5Ii'iAI SII'P,L,E{ SOtqTIOli


a)          TIIE :iIGiIT HAND SIDE
                     This shor s the rigbt       hand side values of
            the variable        ( Ceviational- and.d ecision) .     'l-he

           nurc:r s on the lef t-hand sd.de are varl abl e
                er
           nul"ir er s f or trte basle varlabl es r      The rsat
           values     on the r{-ghf-hand, sid.e represent constants
         of tne basle varibbleso
b)   TTIESUBSTIIUTTONRATAS


            TrI1s shows the vaj:es of aU of last
     iteratlon.       It   ls based, c:1 the colurrr arran€rement
                  +
     o f dT, di, xJ r ln that crCero

c)   THEZJ - CJ i'.iATRIX

            ThLs shows the ZJ - CJ matrj_x of the last
     i teratlon o

d)   Aii EVALUATf 0F 0B.IECT:rE FU]{CTION
                0i'[

            Thr-LsevaLuatlon      s!p1y   represents     ilre Zj
     value of goarsr         rn other vord.s, the values
     present      tlre under attalneJ, portlon   of goalso

e)   Tin SLACK .q.NAIXS
                      IS

            d,U AVAI L{3IE ,pOS U( .I,iE0 -S IJ{r
               rj              -S

            rt    presents    the va'rues of the rlght     hand.
     side and also varues of the negatlve and positlve
     varj-ables for each equationo

f)   VAJ1IABIE
             Ai{AIXSIS
     vA.lrABLE,AI,IO{I{T

            It presents Ure constants of only the
     basic chotce variables,
nr.,..
                                                   .rSItr




AIVAI.YSfS TT{E
         oF    OBJECTI
                     ru

      It'presents   the ZJ values
                                  for the
Bo&lso These values
                       refresent the
attalned portd.on                     und.er
                  of go&lsr
Pnr0luTY
                    UIDERAC}IrEI&l,IHlT
ffi
t



                                  CEAPTERIV
                                  %




                                            )

                          EEQBI4:M
                                SrAgEi,q,rI

       4 t1         qmElui!

                Hinclus tan . Boown.Boverl. ( 3ariclabad.) Is
                                                              a
       prominent org anisatton for proaucinS
                                                     the el-ectric
       iirotors. iI'B.8. produces the trcrcrs
                                                    of several klnds
       which differ    from each other in several aspects
      llke      f r a m e s i z e , I { o r s e p o w e r e i . , p . i , i . r l : u ^ u r b eo f p o l e s
                                                                                               r
       et c .


                   H rilo Jo forecasted. the d.e:iand- the t,otal I{orse
                                                     of
      pol'/er r to be produced. for                      the :/ear 1g32-g3.                 l,ianag
                                                                                                  enent
      es tj-mated a cuuruLative gror+tr cf 1s,,,in the d.euiand.
      o f ilors e power.              Ihe clemand. f sors e Dower l/as d.iff -
                                                 o
      er en t for       every period..+                Frenc ar a ttenp t is rnade to
                                                           e
      iaeet the denrand.
                       for                      every pericl         1n ar] optinal             way
      consldering           procruction rater                fnr-entory, Backorderingr
      overtime etc.               H. B.B. also had the de.,iand. cord. of
                                                              re
      ever? type of uiotor ( iJI numbers) for                                hlre year 1g8hg31
      g i-ven in Tabl-e I               .       Wlth the imowledge of the Las t


                 Four nron
                         ths a,re taken a s one planniry                                   p eriod..
tear    record,       the d.emand.   for erery k1nd. of motor
                                                                    ls
   aS -egS S ed., O.*,tqV1j.6 ' o
                                -t
                                   , for the c ou{) te ye ar 1g g2 _BB, Tob Q.e
                                                     le                       Z
  a]1 atteunc t ls also rnad,e
                                       to rneet r,rith the fluctuations
  in ceuand. for errcry khd.
                                        of notor 1n an opttmal l'ay ._
  3cl each frame rlzer there
                                           were frrther rrany kirrd.s cf
  :rc ;iis    'rith different      specificatiorfs r Therefor e
  c:l-; che representative            rnernber of the each frame size
 ua s cons idered. af ter the
                                        dl scuss ion wi th ,,ianag
                                                                 q r
 -'-aru jac turi:rg services Divi sion.
                                                   The types of nnotor
 r=:e s tilL        too many to make the problem as
                                                              a whcle
 Yer:r larg e to dealt       with.    Iience those types of notor,
tr;i c-: ,ti-d not show nuch      variation    in thej_n rnachining
 tj-:=s    wei'e clubed. together reasonably,.
                                                      It was real_ised.
 t::a : :iris problen can be solvetL by ,iraking
                                                         Aggp€grate
Plan:-'ans uodel, which concentrates on d.eterininlrrg
                                                                   wSich
c 3 -f,:::at:'on of the d.ecision variabl es
                                                   si:oul-d b e utili s ecl
in o: iel' to op timally       adj us t the d.e,.,land. tuations
                                                      fluc
vr  -;ri-n the
                con s traj-nts l f &rf, e

          j,lanagement ofilre conpany al so deslre d. to 1n _
corpc:ate    other relevant aspects such as posslbly
s tac- e eurployurent for     the workersl manageinent
                                                     pollcies
o r 8qa1s rel atLve to lnven tory and vorker
                                                       s ati sf ac tion
1'Ttc' erforuarlCs o
     J                  Therefore    these obJ ec tlves were also
5'l-




  incorporated,       ln    the problen    fornnrJ-atton.   TLre overaLl
  cos t functl0n  was segreg ated. lnto inalor
                                               componer ts
 1o €e Productlon 'rate and.
                               rnventory costs so that r,uJ.,Eg
                                                             e-
 inent can have adclitionar fr-exlbirity
                                           ln penari z.'tg
 devlations   fro m the v,:rious typ es of cos
                                               ts a'd uianagementr
                                                                 s
 p ercep tion of tradaoffs
                              among the cost conponents.

            The rnodel optliaizes         tjre ASgregate procluction
 variabr     es as well      as ce terrnlning   the op tirual p roduc t
 mix r The cornplete prcbl- erai s forrnulatecl
                                                in the form of
 goals and is then soLved.
                             b), uslng coriiputer based. solu_
 tion technique of goal prograrruirlng
                                        f lb I .

            The forlouing       3oa1s are lncorporated in.the
problem; in         o-rce{         p^rio-,,
                                "t

(a)        Sales .teallsation

(b)        I To Iitndt      the cos t associatecl wi th prod.uetlon
           rate   to a sp ec: f:-ed. a-roo,mt,
(c)        To l1mit       the cost associated. with rnventonr
           L evel s to a sp ec if ie ci arooun
                                             t.
(d)        ro prono te vorkers       irctivation   tirroug h rabor force
           s tabj-lityo                                                           t
                                                                                  I
                                                                                  T
                                                                                  t!

                                                                                  il
           There were five       sectlons 1n II.3.g. rlke:


                                                                                  i
                                                                                  I


                                                                                  i
                                                                                  ii
                                                                                  ii
                                                                                  il
                                                                                  il

                                                                                  il
1o       Foundary Sec tion
   2o        I'iachinlng   Sec tton
   3o        i^Iin*ing Seetlon
   4.        Asserrtbly Sectton
   5.        Shaft Processing Sectlono


           ;',anagerr l'tanufacturing Services DiuLsion sugg
                                                               es ted.
   tnat the ,iacirlnLrB Seetion was the only
                                                  crucial Section
  to be considerech Stand.ard. ttmes require4
                                                    for various
  op erations,    per-forned.   in the raachinlng section and.
  o ;her s ec tions were co.llec teC from the
                                                fnciustriaL
  lngineering        Departuent and are r-rsted. in Tabr_e c"           .

            rnventory      carrnng     cost and. Backord.erlng cost
 f or every repre sentative           motor were also }crown from
 - lar:a; eiler: t and are 8 iven in table      q     .     The over tlrue
 1{3s alloved  but not ncre tharr 1o:4of the normal worklng
 hcu's - rhe 'sorkers efflciency coef ficlen t
                                                  for old.
 '^-crker
          & new worker ( rf hlred.) ancl for norrnal
                                                     & overtinre
uoiking     :::urs wer e J<nor*nfrom the l,ianag
                                               er, i,lanufacturing
se rvlc es ..,irrision and are given below:


                                                  -                              ,l

                                               Eier                              i,
                                                                                 rl
                                                          hrs.      - 4r.g:- -
                                                                                 tl



3f fi-c i ency                                                                   :,
                           1rOO          018               1.00
Coefficiit,                                                         1.O0



                                                                                 ,!


                                                                                 I
                                                                                 I
                                                                                 'l
                                                                                 {
                                                                                 lir
                                                                                 l
                                                                                 ,t,
-t
                                               fl tr)Lr::
                 t OLLE CT os
r'7 PD'rn

                       Table          1
     Fra.me rri.se d.emand'o f notors for 1982-83




    1.                 80                             1.0          2600

    2.                 90                             2.O          3500

    3o                1oo                            3.0           4000

                      112                              5.0         6000
    4.
                      132                            10.0          650o
     5r
     6.                160                            15.0         6ooo
                       180                            2 5r 0        1475
     7o

                       200                            40.0           500
      8'
                           225                         60.0          350
      9.
                           250                         75.0           75
         10.
                           280                        1oo.o          1 2 0.
         11.
                           315                        13 0 , 0        BO
          12.
                           35s                         27OrO              30
          13.
                           J
                               r6o                          15        250
          14.
                               180                          40        180
          15.          ,
                               200                          50        230
           16.
                           22s
                                                            ntr,          8o
           17.
                               250                      125               40
           18.
                               315                          270            15
           19.
                               g,
                                180                          25            25
           20.
                                200                          40            40
            2 1.
                                225                           75          30
            22.
                                    250                     100            30
            23.
TABIE 7
         Denand. of motors on quarterly            basl s

So      tr'!Hne    aXrJunet     Peplol0Ctrl                 d iarrol   .FtsOo,
        s iae
                  { H*trAuso                                ApriJ- | 83.
Noo                             N o v r e D e co
                                  rg2
        Tg--
1.         80         729               753                        1118
2o        90          809            1 237                         1454
3.        100        1425               e46                        1 62e
4.        112        1904            19 3 S                        2158
5.        132        2982             2073                         1995
6.        160        2 0 33           1972                             393
7.         180        515               56?                            231
B.         200         106              163                             91
9r         225         110              1qe,                            29
 10.       250          19                27                            53
11.        280          23                44                            50
 12.       315            B               22                            50
13.        355            B                4                            18
          -g
 14.       160          &                 75                           121
15.        1Bo          s6                74                            50
16.        2oo          74              114                             o9

17.        225          29                26                            25
18.        250           4                22                            14
19.       315            4                  6                            5
          S
          'Tso
20c                       I               16                             1
 2 1.      200          1B                1a                             4
 22c       225              6             10                            14
 23o       250                              6                           17
Table 5

