SlideShare a Scribd company logo
1 of 11
Download to read offline
The present paper considers the effect of income and loan
elasticity on demand and determines the buyers’ optional special order,
quantity as well as the optimal time. When the supplier reduces his sale
price, the buyer can offer a discount to push his sale, so as to increase
the profit margin. The paper introduces income and loan availability
elasticity effect in inventory management. The gain equation has been
derived to find out the optimal special order quantity and profit
associated with it under two different conditions i.e. when the remnant
inventory is zero and when the remnant inventory is finite.
.
ABSTRACT:
An Optimal Inventory Model : Income and Loan Availability Elasticity
Dr.J.K.Mantri
Deptt of Comp.Application
North Orissa University
jkmantri@gmail.com
Keywords: Elasticity,Inventory model,Profit,Loan
39 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
INTRODUCTION
The elasticity of demand is an economic terms which refers to the
responsiveness of demand to the change in price. When the demand is not
elastic, the drastic change in price may not affect the demand, for example a
fall in price or rise in price does not change the demand of essential
commodities. In case of a fall in price tends to reduce demand and rise in
price tends to extend demand. But in case of the articles, which are sensitive
to the change in price, the demand increases or decreases, such goods or
product are price responsive. The present paper is devoted to introduce a
new concept i.e. income and loan availability elasticity vis-à-vis inventory
models. Income and loan availability elasticity may be defined as:
E1 = Proportionate change in demand / Proportionate change in (income + loan availability).
The optional policies for no buyers discount and constant demand are
derived in [1]. Optional ordering policies in response to permanent price
increase when demand is assumed to be constant have been well
documented by [2], [3], [4] and [5]. A model to determine the optional
ordering policies for a finite horizon consisting of two distinct time intervals
characterized by different inventory parameters is presented by [6]. Models
which determine the optimal special order quantity when supplier reduces his
price temporarily, assume that the reduced price is in effect buyer’s
replenishment time and the demand rate remains constant [1], [7] and [8]. In
most cases a price discount results in an increase in demand. Ardalan [9]
relaxes demand assumption made in most inventory system with price
change. Ardalan[9] presents a procedure to include any relationship between
price and demand to determine the combined to optimal price and optimal
order quantity.
The present paper considers the effect of income and loan availability
elasticity on demand and determines the buyer’s optimal special order
quantity and optimal time. When supplier reduces the price temporarily, the
buyer may offer a discount to his customers to push his sale and increase
his profit margin. This paper brings in to picture income and loan availability
demand relationship, which deals with classification of products into
essential and non-essential goods. For non-essential goods like Luxuries the
40 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
income and loan availability demand relationship is considerable. We
introduce the income and loan availability elasticity effect in to inventory
analysis and obtain the gain equation to find optimal special order quantity
under two conditions i.e. when there is finite remnant inventory and when it
is zero. We also determine optimal time for placing order quantity when there
is finite remnant inventory and extend it to find the optimal time for placing
such an order. We further modify our model to find cost of saving of special
purchase when supplier announces to increase his sale price by some
amount from a specified date. Finally an optimal ordering policy is
determined to get profit maximization.
MODEL ASSUMPTIONS
The present paper consider the effect of income and loan availability
elasticity because of the fact that in the current liberalized market and
consumerism, the financial institutions are very much liberal in financing
consumer loans at very low percentage of interest, the low rate loan
