OPERATINS RESERACH PP

1. BY
B.BHEEMA RAJU

2. It is common problem in the production
process to find the sequence of the jobs that
will result in least idle time for the better
utilization of equipment.
For example one has to wear socks before
wearing shoe.

3.  It will be most convenient to study job
sequence in the following models
1.n jobs X 1 machine
2.n jobs X 2 machines
3.n jobs X 3 machines
4.n jobs X m machines
5. 2 jobs X n machines

4. 1. n jobs X 1 machine
When deferent letters are to be typed by a
typist he has to decide the order in which he
as to type.
When a student has some questions to
answer
in exam he would first choose the order in
which he has present to make it effective.
In the same way when certain jobs are to be
done in a production on one machine only,
then it is the turn of the engineer to decide
the order of these jobs to process.

5. The following are the rules from which a
person can select for his job shop sequencing
when only one machine is available
1. First In First Out (FIFO):
When the jobs do not require any
preferential
treatment, this rule is considered.
Complaints at telecom departments,
electricity departments, trains on single track
or platform, customers a retailer or a
telephone booth etc., will following rule.

6. 2.Last In First Out(LIFO):
When a machine is dismantled for repair or
overhaul, the parts are put back in LIFO
system. Pipeline laying in water works,
electrical wiring maintenance system will
follow this model. The office filling system,
loading and unloading of trucks,
dressing/undressing shirt and a coat,
wearing/removing socks and shoe are some
more common examples that occur in daily
life to follow LIFO

7. 3. Earliest Due Date (EDD):
Most of the times the production
departments are asked for the probable
time of completion of the job and based on
these promises the production engineer
plants his shop production.
4.Shortest Process Time (SPT):
This is another policy to apply on the
engineering jobs with the concept that the
jobs those take less time to perform are
taken first. A student while writing his exam
would prefer to write the question that
takes lesser time to that takes longer
duration.

8. 5.Longest process Time (LPT):
in contrast to the above , the job takes
longer time will be taken up first and the jobs
which take smaller time will be taken up last.
6.Pre-emptive Priority Rule:
When a job is very urgent , it will be taken
up on priority basis by attending
immediately stopping all other jobs. Under
this rule the highest priority job is allowed to
enter into the service immediately even if
another job with lower priority is already in
service. Doctors use this discipline when
emergency cases arrive to their clinics.

9. 7.Non Pre-emptive priority Rule:
In this case, highest priority goes ahead in
sequence but service is started immediately
after completion of the current service. For
example , a doctor gives priority to a medical
representative , but the gives the
appointment after the finishing the current
job.

10. 8.Priority Service:
Priority is given to certain jobs by the virtue
of their importance or recommendation of
top officials or expediting jobs etc.
9.Select In Random Order(SIRO):
Under this rule the jobs are selected at
random for operation irrespective their
arrival,
urgency , due date etc.

11.  10.Minimum cost Rule:
The jobs are selected in the ascending order
of their costs.
11.Maximum Profit Rule : The jobs are
selected in the descending order of the
profits
In the above the first five are static in nature
and the rest are dynamic

12. Sequencing of the n jobs X2 Machines:
Johnson’s rules:
S.M Johnson’s suggested a sequencing rule
for a situation where is a group of n jobs to
be processed through two successive work
centers .The rule ensures minimum
completion time for the group of n jobs by
minimsing the total idle times of the work
centers.

13. Assumptions for n jobs X2 sequencing:
The following assumptions are usually made
while dealing with sequencing problems.
 1. No passing rule is allowed strictly i.e., the
same order of jobs is maintained over each
machine . In other words , a job can not be
processed 2ndmachine unless it is processed
on 1st machine.
 2.Only one operation is carryout on a
machine at a time

14.  3.Processing times are know and do not
change
 4.Processing time of a job on machine is
independent of other jobs.
 5. Then time involved in moving jobs from
one
Machine to another is negligible
 6.Each operation , once started ,must be
completed.
 7.An operation must be completed before its
succeeding operation Can start.