        Frame         rLn
        Sl'ze         Un1 t                           Group Isb      IInd.    flfrd
                                                      -
                                                            p erl-
                                                             gd_     n.:t"1
                                                                              .n."to:
        Qu 90        ;')
                                          )
        Qu loo         .?175 )                              712o      61e4     (SA6
                                          )                                                 ,?482s
        au 114         o7415 )
                                          )
        Qu 1gz         .8005 )
        Qu 15o       1.31?                    I
    Qu Bo            11485                    lB            3277     3292     2904        1 e4ggs
    Qu 13O           1 o5O4
                                              t
                                              I
    e     160       2 o533 )
                                      )                      110      149      171       e. cs5g
    e 1Bo           2.88              )
    iu zoo          3.109 I
                                  I                          114               232
    I     1Bo       3.357 l                                                              31333

i         2oo       4 . 1 S 2 I)
                              [)                                     132
s         2oo      4 . 2 O 7 T)                                                 96      4 .197
a         225      4e882 )
                              )
s         225      4 rB82 )                                 145      13s      130
                          )                                                             4.996
Qu zzs             5.2'26 )
qztu               5o903              I
                                      Ic
s        250      5.903               I                                        31       6 , 0 41 3
                                      I
Qu zso            6 r31B              I
Qu 2BO            7.979 )
                         )
e 315             I 1435 )                                                    53       8.207
Qu 315           11 .395                          I                  22       50      1 1 oBgS
Qu 35S           1 30 5 6 5                       x                  4        1 8 1B. a 6 s
Table q

                  Inven
                  C os t                                  (Rs.)
A                     182.4                               228
B                     411.2                               514
                      B14oB                              1018.6
                     1257                                1571.4
                      1560                               1950
                      573 o9                              717.39
                     3OO6.B                              3 7 5 8r 6
E                    3804 o4                             4755.5
                     5?60                                7200
i , __           _ g&o           _       _      ,       10poo_
                                                             _        _

                       i'acLe 5
          Productj.on Cost (Jsr) for         every type of ,-tor
SoNoo              GrquB----
1.                     A
                      fI                                1132
2o                    ts                                aqqe


3.                                                      6620
4o                    D                                 loztq
5.                    E                                 12675
6.                     F                                16533
7.                     G                                24431
8.                     TI
                       t-t                              30e1
                                                           1
9.                         I                            4 6800
    10.                J                                70200
g                               I
                                                          I
                                                          I
                          IJ
                      .rl{J
                      +J .rl
                                   ct
                     Fl                                  fp to ro to r-.yA g. m.O n.n
                                                         Ito
                     (U 5                                l@coD-                        cj -_t- C-u
                                                               r{o '-tAO N F{tr e.q e5qqa, Ae                                                                                                                        L F N c?
                     +t F{                                                        Fjto         &-6il                                                                                                                 toSb'o
                                                       l T F S, a o o ' : { o c o o o -
                     39,                               r-r-..B .i;d;dJid ::fffiS ;$$3
                                                       I
                                                              N

                     dP
                      r                                I
                                                       I
                     (D!                               I
       B             r:'t tr                           lt*u,.oro
       o             (d
       H
       L1
                     *)F{
                      oo                               IQA'666Pa$rHEv9339$*au?                                                                                                                                                               .o
       F'l           HP.                                       .      or,cr'i'+S$
                                                       i o o.o o o. b N i.r V. V i i. o , o.
                                                                            .           o                                            .       .
                                                                                                                                                                                                                 3$$$
       a                                               Jo                                                                                                      ,        . . .'.'.                                fu'-.-.                             r
                                                     I
                    fi*l
       $
      Ur.
      H                                              I
      (D
      F.
                                                     lEEq8,8,3 -
                                                     lr-f ,-l r-l r{ '-{
                                                                         RRg.,.999 o.o.o.o.o.o.    o c:oo
      O                                                                            . ;i ; ; rt 1-t Ft r{,_i                                                                                                                                  r{
      r-F                                            I
      F H
                                                                                                                       oacoo                                                    ec                                                           L.)
                                   ho                I                                                                                                                      pE.jq                                ppsi!
                                   (                 loocnc,o,o,oRP1'l:tr:
                                                        ' t ' ' t . o orf r{Nce                                                                                             '.adol                               -.'.a-r
                     Fr .rl                          l'
                    oq                               I
                    +) v,                            lcoc)o)cccDc0o?
                    do
                    *rF{
                    s:t A                            Hq:Eqqg."."*ppp 8888pp 88Ep
                                                                   oQ              .           .       .    .   o .    .    .    .       .                 r        .        .       .        .        .             o .             .           .
                                                     l.
                    o                              I
                    o                              I                                                               so                                                                                        ccrrro@
                                                   I                                                             cttcr)oa                            lcccr{Lcco
                    x                                                                                                                                  qi1tln
                                                                                                                                                       to.t;ac.o.                                            Orrr_rce
                                                                                                                                                                                                             yTTl
,- |
                .r{
                    fr{                            l,, | , I r,,.i,irTy
                                                   I
    x          (nA             ol        o
                                                   t_
    ct.l       o
               &1s
                                        H
                                         a
                                        rn
                                                   |              | |              | tc? | | . i-l-l        . .qqggq sss$gg ss$s
                                                                                                                   . . . ? .. . ..
    . {
    ^ . 4                                          lt                                                                              ? .
    G
                    +
                                                              polgqra()Nto@                                                                           r-t(c)
    5.)             h0                                        tCDol Ot9C-mdf-to$ru:
    iri             dho                                       '-f '-f '-f Ct C,tC{ Ol m crJ$t t! !O                                                    AQeflqrp                                             u;Oo'ot
               Fld                                              aoaaaoaaaaaaaao.a.aoao
                                                                                                                                                       tl C;:V + fj i-                                       C{ V, ${ u)
    -{
    '-1        r-{ 'rt
               F{g
    ,:)
    'I
               ofl p.
                                                              ultO tO tt)tr)LOtOLOU)LOrr1TO
                F{(d                                              . . . . . . . | . o . .                                                                          _ !O!O!OA                                         LOtl?LD
               mF{                                            OOCOOOOOOCICIO                                                                       nU)Nc-Nt<                                                urr-ND.:
                                                                                                                                                       .           . ..   . .                                    .       .       f           .

                uob                                           Ejs€j'RSEr-r@o)oi                                                                   ga(9r
               d
              .r,l E{
              .lJ
                                                              ooob;;qB{8fr$ 3EIs8n .SXSn
                                                                                 ^  QqF
                                                                  aaaaaa.araio.aaarraaa.

              €o
               oE1
              F{.
                                                 I
                                              Iro ro L/)ro tf) rf).ro to u) u).ro tJ?tr)                                                          o
                                                                                                                                                  rJ)totr)U)ulLrl
              CDA                                  . . o . . ..              .     ..                                                                  aaaaaaaaaa
                                                                                                                                                                                                           U)U)tr)u)
                                              l.
                                              lqt p gg ro e to ocro co .', cDc                                                                   -_ (). rtQ CCttt
                      H
                                                XBgsYtqrQq
                                             IERR             .                            .
                                                                                                                                                 Cnr-{('.(or-fo
                                                                                                                                                 (/i           a        a        a       .         .
                                                                                                                                                                                                           to r{@ 6q
                                                                                                                                                                                                           F{O?@;i
                                                                                                                                                                                                                     .       o

              s                              l.                        .       o                   r       rrlOlC.! CCd{tO                        o r{ r{ r{ Ci C0                                          a                           a
                                                                                                                                                                                                           rt -t __l Ci
             .r.l          o
                                             I
                                             lto url Le tr) Le
              F{ Er
             O.                              |Q q t9 t9 to tt trl tr; $t t' str Sr $l                                                          U)rOtotr)tr)tr)                                           |.r)Lr)rOu)
             Ftl (D
                                             Ia-oaaaaaaaoaaa                                                                                       aaaaQaaaoa
                                             l-l           .-f Fl r-{ r-r' rf                          r{ r-l r-f rl   r-f r-{ r-f               r-{ r{            r-f r-l r{ r{                           r-l r-f .-f ri
                                             I

                               I             l.s,c1q                                       .,.foo.orou,o                                                           r{)mtr)
             +)l                             lleSSXgRRl.!tqq dpglTq
                                                              o    .       .           .       ..           orlr{F{40C0                           r
                                                                                                                                                                                                           pq1'j
             3, I
             .r-l C,
                                             t()
                                             l^ ^ _                     rfr
                                                                                                                                                           o rl             r-l rl           t-{            o rf r-f r-t

                                             lto Q tO to .to tO tr) .tO C- p -rOrO ro                                                            pppppp pppp
             3H                              l_:_:_?
                                             l^
                                                        o .       o .N[-     -. i .
                                                         * C - C  tC ' C C  t O r O .
                                                                r                                                          i-f                    oaaaaaoooa
             o
             Eo
             CdN
                                             I
             t{.rl 5
             hoo                             iEEgflfiggRRRRHH*88R8
                                                          888fr8p                                                                                '-lrlNCINCC<l)-td:NN
-

                                                                                                                                                                                                                                                         !"f*lsirFqlqs,
{1.




                              ctwTEtl -_g
                             Goft L PRs)GR{ r"r}1Ncn,PnoB I'Er,,l Rrtr.vruL.sTrsN
                                                                  .
          ( 1)
 PRI9SI,T"Y :

 s ALE IirA,tI SAT
      Si_        r0l!

              Eqn. ( 1)      represents a general relationship.

              rt-1 * Pt = $t + rt                                                            ( 1)

 Where It-1          = Inventory     a t t h e e n c l o f t-1 th                 p eriod.

            It      = Inventory    ab the end of t           f.h   n ov4r J       n , .*l
                                                                                      -
                                                                              -   rv,
                                                                   I7




            p       = ProCuction    ra te cluring t th erlod
                t                                     -o

            gt = Saies tn t th period..


Let (It)*           = Inventory durin{            t th perlo,J.
                -
     ( I g)         = shor tag e clur irrg    t   trr p e' ioci    the

Iire + and -      slEr: above tjre parantheses
                                                mean that, the
quaritr r,los ilislcie the paran theses
                                         can have onr-y + or _ ve
val-ues rcripec'blvely.


         By uslng transforrnation:

        Let                       a>o
                    "*=fal
                          O otherwis e
        a                 lal      a<    o

       4               =Q otherrrise


                                          I
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi
Yogesh Saxena MTech Disseration, IIT Delhi

More Related Content

Similar to Yogesh Saxena MTech Disseration, IIT Delhi

Certificates
CertificatesCertificates
Certificates
DEBADATTA RATHA
 
1. What are the four basic financial statements and what can you l.docx
1. What are the four basic financial statements and what can you l.docx1. What are the four basic financial statements and what can you l.docx
1. What are the four basic financial statements and what can you l.docx
jackiewalcutt
 
Dec 2005
Dec 2005Dec 2005
Dec 2005
guestfbf635
 
The Open-Source Approach for Computational Modeling and Simulation for Earthq...
The Open-Source Approach for Computational Modeling and Simulation for Earthq...The Open-Source Approach for Computational Modeling and Simulation for Earthq...
The Open-Source Approach for Computational Modeling and Simulation for Earthq...
Academia de Ingeniería de México
 
Ball mill operatingmanual
Ball mill operatingmanualBall mill operatingmanual
Ball mill operatingmanual
XDanielx X-kunx
 
BTEC HNC Engineering (marine navigational systems eng.)
BTEC HNC Engineering (marine navigational systems eng.)BTEC HNC Engineering (marine navigational systems eng.)
BTEC HNC Engineering (marine navigational systems eng.)
Joseph P. Campbell
 
MNRE Certificate Of Home Lighting System.PDF
MNRE Certificate Of Home Lighting System.PDFMNRE Certificate Of Home Lighting System.PDF
MNRE Certificate Of Home Lighting System.PDF
Highflow Industries Pvt. Ltd.
 