availability can be considered as an aid to buying capacity so we find a
heavy demand on non essential goods such as luxury items Automobiles,
Ornaments etc. As for example this above effect has an impact not only on
the “Growth Rates of Industrial production of India but also on the
globalization of Indian economy”. The structure of interest (loan) rates and
the growth rates of industrial production in India are cited in Table (1).
The models developed in this paper has taken care of the
simultaneous effect of income change and; loan facilities on classical
inventory models. This concept has very much importance to the stockiest to
go for a better margin of profit and improvement in their sale.
If E1 is the income and loan availability Elasticity, then from its definition.
E1 = Proportionate change in demand/ Proportionate change in (Income + loan availability)
D = Buyer ‘s annual demand;
D1 = Buyer’s annual demand after discount to customer.
D2 =Buyer’s new annual demand after the effect of income and loan
availability elasticity.
Thus, New annual demand = Old demand (Change in income + loan availability)
41 Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
D2 = D1 + (E1 × proportionate change in (income + Loan availability) /100) D1
D2 = D1 [1+ E1 × proportionate change in (income + Loan availability) /100]
D2 = D1 (1+Y+L) where
L = (E1 × proportionate change in loan availability /100)
Where Y = (E1 × proportionate change in income/100)
(1)
P = Suppliers regular price per unit; P1 = Buyer’s regular price per unit;
P2 = Buyer’s sale (reduced) price per unit; C = ordering cost per order,
H = PF = Holding cost per unit per year; F = Annual holding cost as a
fraction of unit cost (carry cost parameters); E.O.Q. = the size of an order
that minimizes the total inventory cost is known as economic order quantity.
Q = Lot size or order quantity in units (a special order quantity);
Tc = Total annual cost
Qr = Regular optimal order quantity = √(2CD/PF) (2)
Further if, ‘d’ is the amount which supplier offers on his sale price and Qd is
regular optimal order quantity using the reduced price.
If income and loan availability elasticity effect is there, then
Qd = [2D2 C/(p-d) F] ½
= [2D1 (1+Y+L) C/(P – d) F] ½
(3)
If however the income and loan availability elasticity effect is not there then
Y = 0;
Qd = [2D1C/(P – d) F] ½
(4)
Q0 = Special optimal order quantity when remnant inventory is zero.
Qq = Special optimal order quantity when remnant inventory is not zero.
Gr = Gain associated with regular policy during Ts;
Gs = Gain associated with special order during TS .
TS = The time interval between the time the buyer receives the special order
of size “Q” and his next replenishment time.
42 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
Optimal Special Order Quantity when Remnant Inventory is zero and
effect of income and loan Availability Elasticity is significant.
Suppose D2 is the buyer’s new annual demand after change in income
and loan availability elasticity of the customer. At replenishment time buyer
places an order of Q units at reduced price (offered by supplier). So the
buyer too offers a discount to his customers on all the Q units. TS is the time
interval after which the suppliers reduced price is not available and buyer
reverts to his usual ordering policy.
Now the gain associated within the time interval TS
Gs = [P2 – (P-d)] Q – [Q2
(P – d) F]/[2D1 (1+Y+L)] –C (5)
If suppliers reduced price and buyers discount were permanent then
classical inventory formula of E.O.Q could be used to determine optimal
order quantity. As a result these are temporary business manoeuvirs and so
this cannot be used, but these can be taken as rudimentary tool to obtain
optimal policy for special order Qd.
If ‘d’ be the discount offered on Qd units then purchase cost of these Qd
units would be (P – d) Qd.
The number of units bought at usual regular price during
Ts = [D/D1 (1+Y+L)](Q – Qd) (6)
Therefore, the total buying cost is
(P – d) Qd+[PD/D1 (1+Y+L)](Q-Qd) (7)
The holding cost of the first order is
Qd2
(P-d) F/2D1 (1+Y+L) (8)
The holding cost during the rest of Ts is
[Qr(Q-Qd)PF]/[2D1 (1+Y+L)] (9)
The total holding cost during Ts is
[Qd2
(P-d) F]/[2D1(1+Y+L)]+[Qr(Q-Qd)PF]/[2D1 (1+Y+L)] (10)
The number of orders placed during Ts is
(1+D (Q-Qd)/D1 (1+Y+L) Qr] (11)
The ordering cost associated with this order will be given by