15.  8.One machine of each type is available.
 9.A job is processed as soon as possible , but
only in the order specified.
 10.All the men/machines work with
consistent, efficiency.
 11 . Setting time is either include process
time or neglected
 12.No reworking is allowed.

16. The Rule:
 Identify the job with lowest processing time
among all the jobs on both the machines
 If this shortest processing time happens to
belong to the first machine then this job is placed
first in sequence, if the shortest processing time
happens to belong to the second work centre,
this job is put last in the sequence.

17.  Modeling
 Simulations
 Tools for simulations
 Software for simulations
 Applications

18. A Representation of an object, a
system, or an idea in some form
other than that of the entity itself.

19. Physical
(Scale models, prototype plants,…)
Mathematical
(Analytical queueing models, linear
programs, simulation)

20.  Simulation is a quantitative technique that
conducting a series of repeated trail and error
experiment on a prototype to predict the behavior
of the original system over a period of time.
 A Simulation of a system is the operation of a
model, which is a representation of that system.
 The model is amenable to manipulation which
would be impossible, too expensive, or too
impractical to perform on the system which it
portrays.
 The operation of the model can be studied, and
from this, properties concerning the behavior of
the actual system can be inferred.

21.  Designing and analyzing manufacturing
systems
 Evaluating H/W and S/W requirements for a
computer system
 Evaluating a new military weapons system or
tactics
 Determining ordering policies for an
inventory system
 Designing communications systems and
message protocols for them

22.  Designing and operating transportation
facilities such as freeways, airports, subways,
or ports
 Evaluating designs for service organizations
such as hospitals, post offices, or fast-food
restaurants
 Analyzing financial or economic systems

23. 1. Define an achievable goal
2. Put together a complete mix of skills on
the team
3. Involve the end-user
4. Choose the appropriate simulation tools
5. Model the appropriate level(s) of detail
6. Start early to collect the necessary input
data

24. 7. Provide adequate and on-going documentation
8. Develop a plan for adequate model
verification
(Did we get the “right answers ?”)
9. Develop a plan for model validation
(Did we ask the “right questions ?”)
10. Develop a plan for statistical output analysis

25. “To model the…” is NOT a goal!
“To model the…in order to
select/determine feasibility/…is a
goal.
Goal selection is not cast in concrete
Goals change with increasing insight

26. We Need:
-Knowledge of the system under
investigation
-System analyst skills (model formulation)
-Model building skills (model Programming)
-Data collection skills
-Statistical skills (input data representation)

27. We Need:
-More statistical skills (output data analysis)
-Even more statistical skills (design of
experiments)
-Management skills (to get everyone pulling
in the same direction)

28. -Modeling is a selling job!
-Does anyone believe the results?
-Will anyone put the results into action?
-The End-user (your customer) can (and must) do
all of the above BUT, first he must be convinced!
-He must believe it is HIS Model!

29. Assuming Simulation is the appropriate
means, three alternatives exist:
1. Build Model in a General Purpose
Language
2. Build Model in a General Simulation
Language
3. Use a Special Purpose Simulation
Package

30.  Advantages:
◦ Little or no additional software cost
◦ Universally available (portable)
◦ No additional training (Everybody knows…(language X) ! )
 Disadvantages:
◦ Every model starts from scratch
◦ Very little reusable code
◦ Long development cycle for each model
◦ Difficult verification phase

31. FORTRAN
◦ Probably more models than any other language.
PASCAL
◦ Not as universal as FORTRAN
MODULA
◦ Many improvements over PASCAL
ADA
◦ Department of Defense attempt at standardization
C, C++
◦ Object-oriented programming language

32.  Advantages:
◦ Standardized features often needed in modeling
◦ Shorter development cycle for each model
◦ Much assistance in model verification
◦ Very readable code
 Disadvantages:
◦ Higher software cost (up-front)
◦ Additional training required
◦ Limited portability

33.  GPSS
◦ Block-structured Language
◦ Interpretive Execution
◦ FORTRAN-based (Help blocks)
◦ World-view: Transactions/Facilities
 SIMSCRIPT II.5
◦ English-like Problem Description Language
◦ Compiled Programs
◦ Complete language (no other underlying language)
◦ World-view: Processes/ Resources/ Continuous