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size ReducedRaheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
rahejadevelopersreview
 
Moisés Serrano - Education and Professional Development
Moisés Serrano - Education and Professional DevelopmentMoisés Serrano - Education and Professional Development
Moisés Serrano - Education and Professional Development
Blue Know
 
diploma_NEW
diploma_NEWdiploma_NEW
1st Semester MBA (December-2014) Question Papers
1st Semester MBA (December-2014) Question Papers1st Semester MBA (December-2014) Question Papers
1st Semester MBA (December-2014) Question Papers
BGS Institute of Technology, Adichunchanagiri University (ACU)
 
Chhabra Thermal Power Plant Report By Chandra Mohan Lodha
Chhabra Thermal Power Plant Report By Chandra Mohan LodhaChhabra Thermal Power Plant Report By Chandra Mohan Lodha
Chhabra Thermal Power Plant Report By Chandra Mohan Lodha
Chandra Mohan Lodha
 
M Tech 2nd Semester (CMOS VLSI) Question papers
M Tech 2nd Semester (CMOS VLSI) Question papers M Tech 2nd Semester (CMOS VLSI) Question papers
M Tech 2nd Semester (CMOS VLSI) Question papers
BGS Institute of Technology, Adichunchanagiri University (ACU)
 
Majestic 12 part 1 of 1
Majestic 12 part 1 of 1Majestic 12 part 1 of 1
Majestic 12 part 1 of 1
Clifford Stone
 
ID and Qualifications
ID and QualificationsID and Qualifications
ID and Qualifications
Bongani Thela
 
Apresentação GECCO-2017
Apresentação GECCO-2017Apresentação GECCO-2017
Apresentação GECCO-2017
Jesimar Arantes
 
Info Quest
Info QuestInfo Quest
Info Quest
Lalita Sinha
 
Oc in pakistan
Oc in pakistanOc in pakistan
Oc in pakistan
International advisers
 
GO
GOGO
Design and Fabrication for Motorized Automated Screw Jack
Design and Fabrication for Motorized Automated Screw JackDesign and Fabrication for Motorized Automated Screw Jack
Design and Fabrication for Motorized Automated Screw Jack
Hitesh Sharma
 

Similar to Yogesh Saxena MTech Disseration, IIT Delhi (20)

Certificates
CertificatesCertificates
Certificates
 
1. What are the four basic financial statements and what can you l.docx
1. What are the four basic financial statements and what can you l.docx1. What are the four basic financial statements and what can you l.docx
1. What are the four basic financial statements and what can you l.docx
 
Dec 2005
Dec 2005Dec 2005
Dec 2005
 
The Open-Source Approach for Computational Modeling and Simulation for Earthq...
The Open-Source Approach for Computational Modeling and Simulation for Earthq...The Open-Source Approach for Computational Modeling and Simulation for Earthq...
The Open-Source Approach for Computational Modeling and Simulation for Earthq...
 
Ball mill operatingmanual
Ball mill operatingmanualBall mill operatingmanual
Ball mill operatingmanual
 
BTEC HNC Engineering (marine navigational systems eng.)
BTEC HNC Engineering (marine navigational systems eng.)BTEC HNC Engineering (marine navigational systems eng.)
BTEC HNC Engineering (marine navigational systems eng.)
 
MNRE Certificate Of Home Lighting System.PDF
MNRE Certificate Of Home Lighting System.PDFMNRE Certificate Of Home Lighting System.PDF
MNRE Certificate Of Home Lighting System.PDF
 
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size ReducedRaheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
Raheja Developers DDA Contract_Raheja EWS Kathaputli Size Reduced
 
Moisés Serrano - Education and Professional Development
Moisés Serrano - Education and Professional DevelopmentMoisés Serrano - Education and Professional Development
Moisés Serrano - Education and Professional Development
 
diploma_NEW
diploma_NEWdiploma_NEW
diploma_NEW
 
1st Semester MBA (December-2014) Question Papers
1st Semester MBA (December-2014) Question Papers1st Semester MBA (December-2014) Question Papers
1st Semester MBA (December-2014) Question Papers
 
Chhabra Thermal Power Plant Report By Chandra Mohan Lodha
Chhabra Thermal Power Plant Report By Chandra Mohan LodhaChhabra Thermal Power Plant Report By Chandra Mohan Lodha
Chhabra Thermal Power Plant Report By Chandra Mohan Lodha
 
M Tech 2nd Semester (CMOS VLSI) Question papers
M Tech 2nd Semester (CMOS VLSI) Question papers M Tech 2nd Semester (CMOS VLSI) Question papers
M Tech 2nd Semester (CMOS VLSI) Question papers
 
Majestic 12 part 1 of 1
Majestic 12 part 1 of 1Majestic 12 part 1 of 1
Majestic 12 part 1 of 1
 
ID and Qualifications
ID and QualificationsID and Qualifications
ID and Qualifications
 
Apresentação GECCO-2017
Apresentação GECCO-2017Apresentação GECCO-2017
Apresentação GECCO-2017
 
Info Quest
Info QuestInfo Quest
Info Quest
 
Oc in pakistan
Oc in pakistanOc in pakistan
Oc in pakistan
 
GO
GOGO
GO
 
Design and Fabrication for Motorized Automated Screw Jack
Design and Fabrication for Motorized Automated Screw JackDesign and Fabrication for Motorized Automated Screw Jack
Design and Fabrication for Motorized Automated Screw Jack
 

More from IndiaEducationrReview

Global Research Report of India by Thomson Reuters
Global Research Report of India by Thomson ReutersGlobal Research Report of India by Thomson Reuters
Global Research Report of India by Thomson Reuters
IndiaEducationrReview
 
Prof pankaj chandna letter
Prof pankaj chandna letterProf pankaj chandna letter
Prof pankaj chandna letter
IndiaEducationrReview
 
2nd International Online Conference on Psychology & Allied Sciences
2nd International Online Conference on Psychology & Allied Sciences2nd International Online Conference on Psychology & Allied Sciences
2nd International Online Conference on Psychology & Allied SciencesIndiaEducationrReview
 
World education Awards
World education AwardsWorld education Awards
World education Awards
IndiaEducationrReview
 
World education Awards
World education AwardsWorld education Awards
World education Awards
IndiaEducationrReview
 
Distanceleraning
DistanceleraningDistanceleraning
Distanceleraning
IndiaEducationrReview
 
Vocational university concept note
Vocational university concept noteVocational university concept note
Vocational university concept note
IndiaEducationrReview
 
List of vc's
List of vc'sList of vc's
List of vc's
IndiaEducationrReview
 
Final essential stepsforhighereducation
Final essential stepsforhighereducationFinal essential stepsforhighereducation
Final essential stepsforhighereducation
IndiaEducationrReview
 

More from IndiaEducationrReview (10)

Global Research Report of India by Thomson Reuters
Global Research Report of India by Thomson ReutersGlobal Research Report of India by Thomson Reuters
Global Research Report of India by Thomson Reuters
 
Prof pankaj chandna letter
Prof pankaj chandna letterProf pankaj chandna letter
Prof pankaj chandna letter
 
Rti, iiit allahabad
Rti, iiit allahabadRti, iiit allahabad
Rti, iiit allahabad
 
2nd International Online Conference on Psychology & Allied Sciences
2nd International Online Conference on Psychology & Allied Sciences2nd International Online Conference on Psychology & Allied Sciences
2nd International Online Conference on Psychology & Allied Sciences
 
World education Awards
World education AwardsWorld education Awards
World education Awards
 
World education Awards
World education AwardsWorld education Awards
World education Awards
 
Distanceleraning
DistanceleraningDistanceleraning
Distanceleraning
 
Vocational university concept note
Vocational university concept noteVocational university concept note
Vocational university concept note
 
List of vc's
List of vc'sList of vc's
List of vc's
 
Final essential stepsforhighereducation
Final essential stepsforhighereducationFinal essential stepsforhighereducation
Final essential stepsforhighereducation
 

Recently uploaded

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
National Information Standards Organization (NISO)
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Celine George
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
TechSoup
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Excellence Foundation for South Sudan
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
paigestewart1632
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
AyyanKhan40
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
Colégio Santa Teresinha
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Nguyen Thanh Tu Collection
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
Wahiba Chair Training & Consulting
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
สมใจ จันสุกสี
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
RAHUL
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
Celine George
 
How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17
Celine George
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Fajar Baskoro
 
How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
HajraNaeem15
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
Priyankaranawat4
 
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental DesignDigital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
amberjdewit93
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 

Recently uploaded (20)

Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
 
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective UpskillingYour Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling
 
Cognitive Development Adolescence Psychology
Cognitive Development Adolescence PsychologyCognitive Development Adolescence Psychology
Cognitive Development Adolescence Psychology
 
PIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf IslamabadPIMS Job Advertisement 2024.pdf Islamabad
PIMS Job Advertisement 2024.pdf Islamabad
 
MARY JANE WILSON, A “BOA MÃE” .
MARY JANE WILSON, A “BOA MÃE”           .MARY JANE WILSON, A “BOA MÃE”           .
MARY JANE WILSON, A “BOA MÃE” .
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience How to Create a More Engaging and Human Online Learning Experience
How to Create a More Engaging and Human Online Learning Experience
 
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
คำศัพท์ คำพื้นฐานการอ่าน ภาษาอังกฤษ ระดับชั้น ม.1
 
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPLAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UP
 
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold MethodHow to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
 
How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17How to Make a Field Mandatory in Odoo 17
How to Make a Field Mandatory in Odoo 17
 
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxChapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
 
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptxPengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
 
How to deliver Powerpoint Presentations.pptx
How to deliver Powerpoint  Presentations.pptxHow to deliver Powerpoint  Presentations.pptx
How to deliver Powerpoint Presentations.pptx
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
 
Digital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental DesignDigital Artefact 1 - Tiny Home Environmental Design
Digital Artefact 1 - Tiny Home Environmental Design
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 