C[1+D(Q-Qd)/D1 (1+Y+L)Qr] (12)
43 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
The gain associated with the usual (regular) ordering policy during Ts is
given by:
Gr=[P2 –(P-d)]Qd+(P1-P)D(Q-Qd)/D1 (1+Y+L)-(P-d)FQd2
/2D1 (1+Y+L)
-Qr(Q-Qd)PF/2D1(1+Y+L)-C[1+D(Q-Qd)/D1(1+Y+L)Qr] (13)
In order to maximize gain the difference between Gr and Gs should be
maximized.
G = [P2 –(P-d)] Q-Q2
(P-d) F/2D1(1+Y+L)-C
-[P2 (P-d)]Qd-(P1-P)D(Q-Qd)/D1 (1+Y+L)+(P-d)F Qd2
/2D1(1+Y+L)
+Qr(Q-Qd)PF/2D1(1+Y+L)+C[1+D(Q-Qd)/D1 (1+Y+L)Qr] (14)
Differentiating G with respect to Q and equating dG/dQ = 0, we get
Q0 = [D1 (1+Y+L) (P2 -P+d)-(P1 -P) D]/[(P-d) F]+[Qr P/(P-d)]
Putting Q0 in Equation (14) to get the optimal value of G = C (Q0- Qd) 2
/Qd2
Optimal Special Order Quantity when Remnant Inventory is not zero
and Effect of Income and Loan Availability Elasticity are significant.
If effect of income and loan availability elasticity is considerable and
there is sufficient remnant inventory, then buyer has two options either to
buy at the reduced price of supplier and subsequently offer discount to his
customer or just avoid the business ploy and follow his usual optimal order
policy.
If ‘q’ be the level of remnant inventory then to determine special order
quantity the difference between Gr and Gs should be maximized. If per
capita income rised and loan availability rises increase in purchasing power
of customer, the gain associated with special order quantity (Gs) and gain
associated with usual ordering policy (Gr) is expressed as -
Gs=Q(P2–P+d)–q2
PF/2D–qQ(P-d)F/D-[(p-d)FQ2
]/[2D1 (1+Y+L)]–C (15)
Gr=[DQ(P1 -P)/D1(1+Y+L)-(q2
PF/2D)]
-(QrQPF/2D1(1+Y+L)]-[DQC/D1 (1+Y+L)Qr] (16)
The increase in gain due to special order is G = Gs – Gr.
G=Q(P2-P+d)-q2
PF/2D-qQ(p-d)F/D-(p-d)FQ2
/2D1 (1+Y+L)-C
–DQ(P1 -P)/D1(1+Y+L)+q2
PF/2D+QrQPF/2D1(1+Y+L)+DQC/D1 (1+Y+L)Qr (17)
44 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
To maximize profit differentiating G with respect to Q and equating dG/dQ = 0
⇒Qq=[(P2 -P+d)D1(1+Y+L)-D(P1-P)]/[(P-d)F]
+QrP/(P-d)-qD1(1+Y+L)/D (18)
⇒Qq=Qo-[qD1 (1+Y+L)/D] (19)
To determine the optimal time for placing special order Qq, a theorem is
deduced: -
Theorem – 1. Higher the income and loan availability elasticity smaller
the level of remnant inventory and it determines the optimal time for
placing optimal special order.
Proof : When remnant inventory is ‘q’ the special order quantity is ‘Qq’
When remnant inventory is ‘q-1 ’ the optimal order is given by
Qq+D1 (1+Y+L)/D.
If Ei is income and loan availability elasticity then new demand due to it is D2
given by D2 = D1(1+Y+L).
Using the gain equation 17, putting Q=Qq when remnant inventory is q units
and gain G as Gq and Q = Qq -1 when remnant inventory is (q-1) units and gain
G as Gq -1 .
Where Qq -1 = Qq+[D1(1+Y+L)/D]
Equation 17 ⇒
Gq= Qq(P2-P+d) –qQq(P-d)F/D - (P-d)FQq2
/2D1 (1+Y+L)
–C-DQq(P1-P) /D1(1+Y+L)+QrQqPF/2D1(1+Y+L)+DQqC/D1(1+Y+L)Qr (20)
For remnant inventory (Qq-1)
Equation 17 ⇒
Gq -1 = Qq -1 (P2 -P+d)-(q-1)Qq -1 (P-d)F/D- (p-d)F(Qq-1)2
/2D1 (1+Y+L)
+QrQq -1 PF/2D1 (1+Y+L)+DQq -1 C/D1 (1+Y+L)Qr
- DQq (P1-P)/D1 (1+Y+L) -C (21)
Here we need to Prove Gq-1 > Gq i.e. Gq -1 –Gq = positive.
Gq -1 –Gq = D1(1+Y+L) (P2 -P+d)/D-D1 (1+Y+L)q (P-d)F/D2
+D1(1+Y+L)(P-d)F/2D2
-P1+P+QrPF/2D+C/Qr (22)
Using equation (18) in equation (22) we get
[Gq -1 –Gq ][D/(P-d)F]=Qq+D1(1+Y+L)/2D (23)
Which is a positive value, this proves the theorem. (Proved)
45 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
Theorem –2
Higher the income and loan availability elasticity larger the level
of remnant inventory and higher is the cost of saving when price rise is
imminent.
Proof: If the supplier changes his sale policy and he stops the discount
given to customer and announces a new increased sale price.
Let P be the amount by which supplier tends to increase his sale price
at some date ti. The units purchased before ti will cost ‘p’ but purchase after
ti will cost (P+p).
If D be the annual demand and Ei be the income and loan availability
elasticity and ‘q’ be level of remnant inventory.
New demand due to income and loan availability elasticity = Old demand +change in demand
D
*
=D(1+Y+L) (24)
The optimal order quantity before price increase
Qr=(2CD*/PF)
½
=[2CD(1+Y+L)/PF]
½
(25)
The optimal order quantity after the price rise will be:
Qr*=[2CD*/(P+p)F]½=[2CD(1+Y+L)/(P+p)F]
½
(26)
To obtain optimal special order size, it is necessary to maximize the cost
difference during td – tr with and without special time order.
Total cost = Purchased cost+ Holding cost + Ordering cost
Tcr=PQs+[QsPFq/D(1+Y+L)]+Qs2
PF/2D(1+Y+L)]+[q2
PF/2D(1+Y+L)]+C (27)
If no special order is placed prior to ti the total cost of the system
during tr to td when several purchases of Qr* are made at new price (P+p)
Tcs =(P+p)Qs+ (Qr* /2)(P+p)F(Qs/D*)+(q/2)PF(q/D*)+(Qs/Qr*)C
Using equation (24) and Equation (26)
Tcs = (P+p)Qs+( ½) [2CD(1+Y+L)/(P+p)F] ½
(P+p)
F[Qs/D(1+Y+L)]+q2
PF/2D(1+Y+L)+(Qs/Qr*)C (28)
To find the optimal order size the difference between Tcr and Tcs should be
minimized G = Tcs-Tcr
⇒G=Qs[p+C[F(P+p)/2D(1+Y+L)]½
-PFq/D(1+Y+L)- [PFQs2
/2D(1+Y+L)]-C (29)
46 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
Differentiating with respect to Qs and putting dG/dQs = 0, we get optimal
special order quantity Qso.
Qso=Qr*/2+p/2PF[2D(1+Y+L)+Qr*F]-q (30)
This is optimal special order size, putting equation 30 in equation 29 we get
the optimal cost of saving associated with Qso
G⇒Qso[p+[CF+(P+p)/2D(1+Y+L)]1/2
–PFq/D(1+Y+L)]- PFQso2
/2D(1+Y+L)]-C
Theorem 3:
If tf <tr the optimal ordering policy is
(i) To order Qq at ‘tf’ if Qq > Qd otherwise
(ii) Order Qr at ‘tr’
Proof: The value of the remnant inventory Qr for which Gr and Gs are equal
can be determined by equating equation 15 and 16.
Q(P2 -p+d)-q2
PF/2D-qQ(P-d)F/D-[(P-d)FQ2
]/[2D1 (1+Y+L)]-C
=[DQ(P1 -P)/D1(1+Y+L)]-[q2
PF/2D]-[QrQPF/2D1(1+Y+L)]-[DQC/D1(1+Y+L)Qr]
Simplifying and putting Q=Qq and q=qc using equation (18) we get
Qq/2=Qd2
/2Qq=Qq2
=Qd2
(31)
Since Gs> Gr for any Qq> Qd as long as Equation 31 holds good and optimal
order size Qq at ‘tf’ would maximize the gain. Otherwise the usual (regular)
ordering policy will be optimal.
47 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
Conclusions
When a supplier reduces his sale price temporarily, then buyer might
follow a policy which increases his demand. However due to income and loan
availability elasticity effect, the change in demand may be much greater than
expected. In fact income and elasticity brings product classification, which is
an important economic consideration. The mathematical treatment of
influence of income elasticity of a buyer’s policy is discussed. We determine
the case of finding optimal order quantity and profit when supplier reduced
his sale price in both situation i.e. with/without remnant inventory. The
special cost of saving is determined when rise in price is imminent and
finally ordering policy is discussed.
48 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org
REFERENCES
1. Ardalan A. 1967, “Optimal Ordering Policies in Response to sale” IIE
Trans. 20 192-194
2. Ardalan A, 1991 “Combined Optimal Price and Optimal inventory
Replenishment Policies When a Sale Results in increase in Demand”
Computers Ops. , Res. Vol.18, No. 18.
3. Bhandari M.R. and Sharma P.K., 1998, ‘Journal of public Budgeting,
Accounting and financial Management”, Spring, Volume X.
4. Brown R.G., “Decision Rules for inventory Management” Holt, Reinchart
& Winston, pp. 21-203, New York.
5. Carlsson C.and Fuller Rs., 1995, “Multiple Criteria Decision Making the
Case for interdependence” Computers Ops. Rs. Vol22,No.3.
6. Dewett K.K and Chand, A., 1996 “Modern Economic Theory” S. Chand.
7. Lev. B. et a, 1981 “Optimal Ordering policies when Anticipating
parameter changes in ECQ systems” Res. Logist Q.
8. Naddor, E., 1996, “ Inventory System”, Wiley, New York.
9. Petterson, R. and Silver, E.A., “Decision system for inventory
Management and Production Planning” Wiley, New York.
10. 10.Raman, A. and Fisher, M., 1996 “Reading the cost of demand
Uncertainty Through Accurate Response to Early Sales” Os. Res. Vol.
44, No.1.
11. Song, J.H. and Zipkin, 1993 “ Inventory Control in Fluctuating Demand
Environment” Ops, Res., Vol.41, No.2.
12. Taylor S.H. and Bradley, C.E., 1985, “ Optimal Ordering Strategies for
Announced Price Increase” Ops., Res.
13. Tersine R.J. (ed), 1998, “Principles of Inventory and Materials
Management” North Holland, New York.
14. Tersine, R.J. and Grasso, E.T., 1998, “ Forward Buying in Response to
Announced Price Increase” J. Purchase, Mater Mgmt.
49 | Page
International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49
www.ijres.org