34.  MODSIM III
◦ Modern Object-Oriented Language
◦ Modularity Compiled Programs
◦ Based on Modula2 (but compiles into C)
◦ World-view: Processes
 SIMULA
◦ ALGOL-based Problem Description Language
◦ Compiled Programs
◦ World-view: Processes

35.  SLAM
◦ Block-structured Language
◦ Interpretive Execution
◦ FORTRAN-based (and extended)
◦ World-view: Network / event / continuous
 CSIM
◦ process-oriented language
◦ C-based (C++ based)
◦ World-view: Processes

36.  Advantages
◦ Very quick development of complex models
◦ Short learning cycle
◦ No programming--minimal errors in usage
 Disadvantages
◦ High cost of software
◦ Limited scope of applicability
◦ Limited flexibility (may not fit your specific
application)

37.  NETWORK II.5
◦ Simulator for computer systems
 OPNET
◦ Simulator for communication networks, including
wireless networks
 COMNET III
◦ Simulator for communications networks
 SIMFACTORY
◦ Simulator for manufacturing operations

38. Many people think of the cost of a
simulation only in terms of the software
package price.
There are actually at least three
components to the cost of simulation:
1.Purchase price of the software
2.Programmer / Analyst time
3.“Timeliness of Results”

39.  System
◦ A group of objects that are joined together in
some regular interaction or interdependence
toward the accomplishment of some
purpose.
◦ Entity
◦ An object of interest in the system.
◦ E.g., customers at a bank

40.  Attribute
◦ a property of an entity
◦ E.g., checking account balance
 Activity
◦ Represents a time period of specified length.
◦ Collection of operations that transform the
state of an entity
◦ E.g., making bank deposits

41.  Event:
◦ change in the system state.
◦ E.g., arrival; beginning of a new execution;
departure
 State Variables
◦ Define the state of the system
◦ Can restart simulation from state variables
◦ E.g., length of the job queue.

42.  Process
◦ Sequence of events ordered on time
 Note:
◦ the three concepts(event, process,and activity) give
rise to three alternative ways of building discrete
simulation models

43. System Entities Attributes Activities Events State
Variables
Banking Customers Checking
account
balance
Making
deposits
Arrival;
Departure
# of busy
tellers; # of
customers
waiting
Note: State Variables may change continuously (continuous sys.)
over time or they may change only at a discrete set of points
(discrete sys.) in time.

44.  Pure Continuous Simulation
 Pure Discrete Simulation
◦ Event-oriented
◦ Activity-oriented
◦ Process-oriented
 Combined Discrete / Continuous Simulation

45.  Less time consuming
 Sharpen the managerial Skills
 Doesn’t Disrupt the Real situation
 Gives better understanding to Managers
 Easy to use for non-technical managers also
 Less expensive
 Nearest relation between the Real and
Simulated model
 Scopes to study Environmental and Related
changes

46. Monte Carlo simulation is a computerized
mathematical technique that allows people to
account for risk in quantitative analysis and
decision making. The technique is used by
professionals in such widely disparate fields
as finance, project management, energy,
manufacturing, engineering, research and
development, insurance, oil & gas,
transportation, and the environment

47. In this competitive world,it is essential for an
executive to study or at least to guess the
activities of the competitor. Moreover he has
to plan his counter actions when his
competitor uses certain technique. Such war
or game is a regular feature in the market
which aims maximize the profits and
minimize the losses. So, the competitive
situation is called game.

48.  There are finite number of competitors called “players”
 Each players has a finite number of actions which are
called as “ strategies”
 No player knows his opponent’s strategy until he decides
his own strategy
 The game is a combination of strategies in certain units
(generally money) which determines the gain or loss
 The figure shows the outcome of strategies n a matrix
form is called “pay off matrix”

49.  The player playing the game always tries to
choose best course of action which results in
optimal pay off called as “optimal strategy”
 The expected pay off when all the players of the
follow their optimal strategies is called “Value of
the game”. The main objective of a problem of
games is to find the value of the game.
 The game is said to be “fair game” if the value of
the game is zero, otherwise it is known as
“unfair”