Yogesh Saxena MTech Disseration, IIT Delhi

  • 1. , ,f,,f+[i':l*t rP ql r' ..rl:.1?"i :::'lJt,l.; ?fdJ:, #ii,f,i* + rllt{^ tii:: ',;:,"8:;i,.':,i:..:t.-, tt ,ACr, -i., r'+ l) ir l:'J,?i ;ic'l;;k:'"'| r ; :i^"i: :, "1.:,:'nL,' ,,;,;:,,;;i:ii'11,., ;fiij'.:;lf ' ;;i1;1 {#ffit'rt:i iiii,ii#ilii::;ii ltir,'.ri ' Ii::i; ;, St.l . r i " - ' . t a l .r,i;";iTij|,:s.;;r- - l j:ti1;;|i; i5;:;',: iiiiii'ilJr 'i*ir:. ffiffiffi
  • 2. GOAI PROGRAMMING AIPNOACETO ACGREGAMPRODUCTIOH PI,AI{NING I A CA,SESIIIDY A Thesls submltted. In Parttal lrlfilnent of the Reqrrlrementsfor the Degree of }IASMR OF TECIINOIOGY BY YOGESHSA:GNA ,i'd r0 TiIs DEPART}MVT MECHANICAI OF M{G]NEERING ? rNDrAlIrNsTrrutB oF TEcHIIOIocy, DEIHI 1982
  • 3. This is to certily that I'lrr Yogesh Sarcenaworked. for his i{. Tecirr proS ec t r'Goal prog ransdng Approaci:. to Aegregate productlon Planning : A ease strdyrr r:nd.er rV sup ervi sion in the i,iechanic aL Engineering Depar tiuento Ind.ian Ins titute o f Technologyr Del jrl e I further certify that tn-ls proJ ect has no t been taken up before for the award. of any degr€er ,i ( DF.' I,i. SIIIGH) . Deptt. of i'ieeh. Engg. I.I.TrDellti.
  • 4. g 9-$J E N.p A C_$_N. br_,L D_ 0 I aJngrcattry ind.ebt€d. to Dr. N.Singh my pro j ect supervl sor and. express ry g rati tud.e for his af fec tionate and encourag tng guld,anceo During the year in wlrieh I worked. uncler hiln I forrnd. hls invaluable adl.Lce of g reat he1P. Thanlrs are also d.ue to I4r. G'DrSardanae Gen, r"ianas K .Ganpathy r i'ianager, l'lalru- "l;pt?; facturing for provioj-ng roe inva^]-uable Senrices, ' h elp and. suggestions . I aJ so acls"Ioi^IJ e '*[ th t]rank s the he]p e€ extended by llr. Sond|rl l Indlts trial nngineer and. other staff of llj-nd.rrstan Bro'nrnBovffr. Thanks are al-so due tc the s taf f o f C o n r p u t e rC e n t r e , I . I . T . Delhlr I . I. TrDelhl =)*'l-f<^^ 19E2. (YoGESHSAlGliA)
  • 5. LB_S T R A C_T In this thesls an attempt has been mad.eto analy s e the Agg reg ate Proclrrction p] annlng o f Hindustan Brown govd, Far idabad, op tirnally. The denand of the noicr s w:tth d.ifferent specificatlons ve re no t the c ons tant during the planning horizon of on e year io€r 1982-83? Consisting of three plaruring period.s. To meet wltir the fl-uc fuations in demand.e Ag g regate Plannlng mo,iel was formirlated., which concerr- trate s on d.etermining lrhich comblnatton of the d.eclsion variables J.il<e prodirction Taie, inventoryl backord.ering over tiile etc. should be r-rtilis ed. in order to optimally acUus t tlre demand fluc tuation s wi th-tn the con sl"raln ts i f BnX. The AggregaLe planrring moder-was formulated. in the form of goal s wi thr dlf f erent prloritieso The problen was then solved by uslng r'Coraputerlsed.technique o f S .i'i. Lee to solve the CoaJ- Prog ramnrlng ProbL errls The rr, decis icn variabl es were obtained for all the planning p eriods.
  • 6. C O N T E N T-S Page 1r INTRODUCTION 1.1 Oeneral t fl 1 oz $eg reg at e prod.uctlon p1 annlng i L General Form tl 1 o3 lirqlest structure of Aggregate Prod.uctlon plannlne 1.4 I'Iul tl s tag e AgSreg ate pl annlng Sys tem 5 1r I rO Intpor tance of 'loal prog raJxalng G 1.6 The Goal Prograuxning Concept a 1o7 0 bJ ec tive Func tion ln Goa-l p rog ra$ming 3 1.8 Rankire & weighr.Lng of i'iul tlpl e g oal s 3 2. IJTEiiATUiiE nnVIS^I 11 3o GOAL PnOGRAi'Ii'IIliG A I,',.,A,[E,.1ATICAL AS ICOI L 3.1 General i'iath einatical ;,iocieI LI 3o2 Step s o f the Siuplex method of Goal L2- Prog rarunlng 3.3 Computer based Solution of Goal L6 Prog raminlng 3o4 Flow Di aeraul 4. PROCIE;.ISTA'IE.i.fiI{ T 3L 4.1 General 3L 4o2 Data Oollection Tabl_es 3G 5o GOAL PRG RAi,li,iN,IG}-IJrd,ir.JLArIOl,I ql 6. SOLUTIUI] At,iDO iiEjitS 55 7. S UGGESTIuI'jS FOn FIJliIiG.,t yjr,,rrK 58 Bo REFEREJ]CBS 53 9. APPENDIX
  • 7. CHAPTER I - rNT,Rg.pucTIoN 1 .1 GH'IEF4,.L : i'lost manag ers want to plan and, control operatlons at the broades t revelthro ugh some rrrnd. of aggreg ate pl'annlng that by passes detalls of indlrridual prod.ucts and detailed schedrrllng of facillties and. personirelo i'ianagemer:t would. tr.eal $r:ith baslc relevant d,ecisions of progra.uaud.nggtne use of resourC€sr Thls ts &ccon_ -pllshed by reviewirrg proJ ected. enpl0yment levels and by setting actlvity rates trat can be varied. wlth rn a Blven errploynent level b7 varytng hours ruorked, ( worklng overtirne or rrnd.ertiiie) r Once ilres e basic d.ecislons have been mad.e for the upconlng perlod, detalled. sched.rrltng ean proceed. a t a lorser level rvi thln the cons traln ts o f the bro ad. pIan. Finally last rnlnute ciranges tn actlvtty levels need to be uade with the realisatlon of thelr posslble ef fects on ttre cos t of clnnghg prod.uctton level, and on lnventory costs lf they are a part of the sJ,:S temo -
  • 8. 1oZ AC.CRECATF g s The Aggregate prod.uctl0n plan'ing problen ln lts most generar form ear be stated. as forlows. Given a set of forecasts of d.emand,, what shorrl. be for each period a) Itre size of work forcel l{t b) Ihe rate of prpductlon, pt c) The QuantltY shlpped, Str The resrrrtrng lnventory per month can be deter_ nlned. as f; = It-1 + pt - St. The problen ls 'sua{y resolved analytlcarly by mlnlntzlng the e :rpected to tar cost over a g i.ven Flann- -lng horrzon consrsting of soc* or arl of the fouowfus cost coqponents: a) Ihe Cost of regular payroll and,over tlne b) The cost of chanelng the productl0n rate from one perlod. to the next c) The cost of carrfing jnventory d) Cost of shortag es resul tlng frour not meettrg the d.ennand. The solutron to ttre problem ls greatly srncpll_ -fled' lf average d.emand over the prannlng horlzon is expeeteti. to be constant.
  • 9. The compl-exlty ln the Aggregate production Plannlng problen arlses fr"on the fact that tn most situations d.enrand. fer perlod. ls not ccmstant but are subJ ec t to subs tantlal ff-uc baablon and the ques tlon atLs es as to how the se func tions should. b e absorb€d.. Assunlng that there are no problems ln receivjng a constant supply of raw materials and. labour at a fixed. wage rate, the problem ouy be seen by eonsld.erlng thr ee Pure al ternative ways o f r e spondlng to such fluc fuations o a) A lnci'ease in orders ls met by hirirrg anC a d.ecrease 1n orders ls accotapll sned b1'.layoff s. b) i.iain tenance of constant work force, adJus ting productlon r ate to orders by working ovelrtlme and wrder t1 ure ac c or dlng ly . c) i,ialntenanee of a constant work force and constant pTo duc tlon rate r allow-tng lnventories and order b acl0og s to fluc t,aate . d) l,iajn tenance of c snstant wor k force and mee the t fluetuation i.:n demalid.through planned bacKlogs o r by sub con trac tlng exce s s d.e marrd, r In generalr none of the so-called. pure a-lternattvesl dlscus s ed w111 prove be s t, but rather some courblnation
  • 10. o f ttrem. ord,er flue ttratl0ns showed. g eneral be In l absorbed, partly bD' inventorxr parily by overtlme, and partJ.y by fririne and, Iayof,f,s and the opttuun eqphasls of these factors lnlll depend. upon the costs ln any parttcular factoryr 1.3 u PRosrFS : The structure of t'e Aggregate plannfrg problen is represented. by tlre slngle stag e sys tem trer the plan'lng horlzon ls only one period a'ead.r the state of the system at ttre e'd. of perlod. 1s d,efined. by wo, Pe and ror the Asgregate work force slzel productlon or ac tlvibl' rate and. jnventory leve1, respectlvely. 'rhe end'lng state c qrd.lttons beeoure the 1nltlal condtttons for the upcourlng perrod. 'rle have a forecast of the requlrements for the upconlng perlod.s through soge proc €ss o Deelsions are nad,e that set the slze of the work force and' prod.uetron rate for the up-cond.ng perlod.. The d,eclsions ma,ie uray call- for hlrlng or layj_rrg off personnelt thus expand.lng or contracttng ttre effcctlve capacity of the productJ.ua system, The uork force slzel together lrrth the d,ec1slon on actlvrty rate durc-ns the pertodl tlren d.eterrnrnes the requlred. arrcunt of
  • 11. 5 overtimel lnventory levels or back ordering r whether or not a shlft nust be added or deleted. and other posstble changes tn operating procedur€o 1o4 : Ftg . shows a mrrl tl s tag e agg reg a te pLanntng sys teun vhere the horlzon has been expand.ed, th for _ w"l e cas ts for eac' perl0d.o u*" obJec tive 1s to nake the declsions eoncernlng the work force slze and. productton ra te for the upconing p erlo d., In clolng so r however we consid,er the sequenee of proJ ected decisions ln relation to forecas ts and their cos i effectso The declsion for the upcorntng perl0d, ls to be arf,ected. by the futr*e perl0d. forecasts a:d. the declsl0n process nnrs consld'er the cost effects t of the sequence of d,eclslons. Tir e conn ec tlng rtnks b e tween the s everal s tag es ar e the w, pr and. r values that a^re at the end. of one perlod and the beglnnlrrg of the nextr The feedback loop frour the d'ecision process ru4ylnvolve some lterative procedure to obtaln a solutl0no The seguentlal nature o f the declsions should. be kep t 1n mlnd.. All d.eclsions are rlght 01' wrong only ln terrns of the sequence of declstons over a perlod. of tlne. h€