More Related Content

Viewers also liked

BIM based organizational learning
BIM based organizational learningBIM based organizational learning
BIM based organizational learningIJRES Journal
 
Programme Exit Survey (PES) Report
Programme Exit Survey (PES) ReportProgramme Exit Survey (PES) Report
Programme Exit Survey (PES) ReportIJRES Journal
 
Fuel Cell: Survey and Analysis
Fuel Cell: Survey and AnalysisFuel Cell: Survey and Analysis
Fuel Cell: Survey and AnalysisIJRES Journal
 
Decision Support System for Energy Saving Analysis in Manufacturing Industry
Decision Support System for Energy Saving Analysis in Manufacturing IndustryDecision Support System for Energy Saving Analysis in Manufacturing Industry
Decision Support System for Energy Saving Analysis in Manufacturing IndustryIJRES Journal
 
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...IJRES Journal
 
Independent Control Of Active And Reactive Powers From DFIG By Logic Fuzzy
Independent Control Of Active And Reactive Powers From DFIG By Logic FuzzyIndependent Control Of Active And Reactive Powers From DFIG By Logic Fuzzy
Independent Control Of Active And Reactive Powers From DFIG By Logic FuzzyIJRES Journal
 
The bionic flapping-wing drive mechanism analysis and design
The bionic flapping-wing drive mechanism analysis and designThe bionic flapping-wing drive mechanism analysis and design
The bionic flapping-wing drive mechanism analysis and designIJRES Journal
 
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...Grupo de Economia Política IE-UFRJ
 
Consumer and Producer Surplus
Consumer  and Producer SurplusConsumer  and Producer Surplus
Consumer and Producer SurplusGene Hayward
 
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...IJRES Journal
 
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...IJRES Journal
 
Analyze ball screw feeding system dynamics simulation Based on the ADAMS
Analyze ball screw feeding system dynamics simulation Based on the ADAMSAnalyze ball screw feeding system dynamics simulation Based on the ADAMS
Analyze ball screw feeding system dynamics simulation Based on the ADAMSIJRES Journal
 
Enhanced Image Compression Using Wavelets
Enhanced Image Compression Using WaveletsEnhanced Image Compression Using Wavelets
Enhanced Image Compression Using WaveletsIJRES Journal
 