50. Terminology:
 Strategy: It is defined as set of rules while playing
the game
(a) Pure strategy : If the player select the same
strategy each time then that is called as
Pure strategy
(b) Mixed strategy : When the players uses the
combination of strategies that is called as
Mixed strategy
 Optimum strategy : A course of action or play
which puts the player in the most preferred
position is called Optimum strategy

51.  Value of the game:
It is the expected pay-off of play (final result)
when all the players are following their optimum
strategies.
If value of game V=0, then fair game, and
If V≠ 0, then unfair game.
 Two persons – Zero sum game:
When two players are playing the game and, if
loss of a player is gain of other and vice versa,
then it is called as two persons – zero sum game.

52. Payoff Matrix:
A two persons-zero sum game is represented by
a matrix as shown below
A’s pay-off matrix:
Column Player B
B1 B2 B3
A1 a11 a12 a13
Row
Player A : A2 a21 a22 a23
A3 a31 a32 a33

53. B’s pay-off matrix:
Column Player B
B1 B2 B3
A1 -a11 -a12 -a13
Row
Player A : A2 -a21 -a22 -a23
A3 -a31 -a32 -a33

54.  1. two persons games:
If only two players are playing the game
that type of game is called two persons game
ex: playing chess
 2. Multi person game:
If more than two players are playing the
game that type of game is called multi
persons game
ex: playing football,cricket.

55.  Zero sum game:
If loss of one player is gain of other player and
Vice versa then that game is zero sum game
 Non-zero sum game:
If loss of one player is not gain of other player
and Vice versa then that game is non-zero
sum game
 Deterministic game:
If the game yields a solution with single
strategy then that is called as deterministic
game

56.  Probabilistic game:
If a player adopts more than one strategy
with some probabilities that is called as
Probabilistic game
 Fair game: If value of game is zero i.e.,
neither player wins nor loss(drawn) that is fair
game
 Unfair game: If one player wins and other
losses ( value of the game is non zero i.e.,
may be positive or negative) that type of
game is called unfair game

57.  These type of games are two types
 Deterministic with pure strategy
 Probabilistic with mixed strategy
To solve these problems two types of methods
are there
1.Minimax-Maximin principle
2.Dominance principle

58.  Step 1: Write pay-off matrix
 Step 2: Select the minimum value of each row
of the pay –off matrix and encircle the
element
 Step 3:Select the largest among the row
minima found and write beneath the row
minima
 Step 4: Select the maximum value of each
column of the pay –off matrix and
enrectangle the element

59.  Step 5:Select the minimum value among the
column maxima found and write this at the
right end
 Step 6:If Max (Rmin)=Min (Cmax) then saddle
point exist. Thus saddle point is found at the
element on which both circle and box are
enclosed. This saddle point is also called as
value of the game

60. In certain cases no pure strategy solutions
exist for the game. In other words saddle
point/ value of the game does not exist.
Here we will adopt the Algebraic method we
will use to solve the problem
Player B
B1 B2
A1 a b
Player A
A2 c d

61. No machine is immortal and immune
completely to any failures. No matter how
safety you run . How closely you follow the
instruction of the manufacturer or supplier,
how best you maintain to its standards and
specification perhaps we can only try to
prevent or prolong the occurrence of failure
if we know the probable reason for its
occurrence.

62. The awareness of the equipment often makes
the engineer so confident that after the
rectification of the failure he will be able to
assure the production manager about its
running condition.
Types of failures:
1.Early failures (infant failures)
2.Random or rare event failures (youth failures)
3.Old age failures

63. Failure costs:
While analyzing the machine failure we are
concerned with the following costs.
1. Purchase cost
2. Salvage/ Scrap /Resale/Depreciation cost
3. Running cost/Maintenance, Repair and
Operating costs (MRO)
4. Failure/damage cost

64. Year
n
Cost
C
Salvage
Value
S
Running
cost
R
Depreci
ation
Cost
C-S
Cum.
Running
cost
∑R
Total
Cost
TC=
(C-S)
+∑R
Avg.
Cost
= TC/n