  • 12. 1o5 : Organizattonal obJectlves vary aecord.ing to the elraracteristicse typesr FhtlosoptXr of &anageuentl so partierrlar environuenta-l (o ndlttons of the organr_ aat10n' There ts no slngle raelversal goal fo.. a,. org anrzatl0ns. rn boayr , cf,rnand.c business envlronment, fl*ns Flace g reat emptrasls on soclal responslblll ttes social contrlbutlons, e publlc relatlons r lndustrlal and 1abor relatlonsl €tcr rf we grant that roanagerent has m.[tlple conffls_ tlng obJ eetives to achi€ver the d.eclslon crlterta should arso be nru' trdlnensl0nal0 ,rh1s tupr_les that when a decislon lnvoLves nultlple goa_1sr the_quantltatlve tecl:nlque used. should. be eapable of hand*ne muLtlple dectsj-on criterlao The llnear programudrg teehnlque has a llelted value for problems hvolvlng rruLttple t oal sr The primary dlfflcurty i.rrth llnear progsamm{ng ts not its inablllty to refrect connplexreallty. Rather, lts dlfficuJ-ty lles rn the unldlmensl0nallby of the obJ ective Jnctionl vrhleh requtres cost or proflt fuifor- matl0n that 1s often alnost lnposslble to obtalnr To
  • 13. .: ,! 1 overcone the urld,lnenstonallty of the obJ ecttve f*rrctton requlred. ln the llnear prograrrrnilng, efforts have been natr"eto convert varl0us goals, costs, or value neasure lnto one crlterton, nanely utlllty. However exact neasurernent of uttllty ls no t a slropl e mattere f'Ience1 d.ec1s10n naklng throug h llnear programmtng vla a uullw fraretl0n is onry feaslble ln a theorettcal serseo Goal progra^urrd.ngts a mod.ification and. extensl0n of L'P' ' The goal progra-mrnlns approach ls a technlque tha t t s capable of handlr'g deelslon probleros that dealtvlth a slngle goal wtth nrrltlple subgoals., as well asi problerus wlt' multJ.ple 80a1s wlth n*ltlpte sub goalso irle can solve the se prdblerns us jng Lrp r ^rbth j{ul tlple obJ ee tives o For t'rts r w€ nay ln trod.uce o ther than the obJ ective fr:nctlon, as rod.el constralnts. The l.p- rccel r equires ttrat the cptlnum solutton nrrst satlsf! all constralrrts. Furttrermore, lt ls assumed here that equal lnportarrce 1s attached. to varlous obJ ecttves r However in reall wr such assurnp t10n are obsurdo trtrst of arl, it ls quite posslbre that arl tl:e constratnts of the problem can not be satisfied..
  • 14. such a problera 1s called. rlnfeasiblerro secondly all eonstralnts do not have equal lcportanc€o there- fore goal progranrnlng vhech renpves al.r. such dlffteul- tles ls us ed. to solve such probleins. 1.o ru&_QOAt q)i,tgEF.T lR0GRAtl},IryG : The concept of goal progyarnr4ingwas first lntro- d'uced by A' Charnes & l'^lol{oCooper as a tool to resoLve lnj'easible linear prograrnrd:rg problefis o Ttrls technlque has been rrrther reflned. by yorJ lri & s rl,lrlee and. o thers r Goal progran,ulng wnd.chis s pecial extenslon of llnear programrulng, ls capable of solvlng declslon p robl ens with a slngle g oal or uul tlpl e g oal s o The goals set by tlre ttanagenent are often achlevable only at the erpense of other goals. zurfher-no!€ these g oal s are ln couunensurable i o€. they cannot be measured. on the same unlt scsl€r Thus there 1s a need. fcr establishlng a hlerarcly of tnportance aupng these confllctlng goal s so that low ord.er goals a.re consld.ered. only afLer the hrgher orders prlorlty goals are satisfied or have reached. the point beyond wlrlch no furtlrer lqprovement j.s deslrableo Hence the problen can be solved. by goal pfogrenryr{ng tif the uuaagement can provide the ordtnal ranklng of the goals tn tenms
  • 15. si *?. rt .1. of thetr tuportance & arl relattonshlp of the rcd.elr Econonl'caily spealclngr the msnager faces the problen of the allocatlon of scrace resourc€so ft ls not always posslble to achleve ttre wery goar f*lly to the extent d.esrred.by i'anagement. Thus, wrth or wl thout Plogramnlng the manag , er attaches a c er taln prtor _ -1ty to the achreveinent of a partlcurar goal. the true value of goar- progrannrins ir, there-or.€1 the sorutron of proble'Sl lnvolrnlng !rutttp1e, confltet,,'g goals acco'ulng to tlre i'ianag r s pr10r1ty er s truc tur.e. 1.? : rr: goal programmrpg rnstead. of try1ne to haxrorise or nlnlnlae the obJec tive crlterlcm dlreetly as ln rlnear progranndng, 1t trles to nlnfudze the d.errrattons anong the goaLs and wl th ln Lhe g lven sets of constralnts. rhe devlatlonar vartable is Tepresented. two ln dimsrsl0ns 1n the obJecttve functl0n, a posttlve and. a negatlve deviatlon fr"om each subgoal and/or con_ s trainto Then the obJ ectlve functlon becones trre ninl- -wLza*ton of these d,evlatlonsl based,on the relatlve lnpor tance or prlorlty as srgned. to then. 1 .8 0AIS : in order to achleve the ord.lnal soLutlon-that
  • 16. lsr to achle ve the goals aecord.lng to thelr lryortaneel (-) Begatlve and Sr posltlve devlatlons about the goal must be ranlced accord.Jng to the r,prerytiver' priority factorso In thls way the low-ord.er goals are consl- dered only after higher- ord.er goals are achleved as deslred. The I'Preerrytlvet' priority factors have the relationship of pJ the multlplicatlon of De however large lt may be, cartuot rnakepJ+1 greater thran or equal to pJ. The next step to be consldered tn the goal prog ramrnlng i s the welg h-tng c.if devlatlonal variable s at the same priorlty leve.lr rf any goal involveb many deviational variables and lre want to glve prlorlty to one over the other, thl.s can be achieved. by assigning dj.ff er ent l.Ielghts to tl:e s e deviational variabl-es at the sarne prlorlty leveI. At the sarneprlorlty levelr the subgoal which acguires manrfuouui dlfferenttal qeight w111 be satlsfled first & then lt wLLl go t o the next. Ihe crlteria for ,leterinlnlng the different veights of the devlatlonaL varlable could be the rnlnl rnlzatton of opportwtiW cos t or regret. Therefore, d.evlatlonal varl- ables on the s ame priorlty level must be coulrrensurable, although deviatlons that are on the dlfferent prlority levels need no t be conrnensurable. i; ,.1- # &'
  • 17. :" -:TT cHAPTE& rr The Productlon plannlng problen ts concerned. vt th sp eclfylng the optlmar quantlttes to be prod.uced. 1n or.der to rneet d.enrand, for a speclfled. planntng 'orlaon' t'lary nod'else each of vblch has lts pros cons, have been d. and. evel0ped to help to solve trrls probl em. 'Productd'on nlan'lng 1s of a hlerarchical naturee since each level of the organl zatLon jr[erar.;*tlc1_ -p8 tes rrr t he plan'lng process wlth d.lfferent braphaslsr scoPer and planning hortz6n. Those operattrng at the strategtc level are prlnarlly concerned. v,*ft the 10ng_ r''nge plans of the org anLzatl0n as a whoJe. This requlres sl'nrl taneous consld.eratlon of the dlfferent func tional policles and tirelr coordlnatlon so that tLre f trnt s frarc tlonal s trateg ies b e consls tent r*rth each otherr As we go from the top level to t|re tactlcal and opela tlonal levels r planntng horlzon d.ecrease and ttre degree of uncertatntby Ceereases. However, the d ep en d'ence b e bween the frnc t10na1 ac t1v:Ltl e s t s byplcaly coordlnated. more at the tactical level than ; Ir
  • 18. lz -' L , ,tsi ''- {', : at the operatlonal levelr Thls also hints at the hlerar- - chlcal lnfornatlon problems associatal u:tth prod.ucfi,on plannlng slncb pl-ans at any glven l_evel are based. on the inforunatlon before the factl and trren upd.ated. ? accordlng to the lnformatl0n feed.-back after the f aet. productlon plannlng nooels t ] lntroduced. in the Li teratrere trffer ln thelr oriertation, scope, co n ten ts & n ethodology. Ilowever e lre can cras s ify thes e models ln two r.raln categor.i es ; deserlp tlve & normative. Dggglpttve i,rod ef,S 3 Descrlptlve nodels alm pf descrlblng the process by whlch procluctlon plans are determlned ln practice. The rnaln examples of such rnodels are! 1): t lo] rntrod.uced br Bownan ( 1gfu) and extend.ed by Kumren ther ( 1969) thls , nod.el assunes that manager behave efflci entry an average, but suf fer frora 1n- - cons ls tency and. blas es to recent events o Lrnear FRE8 regresslon ls used. to d.evelop decislon ruJ.es for actual productlon ancl vork force oeclstons uttlizlng
  • 19. r ':.' i ..r - l.*;i 1 lnd.epend.ent vartables such as pas t sq,les and. logged produetlon, tnventoryr ard. work forceo lhts nod.e1 ls very f'exlble ln belne not restrlcted. to a partt- cular frrnctl0nal beharrour of ttre cost elernents 1nvo1ved.. t, A Serl0us d.rawbackof the proeed're I ls tire essentially subJective selectfq of the form of the ruler rt very easily can be sereete. ln co*ectlyo i.1) ljre-s ): Ti:e marn id.ea of thl s model is to proeeed in sequence s tartlng from a prespecifled. acceptable range of inventoryr and set accordtngly the llne_shlft levels of ruork forceo rhen ad.Just these according to the rar'rge of lnventory d.eviatlon frorn lts pernlsdlble r8'.g e r r J' devlatl0ns occur too frequentlyl then the acc ep tabl e Level inven tory rang es ar e subJ ec t to ad.J t- us - ilentr r11) : cExtensrve work has been c a*ied. ] out rn thls fleld' uslng dlfferent statlstlcal and.mathenatlcal approaehes lncludlng vronte carl0r saryll,,g, and.conputer anal0gu€o rn t, he nodell introd.uced. by vlrgln ( 1966),
  • 20. tFre slurrlatton starts wlth a productlon plan basirti on past e{perlence of the flrn, and, then cLrangessre ln troduced. 1n enployment levele ov€rtlne1 lnventorles , sub -contractjng r and so forttrl untll a loca] opexst:lg cos t mlrrlmunr ls achiwed.r 0 ther slnrrlatlon nocleJ.sln bhl.s regard. axe developed by Enshoff and Sisson ( 1g?0)r and by tlayior ( 19?1) r using both discrete, and contlnuous events sinnrlation. An lryortant feature of slurulstion ls that stoehasttc d.ernand pattern can be lncorporilted ln the uodel o Thls p erml ts the analysls of the forecast error on strategy developme:t. No_rILE tlv.e_ liosl el s : a Tire corunon focus 1n normative rrcCels ls on wirat prod.uctlon planners should dor i,lodels of thjs category are f:r ther clas sl fied. into class€sr (1.) Aggregate PLannirg irpdels; Ilrelr -- - - comrnonobj ec tlve ls to d,eteruilne the optlmal production quarttlty to produee anci r,rork force leve] to us e ln aggregate for a cordng ts plannlng horlLcut. j.iod,els ln thls class are elther exact or lreurlstlc.
  • 21. T! E{Acr }rQgJ$ : tarrsportatl0n I'{ethod foruulatlon of tsowraan ( 10s61 L 1 l proposed. the dis trlbutl0n rnod.el 0f llnear progra-ur'ring fo:: Asgreg ate planning , Th[s mod.el f ocus s ed' on tJ:e obJ ee ttve of ass lgnlng units of produc tive capact ty, s o that procluction plus s tora€ e cos ts were ,u''.luc-sed. and, sales d.ernand. l'as met with iJl the cons tralnts of avaiJ.abL e capaci ty. Thls nrodel d.oes not aceornrt for prod.uctlon ehange cos tsr Such as hirlng & layoff of personnell and. there is no co s t p enal ty for baekor,J.erlng or 10 s t sal es . The slrnplex iuethod. of llnear prograoro,lng urakes 1t possible to inclu3.e prod"uction level change costs and inventory shortag e costs in ihe r.,roclel. Iianssnan and' lless a+r d.ever-oped slrrplex *rodel a usr'g work force an. prod.uctl0n rate as lnclependrentdee1s10n varlables ancl in terus of the coiliponents of the cos t moderr arl cost frure tdons are consrclered, rlnear. One of the basic wealaress of llnear prograurmlng 3pproaches ( ana rcst oQrer aggregate planriing technlqees) is the assL'nrption of d,eterud.nls tic demand.o Another short-contrrg of tlre llnear progranunlrrg urod,el ls the I t il
  • 22. regutrenent of llnear cost frrctloDso iloweverl ttr.e po- sslbiLiby of piece rrrlse ltnear{.ty lnrproves the vatre}ty. Holtr l,iodtellanl and. S1rcn t lLl gave tLre well lceown mod.el ln whlch they mlntnlze a qua{ratlc cost f:nctlon and come up with a llnear decision rure that solves for op tlrnal Agereg ate prod.uction rate and. work force size for al-l the perlod.s over tLre plannlng horlzon. L.i).R. has nany advant&g€s o First the nod.el ls optlmld-W and the two decislon rules, once d.erlvede are slniple to apply. In ad.dltion the rcd.el 1s dynamig and representattve of the unrltlstage klnd. of sys temo But quadrattc cost structure nay have severe llmltation and. probably d.oes not ad.equately represent the cost s truc tur e o f any or€ ani zatlon . tsergstron and sulth E 2 7 extended. the capabl- - li tie s of the L. D .3 . mod.el 1n two new dlr ec tlons . Be- -c&u.s€ of the a€gregate natrrre of L.D.R. tE tt 1s not posslble to solve dlrectly for the optlnrnrmprod.uctlon ra t es for lnd.ilrldual produc ts . The d,evelopnren and. t applicatlon of thre l.DR rnod.el- suggests that it 1s now operatlonalLy feaslble to remove the requlrement of an adgregate productlon dluenslon ln plannlng mod.elso
  • 23. Further-toorer glven ttrre availr,b1llty of rev€nue curres for each product in each tlme perlod. the MDRnrcd.el can d.eterrntne optlnal prod.uctionl sales1 rnventoryr and work force levels so as to raaxLrd-ze proflt over a specified. tlme horlzon. il nnpence Burbridge & CZf presented.a uulti;ole goal llneal programrnlng moclel consld.ering comrrcrrly occurlng goals of tlre firin 1n coord.lnatlng prodrrction and 1ogis tic planning . Tlre solsflon technique for l,'-Ls tnodel I^ILll- ]:c a cci-rl-Jute':rze:I .rr1 bi.i1 c coj:cLir,: il;r.o.,l-oj._r.'r c f the revisecl simplex methoC. Good.man a f C presented. goal prog"u*.,[rre approach to soLving non-lrnear agtregate plannlng iocr.els. rf actual cos ts ( i{iri'g ct firing cost, overtime & lclebl,ne, rnventory &' shortag e cos t) can not L. satisfactorlly e repres entad quafu'atically, then the solution b eeornes u}cre conplex. One approachr to i:andllng these inoie corr- pl ex moclels i s to atLet:pt fon:u:latlon o f arr apl)roxirnating l_lnea"r mod.el to the originaL non llnear cost teruis an d' to apply souie vari ate o f the s iunplex metirod.. Thi s approaclr offers the re*' advantage of at least provid,tng an optlual solutton to the mocler usecl and. ls b a^d.ed.
  • 24. upon the goal progra.nnrtng in thls peperr Tang and Adulbhan r B ] proposes a 11near prog - rarunlng formul-atlon of Aggregate prod.uction planning problem 1n the context of heaqy uianufactrrying lnd.ustry. A bastc rrroclel is first rLevelopeci to rnd,nlrrd-ze the total cost of prod.uction which 1s assumed. be piece- to wise linear. Tire basic updel is then transforre.d. into a llnear progra^m.:alng inoCel to seek an optlmal solutlon for a serj-es of plannlng periods wtthln the pl annlng horlzon. Jaaskalainess, v t 6) h a s p r o p o s e d .a g o a l prograrunlng inodel for the sclied.ullng of produc tlon, eatployment and. j-nventorj-es to s atl sf}r lcno.'nrn d.emand. re qulrernent over a finl te tlme horlzon. Thi s mod.el sets tnree separaue and inconpl_etegoals, the Level of productlonr einployment and. lnventories r Thornasand HiJ-1 Lg I forunrlated a nmlti-obJ ectlve pr.od.uctlon plannlng modeJ as a goaf progran which c apt taliz es on tire s treng tirs of g oa1 progranmlng in 1n,- - corporatln8 mul tiple behavloral and, economlc consld.erations in to the analysl s r Thls flceurr paper lncludes the aspectsr lgnored. by Goo,iuran a I C and.Jaakelalnenf 61 .
  • 25. Ja.raesPo Ignlzlo t, 5 f tras atterpted' to provld'e loo}<, at the relatlvelJ nev field of goal a brief under a preemptlve priorlry structure' programmlng goal prograd-ng raodel presented' As such, the general realistlc and' rather n:fr'ural ls vlewed as a practlcall world representatlon of a wtd,e varj-ety of nany real probl ens r ileuristlcs Models 3 paralnetrlc plarrrdrry nod'el b)' (a) The Procluctlon J one s ( 19?5) .TtrLs model as sume the exis tence s work force of tvro basic declsion rules addrosSlng each of and. productlon levels respeetivelyl suin of rates whlch 1s expressed' a*s a welghted durlng the plannins required. to meet frtr8 e sal es horizon. (b) A Swltch rule proposed. by Elmaleh and' Ellon 019?4)' Theyspeclfytlrreeinventorylevels,arrd.tirree by various prod.uctlon 1eveIs, to be obtalned' over a hlstori- combjnatlons of control parameters for w$orl -ca1 dernand series, and chooslng the set to dlscrete levels, such production ls linlted as food' and. chemica-ls '
  • 26. (c) Search Declslon Rulesl - taub erb, extend.ed. tJ1e computer slnoulatton metho d.ology to lts qlti.urate ggl eralib,v by d.eveloplng technlqugs calIed. Search Decislon Rules LlO J' l'11-1 Iie defined. C1g1 as a frarction of (i'ttt Ptt I 0 t) and. then ldentified. the values within CtOt bY the folIowlng veetors: Declslon Veotors = Pt, Wt Stag e Veetor = Ht-1, It-lI Paraneter Vector = C o s t C o e f f i c l e n t s at timee t for d'eclslon vectors trrat SDR searcires d.lrectly red.uce CIOT. Couiputer search routi-nes atterrpt to s tag es sinirl tarreously g enera ting trial q&x op tlniz e all d.ecisions per lieratlon. The search procedure terruinates when successlve tterations resr:J-t in sna-ll reduc tlon in Cf0T'
  • 27. ii!- 0ITAPTFR rrr . '' cOrq,.t 4g-4 liATHEl,la_TIcAt USIE .p&w54l0'fiNc I09IL ', 3o1 G4{ER4'.I, : ]'{oDE} },tAIrEuj[TI.Cg, The goa.l prograrnrnlng tlas ortgtnally pDoposed. by Chanres & Cooper for a linear mod.elo lllhlch has been further d.eveloped W unny othersr A preferled sol.utton ts one whlch nlnlnt zes the d.errlatlons from the set goa1s, Ihus a sturple llnear goal prograrnmlrg problem fb.rnulatton ls shor,nr belou: r -+ i'linlnlze Z = 2 p'J (q+q- ) Jt = 1 n + SubJect to z arJ t xr JA + d,l - q - = b 1 f O f i=lrooolll J=1 + *J ,d; ,di wnere E xq. =0 xJ = Dectslon varlables to be found K = Number of prlorlty n = Nunber of declslon varlables m = Nunrber of goals b1 = GoaI set by ttre deelslon maker pJ, = The Breenptlve wergbts suclr that pJ I
  • 28. In addl tlon to s e ttlng g o aJ. for s the obJ ec tlves 1 the decision maker must also be able to glve an or- d,lnal ranking to the obJ ectives. The ranking ean also be fotmd. out by paired colnparison nrethod whlch provid,es some check on the consi-stency ln the value J udg ement of the decision makerr In tf s nethod the d.eclslon maker ls asked to compare the goals two at a same tlme and. indicate r*'htch goal is the upre inportant ln the palr. Thls procedure is appllecl to all combjnations of goal pairs. Thls analysls results ln a complete ordlnal ranking of the goals ln terms of their lnPortancer t The goal prograunlng ut1-llses tbe siunplex nethod o f solving the linear prog ramrnlrrg probl en. !{or,rever s everal modifications are required and that ls why the slmplex rnethod. of goal progranralng is often ref erred, to as the t'modifled slmplex methodorr 3 o2 srEts ,0LIlE-F.r]/IplF,ic ; 9L,cOlI,,3n09n4'l.t',is'i9 lF3j{Oe S-J: Set up the |nltial table flora goal progra.nning fornulation. We assume that the lnttlal solutlon 1 s at orr€ j3e Therefore all the neg ative deviational variables in tlre mod.el constralnt nrmst enter the
  • 29. so].utlon base lnltiallJ. Preare a table as shown below: c1 Variabl e RI{S + d, oorl di oorl X1 oor bi CU 'J - cJ PS 'D4 P3 P2 P1 Fill up ttrl s tabre 1r € r all .i J&b+ . The cJ colum wtlr contaln the coeffleient of d.evlational varlabre because thes e vartables only enter the s oJ.utlon firs to fn the (ZJ _ Cj ) matrlxr l1s t ttre prl0rlty level ln the variabre columrr fbon l0west at the Gop to the hlghest at the bottomr Calcr.&ate the Z1 values a'c1 record. it into the RHScorruorl carc*late
  • 30. the ZJ - C3 Values for eacb columr and.record. lt ln the approprlate colu.umo S tep 2 : 4e.tsrgml.ne _bhe ne.v SnteJ:l,pg Vali,ablg: Flrxl the highest prlorlty Level that has not been attalned coryletely by exaurlning the ZJ values ln the nHS columro After d.eternlnlng this, f1nd. out the hlghest zJ -cJ entry columrr rle variable of this colurn wILl enter the solutlon bas e ln tlre n ext i teration . In cas e of tie, cLreck the next lower prlority Level- and s el ec t the colun:I that has the g reater valueo If at thls stage, the tle carrrot be lbr.oken, choose one on an arbitrary basis' The other columr will be chosen in subsequent lterations. rhis is Imor,ar as key colttur. Step 3 3 ])elg rrxfn e- tbg_!egvlps_yari-+19 ,, Solutl_on- b_a,$S Dirt:ide the values of Rits by the coefftcients ln the key colrurr r Thls wlll- g lve the nelr ruIS val-ue s o Select the ro,J whlch has the aininun non-o€gatlve value. The variabre tJs that row wiJ-r- be replaeed. by bhe varl- abre ln the key eolumr in the next lterationo rf
  • 31. there exts ts a tle, f,Lnd the ro*r that has the variable with the higher prlority faetor. rn this way tire higher order goals nilt be attained. first and thereby red,uces the nrrmber of iterationso Step 4 : Delgrn+ins tl€ nelr .sglu!ro!: First find. tJre ner.r?Jis and. co_€fficients of thre key row by d.ivid.lng old values by the plvot element i r €o the erernent at tl.e lnrersec tion of the key row and key colunr. Then fina the new var-ues for all o:irer rol/s qr usi::g the c:j-c-r-,._ai.-o;.t :j..,oce,.._;Je : c.f ( ui-.i t't:e - ( Intersectlonal element of that now x i,leu "r vaLue ill the Key row iJr the sarire coluriur)) . lrlow courplete tire tacle by find.jns ZJ and Zj _ Cj vali:es for ilre p rio ri V rors o Siep O : Analyse tne goal attain:rent revel of eacjr goal b1- checki'g ;ire zJ value for eacrr pr"lority Tou. rf rhe zJ values are all zero, u.nis is tJre optimal soLutlonr Ihenr lf there are posi_tive Zj _ Cj va]ues in the rowl d.eternrlne whether there ar.e neg ative ZJ _ CJ values a t a hlgher prlorl ty leveL r', the sarfle eolunnrr
  • 32. "26', I f there i s n egative ZJ{J value at a higher prlorlbf level for the poslttve ZJ _ CJ value fu the row o f tntere str the solutlon is optlnal. F1nally1 tf there exlsts a positlve ZJ{.J value at a certaln prlority 1evel and. there ls no neg ative ZJ r CJ value -at' a hlgher pfloriw level ln the sai^,e cor-urnn,tiris is no t an optlmal solutio'o Hence return to step 2 and, con tlnue. Flg ot.deptcts ttre slnpl ex solutton proc edure for g oal progra"umr:Lngproblems ',' the form of Jf-ow ci:art, 3.3 @ : { In ord.er for goal prograrnrntng to be a usefUl managenent sclence technlque for d.ecision analysis, a compuLer-based,solutlon 1s an e ss ential reguireuren t. Lee t 13 ] presented. a colxputer-based solution procedure of Goal Progranmj.ng 'rrhich can be used. to solve the problem after sultable mod.ificationsr The l-l sttng o f the prog rauup is shourn in Appelndtx ro r t dlscusses the data input for the con-outer so1ut10n, the lnput proc ess the proe r es s for careuratlng the resultsl and, flnally ure proced.ure for prrnt out of the re sul ts o The d.ata lnput ls dl scus s ed. bel0w and. the corylete llst of data lnput is shown in Append.ix II,
  • 33. z-lk 1. ;*-= ?r.o hl eul g.ar4; card and. defines the ::-;":: ;:il":':: H:. numb'f varlables and. nurnber o f pt i r,'/1= 3s as slrown belov: / a: i{Rows 1-IVA.R NPRT 2. ;-e S:qn Carg: .':-? s scond card descrlb es the direction of con- s tralr t ?,*, o " both directions ,t .H al'e possibleot' ,' !-' ,, Iess th3.rrr', tt iU r'ExactJ.y Egual .r, tr /) tt r,Sreater tltap.r, 0n e or. i t/,,i!- :evlational- varlable s Af a cons tan t rrnrs t app ear l./' 7.-e obi eetive flrctionr If nelther d,evlationC var Lab I rt Q ?" ar s in the obJ ective frnc tlon, it 1s pos sLttl,, E'nzz both deviational varlables nay end. up ln tho tru-T and. the - cons tralnt -s d; . d1 = 0 wLLl fittl, be neto 3. 1I: ,l,l rtse c ards are t pre fac ed. by a n ae' c ard wlth trO&l-rf puuChedo
  • 34. !,,i x All other gard.s are punehed. ln the folr.owing rn=rrY]gro f ernlation Rov jn whlch Pr iorlty Welght ieqlation a_Dpeared ir -trlj t-l These carc.s sp eclf! the technclog ical cterricients oi ine choice vciables. loer ( a1J) r and are prrnched. i - tre folloivlns rcrrr€r o The fir s t card ls punched. vi --:: the word. ,')A.I-qrr, onlyr .3. .- ix wlfl ch o Colunnn ln uhl ch aij app eared Value of aU aif appeared.
  • 35. 2?r=i 5. The .3iFlt-Han$-S i4e:g args The flrst eard. is punched with trre word trRIGHTtr onlyr Rest card.s are punched with the values of Right hand side of al-J- the equatlons r Angir sl s o f the_9ornprrler 0! tpgli The Computer soLutlon of goal prograrn provides the folloiring output; Computer print out of lnput dara ( the rlght hand slde, the substj. brtion rates, and the obJec tive frnctlon) , the fixa-l sirrplex solutlon table ( lncLudlng Zj - CJ matrix an d. evalua tlon o f ob j ective fr:nc tion) , slack analysls , varlable analysisr and the analysis of the obJective. The lmpor tant ones are elaborated bel-ow: T:Ii 5Ii'iAI SII'P,L,E{ SOtqTIOli a) TIIE :iIGiIT HAND SIDE This shor s the rigbt hand side values of the variable ( Ceviational- and.d ecision) . 'l-he nurc:r s on the lef t-hand sd.de are varl abl e er nul"ir er s f or trte basle varlabl es r The rsat values on the r{-ghf-hand, sid.e represent constants of tne basle varibbleso
  • 36. b) TTIESUBSTIIUTTONRATAS TrI1s shows the vaj:es of aU of last iteratlon. It ls based, c:1 the colurrr arran€rement + o f dT, di, xJ r ln that crCero c) THEZJ - CJ i'.iATRIX ThLs shows the ZJ - CJ matrj_x of the last i teratlon o d) Aii EVALUATf 0F 0B.IECT:rE FU]{CTION 0i'[ Thr-LsevaLuatlon s!p1y represents ilre Zj value of goarsr rn other vord.s, the values present tlre under attalneJ, portlon of goalso e) Tin SLACK .q.NAIXS IS d,U AVAI L{3IE ,pOS U( .I,iE0 -S IJ{r rj -S rt presents the va'rues of the rlght hand. side and also varues of the negatlve and positlve varj-ables for each equationo f) VAJ1IABIE Ai{AIXSIS vA.lrABLE,AI,IO{I{T It presents Ure constants of only the basic chotce variables,
  • 37. nr.,.. .rSItr AIVAI.YSfS TT{E oF OBJECTI ru It'presents the ZJ values for the Bo&lso These values refresent the attalned portd.on und.er of go&lsr Pnr0luTY UIDERAC}IrEI&l,IHlT
  • 38. ffi t CEAPTERIV % ) EEQBI4:M SrAgEi,q,rI 4 t1 qmElui! Hinclus tan . Boown.Boverl. ( 3ariclabad.) Is a prominent org anisatton for proaucinS the el-ectric iirotors. iI'B.8. produces the trcrcrs of several klnds which differ from each other in several aspects llke f r a m e s i z e , I { o r s e p o w e r e i . , p . i , i . r l : u ^ u r b eo f p o l e s r et c . H rilo Jo forecasted. the d.e:iand- the t,otal I{orse of pol'/er r to be produced. for the :/ear 1g32-g3. l,ianag enent es tj-mated a cuuruLative gror+tr cf 1s,,,in the d.euiand. o f ilors e power. Ihe clemand. f sors e Dower l/as d.iff - o er en t for every period..+ Frenc ar a ttenp t is rnade to e iaeet the denrand. for every pericl 1n ar] optinal way consldering procruction rater fnr-entory, Backorderingr overtime etc. H. B.B. also had the de.,iand. cord. of re ever? type of uiotor ( iJI numbers) for hlre year 1g8hg31 g i-ven in Tabl-e I . Wlth the imowledge of the Las t Four nron ths a,re taken a s one planniry p eriod..
  • 39. tear record, the d.emand. for erery k1nd. of motor ls aS -egS S ed., O.*,tqV1j.6 ' o -t , for the c ou{) te ye ar 1g g2 _BB, Tob Q.e le Z a]1 atteunc t ls also rnad,e to rneet r,rith the fluctuations in ceuand. for errcry khd. of notor 1n an opttmal l'ay ._ 3cl each frame rlzer there were frrther rrany kirrd.s cf :rc ;iis 'rith different specificatiorfs r Therefor e c:l-; che representative rnernber of the each frame size ua s cons idered. af ter the dl scuss ion wi th ,,ianag q r -'-aru jac turi:rg services Divi sion. The types of nnotor r=:e s tilL too many to make the problem as a whcle Yer:r larg e to dealt with. Iience those types of notor, tr;i c-: ,ti-d not show nuch variation in thej_n rnachining tj-:=s wei'e clubed. together reasonably,. It was real_ised. t::a : :iris problen can be solvetL by ,iraking Aggp€grate Plan:-'ans uodel, which concentrates on d.eterininlrrg wSich c 3 -f,:::at:'on of the d.ecision variabl es si:oul-d b e utili s ecl in o: iel' to op timally adj us t the d.e,.,land. tuations fluc vr -;ri-n the con s traj-nts l f &rf, e j,lanagement ofilre conpany al so deslre d. to 1n _ corpc:ate other relevant aspects such as posslbly s tac- e eurployurent for the workersl manageinent pollcies o r 8qa1s rel atLve to lnven tory and vorker s ati sf ac tion 1'Ttc' erforuarlCs o J Therefore these obJ ec tlves were also
  • 40. 5'l- incorporated, ln the problen fornnrJ-atton. TLre overaLl cos t functl0n was segreg ated. lnto inalor componer ts 1o €e Productlon 'rate and. rnventory costs so that r,uJ.,Eg e- inent can have adclitionar fr-exlbirity ln penari z.'tg devlations fro m the v,:rious typ es of cos ts a'd uianagementr s p ercep tion of tradaoffs among the cost conponents. The rnodel optliaizes tjre ASgregate procluction variabr es as well as ce terrnlning the op tirual p roduc t mix r The cornplete prcbl- erai s forrnulatecl in the form of goals and is then soLved. b), uslng coriiputer based. solu_ tion technique of goal prograrruirlng f lb I . The forlouing 3oa1s are lncorporated in.the problem; in o-rce{ p^rio-,, "t (a) Sales .teallsation (b) I To Iitndt the cos t associatecl wi th prod.uetlon rate to a sp ec: f:-ed. a-roo,mt, (c) To l1mit the cost associated. with rnventonr L evel s to a sp ec if ie ci arooun t. (d) ro prono te vorkers irctivation tirroug h rabor force s tabj-lityo t I T t! il There were five sectlons 1n II.3.g. rlke: i I i ii ii il il il
  • 41. 1o Foundary Sec tion 2o I'iachinlng Sec tton 3o i^Iin*ing Seetlon 4. Asserrtbly Sectton 5. Shaft Processing Sectlono ;',anagerr l'tanufacturing Services DiuLsion sugg es ted. tnat the ,iacirlnLrB Seetion was the only crucial Section to be considerech Stand.ard. ttmes require4 for various op erations, per-forned. in the raachinlng section and. o ;her s ec tions were co.llec teC from the fnciustriaL lngineering Departuent and are r-rsted. in Tabr_e c" . rnventory carrnng cost and. Backord.erlng cost f or every repre sentative motor were also }crown from - lar:a; eiler: t and are 8 iven in table q . The over tlrue 1{3s alloved but not ncre tharr 1o:4of the normal worklng hcu's - rhe 'sorkers efflciency coef ficlen t for old. '^-crker & new worker ( rf hlred.) ancl for norrnal & overtinre uoiking :::urs wer e J<nor*nfrom the l,ianag er, i,lanufacturing se rvlc es ..,irrision and are given below: - ,l Eier i, rl hrs. - 4r.g:- - tl 3f fi-c i ency :, 1rOO 018 1.00 Coefficiit, 1.O0 ,! I I 'l { lir l ,t,
  • 42. -t fl tr)Lr:: t OLLE CT os r'7 PD'rn Table 1 Fra.me rri.se d.emand'o f notors for 1982-83 1. 80 1.0 2600 2. 90 2.O 3500 3o 1oo 3.0 4000 112 5.0 6000 4. 132 10.0 650o 5r 6. 160 15.0 6ooo 180 2 5r 0 1475 7o 200 40.0 500 8' 225 60.0 350 9. 250 75.0 75 10. 280 1oo.o 1 2 0. 11. 315 13 0 , 0 BO 12. 35s 27OrO 30 13. J r6o 15 250 14. 180 40 180 15. , 200 50 230 16. 22s ntr, 8o 17. 250 125 40 18. 315 270 15 19. g, 180 25 25 20. 200 40 40 2 1. 225 75 30 22. 250 100 30 23.
  • 43. TABIE 7 Denand. of motors on quarterly basl s So tr'!Hne aXrJunet Peplol0Ctrl d iarrol .FtsOo, s iae { H*trAuso ApriJ- | 83. Noo N o v r e D e co rg2 Tg-- 1. 80 729 753 1118 2o 90 809 1 237 1454 3. 100 1425 e46 1 62e 4. 112 1904 19 3 S 2158 5. 132 2982 2073 1995 6. 160 2 0 33 1972 393 7. 180 515 56? 231 B. 200 106 163 91 9r 225 110 1qe, 29 10. 250 19 27 53 11. 280 23 44 50 12. 315 B 22 50 13. 355 B 4 18 -g 14. 160 & 75 121 15. 1Bo s6 74 50 16. 2oo 74 114 o9 17. 225 29 26 25 18. 250 4 22 14 19. 315 4 6 5 S 'Tso 20c I 16 1 2 1. 200 1B 1a 4 22c 225 6 10 14 23o 250 6 17
  • 44. Table 5 Frame rLn Sl'ze Un1 t Group Isb IInd. flfrd - p erl- gd_ n.:t"1 .n."to: Qu 90 ;') ) Qu loo .?175 ) 712o 61e4 (SA6 ) ,?482s au 114 o7415 ) ) Qu 1gz .8005 ) Qu 15o 1.31? I Qu Bo 11485 lB 3277 3292 2904 1 e4ggs Qu 13O 1 o5O4 t I e 160 2 o533 ) ) 110 149 171 e. cs5g e 1Bo 2.88 ) iu zoo 3.109 I I 114 232 I 1Bo 3.357 l 31333 i 2oo 4 . 1 S 2 I) [) 132 s 2oo 4 . 2 O 7 T) 96 4 .197 a 225 4e882 ) ) s 225 4 rB82 ) 145 13s 130 ) 4.996 Qu zzs 5.2'26 ) qztu 5o903 I Ic s 250 5.903 I 31 6 , 0 41 3 I Qu zso 6 r31B I Qu 2BO 7.979 ) ) e 315 I 1435 ) 53 8.207 Qu 315 11 .395 I 22 50 1 1 oBgS Qu 35S 1 30 5 6 5 x 4 1 8 1B. a 6 s
  • 45. Table q Inven C os t (Rs.) A 182.4 228 B 411.2 514 B14oB 1018.6 1257 1571.4 1560 1950 573 o9 717.39 3OO6.B 3 7 5 8r 6 E 3804 o4 4755.5 5?60 7200 i , __ _ g&o _ _ , 10poo_ _ _ i'acLe 5 Productj.on Cost (Jsr) for every type of ,-tor SoNoo GrquB---- 1. A fI 1132 2o ts aqqe 3. 6620 4o D loztq 5. E 12675 6. F 16533 7. G 24431 8. TI t-t 30e1 1 9. I 4 6800 10. J 70200
  • 46. g I I I IJ .rl{J +J .rl ct Fl fp to ro to r-.yA g. m.O n.n Ito (U 5 l@coD- cj -_t- C-u r{o '-tAO N F{tr e.q e5qqa, Ae L F N c? +t F{ Fjto &-6il toSb'o l T F S, a o o ' : { o c o o o - 39, r-r-..B .i;d;dJid ::fffiS ;$$3 I N dP r I I (D! I B r:'t tr lt*u,.oro o (d H L1 *)F{ oo IQA'666Pa$rHEv9339$*au? .o F'l HP. . or,cr'i'+S$ i o o.o o o. b N i.r V. V i i. o , o. . o . . 3$$$ a Jo , . . .'.'. fu'-.-. r I fi*l $ Ur. H I (D F. lEEq8,8,3 - lr-f ,-l r-l r{ '-{ RRg.,.999 o.o.o.o.o.o. o c:oo O . ;i ; ; rt 1-t Ft r{,_i r{ r-F I F H oacoo ec L.) ho I pE.jq ppsi! ( loocnc,o,o,oRP1'l:tr: ' t ' ' t . o orf r{Nce '.adol -.'.a-r Fr .rl l' oq I +) v, lcoc)o)cccDc0o? do *rF{ s:t A Hq:Eqqg."."*ppp 8888pp 88Ep oQ . . . . o . . . . . r . . . . . o . . . l. o I o I so ccrrro@ I cttcr)oa lcccr{Lcco x qi1tln to.t;ac.o. Orrr_rce yTTl ,- | .r{ fr{ l,, | , I r,,.i,irTy I x (nA ol o t_ ct.l o &1s H a rn | | | | tc? | | . i-l-l . .qqggq sss$gg ss$s . . . ? .. . .. . { ^ . 4 lt ? . G + polgqra()Nto@ r-t(c) 5.) h0 tCDol Ot9C-mdf-to$ru: iri dho '-f '-f '-f Ct C,tC{ Ol m crJ$t t! !O AQeflqrp u;Oo'ot Fld aoaaaoaaaaaaaao.a.aoao tl C;:V + fj i- C{ V, ${ u) -{ '-1 r-{ 'rt F{g ,:) 'I ofl p. ultO tO tt)tr)LOtOLOU)LOrr1TO F{(d . . . . . . . | . o . . _ !O!O!OA LOtl?LD mF{ OOCOOOOOOCICIO nU)Nc-Nt< urr-ND.: . . .. . . . . f . uob Ejs€j'RSEr-r@o)oi ga(9r d .r,l E{ .lJ ooob;;qB{8fr$ 3EIs8n .SXSn ^ QqF aaaaaa.araio.aaarraaa. €o oE1 F{. I Iro ro L/)ro tf) rf).ro to u) u).ro tJ?tr) o rJ)totr)U)ulLrl CDA . . o . . .. . .. aaaaaaaaaa U)U)tr)u) l. lqt p gg ro e to ocro co .', cDc -_ (). rtQ CCttt H XBgsYtqrQq IERR . . Cnr-{('.(or-fo (/i a a a . . to r{@ 6q F{O?@;i . o s l. . o r rrlOlC.! CCd{tO o r{ r{ r{ Ci C0 a a rt -t __l Ci .r.l o I lto url Le tr) Le F{ Er O. |Q q t9 t9 to tt trl tr; $t t' str Sr $l U)rOtotr)tr)tr) |.r)Lr)rOu) Ftl (D Ia-oaaaaaaaoaaa aaaaQaaaoa l-l .-f Fl r-{ r-r' rf r{ r-l r-f rl r-f r-{ r-f r-{ r{ r-f r-l r{ r{ r-l r-f .-f ri I I l.s,c1q .,.foo.orou,o r{)mtr) +)l lleSSXgRRl.!tqq dpglTq o . . . .. orlr{F{40C0 r pq1'j 3, I .r-l C, t() l^ ^ _ rfr o rl r-l rl t-{ o rf r-f r-t lto Q tO to .to tO tr) .tO C- p -rOrO ro pppppp pppp 3H l_:_:_? l^ o . o .N[- -. i . * C - C tC ' C C t O r O . r i-f oaaaaaoooa o Eo CdN I t{.rl 5 hoo iEEgflfiggRRRRHH*88R8 888fr8p '-lrlNCINCC<l)-td:NN - !"f*lsirFqlqs,
  • 47. {1. ctwTEtl -_g Goft L PRs)GR{ r"r}1Ncn,PnoB I'Er,,l Rrtr.vruL.sTrsN . ( 1) PRI9SI,T"Y : s ALE IirA,tI SAT Si_ r0l! Eqn. ( 1) represents a general relationship. rt-1 * Pt = $t + rt ( 1) Where It-1 = Inventory a t t h e e n c l o f t-1 th p eriod. It = Inventory ab the end of t f.h n ov4r J n , .*l - - rv, I7 p = ProCuction ra te cluring t th erlod t -o gt = Saies tn t th period.. Let (It)* = Inventory durin{ t th perlo,J. - ( I g) = shor tag e clur irrg t trr p e' ioci the Iire + and - slEr: above tjre parantheses mean that, the quaritr r,los ilislcie the paran theses can have onr-y + or _ ve val-ues rcripec'blvely. By uslng transforrnation: Let a>o "*=fal O otherwis e a lal a< o 4 =Q otherrrise I