Economic system Vs Capitalist Economic System (English)
Economic system Vs Capitalist Economic System (English)Economic system Vs Capitalist Economic System (English)
Economic system Vs Capitalist Economic System (English)Naveed Butt
 
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) Module
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) ModuleFabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) Module
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) ModuleIJRES Journal
 
Pavneet singh kohli ppt micro & macro Economics (10.1)
Pavneet singh kohli ppt micro & macro Economics (10.1)Pavneet singh kohli ppt micro & macro Economics (10.1)
Pavneet singh kohli ppt micro & macro Economics (10.1)pavneet singh kohli
 
Elasticity Ppt
Elasticity PptElasticity Ppt
Elasticity Pptmar_09
 

Viewers also liked (20)

A120104
A120104A120104
A120104
 
BIM based organizational learning
BIM based organizational learningBIM based organizational learning
BIM based organizational learning
 
Programme Exit Survey (PES) Report
Programme Exit Survey (PES) ReportProgramme Exit Survey (PES) Report
Programme Exit Survey (PES) Report
 
C142530
C142530C142530
C142530
 
G124549
G124549G124549
G124549
 
Fuel Cell: Survey and Analysis
Fuel Cell: Survey and AnalysisFuel Cell: Survey and Analysis
Fuel Cell: Survey and Analysis
 
Decision Support System for Energy Saving Analysis in Manufacturing Industry
Decision Support System for Energy Saving Analysis in Manufacturing IndustryDecision Support System for Energy Saving Analysis in Manufacturing Industry
Decision Support System for Energy Saving Analysis in Manufacturing Industry
 
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...
Experimental Evaluation of effect of filler on tensile behaviour of E-glass/e...
 
Independent Control Of Active And Reactive Powers From DFIG By Logic Fuzzy
Independent Control Of Active And Reactive Powers From DFIG By Logic FuzzyIndependent Control Of Active And Reactive Powers From DFIG By Logic Fuzzy
Independent Control Of Active And Reactive Powers From DFIG By Logic Fuzzy
 
The bionic flapping-wing drive mechanism analysis and design
The bionic flapping-wing drive mechanism analysis and designThe bionic flapping-wing drive mechanism analysis and design
The bionic flapping-wing drive mechanism analysis and design
 
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...
Macro/Micro interactions : Economic and Institutional Uncertainties and Struc...
 
Consumer and Producer Surplus
Consumer  and Producer SurplusConsumer  and Producer Surplus
Consumer and Producer Surplus
 
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...
Politeknik Kota Kinabalu Programme Exit Survey (PES) for Diploma in Electroni...
 
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
Modeling and Simulation of Virtual Prototype of the forming Machine based on ...
 
Analyze ball screw feeding system dynamics simulation Based on the ADAMS
Analyze ball screw feeding system dynamics simulation Based on the ADAMSAnalyze ball screw feeding system dynamics simulation Based on the ADAMS
Analyze ball screw feeding system dynamics simulation Based on the ADAMS
 
Enhanced Image Compression Using Wavelets
Enhanced Image Compression Using WaveletsEnhanced Image Compression Using Wavelets
Enhanced Image Compression Using Wavelets
 
Economic system Vs Capitalist Economic System (English)
Economic system Vs Capitalist Economic System (English)Economic system Vs Capitalist Economic System (English)
Economic system Vs Capitalist Economic System (English)
 
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) Module
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) ModuleFabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) Module
FabricationofThin FilmUsing Modified Physical Vapor Deposition (PVD) Module
 
Pavneet singh kohli ppt micro & macro Economics (10.1)
Pavneet singh kohli ppt micro & macro Economics (10.1)Pavneet singh kohli ppt micro & macro Economics (10.1)
Pavneet singh kohli ppt micro & macro Economics (10.1)
 
Elasticity Ppt
Elasticity PptElasticity Ppt
Elasticity Ppt
 

Similar to Optimal Inventory Modeling of Income and Loan Elasticity Effects

IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...
IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...
IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...IRJET Journal
 
study of an integrated inventory with controllable lead time
 study of an integrated inventory with controllable lead time  study of an integrated inventory with controllable lead time
study of an integrated inventory with controllable lead time preplo
 
An eoq model with time dependent demand rate under trade credits
An eoq model with time dependent demand rate under trade creditsAn eoq model with time dependent demand rate under trade credits
An eoq model with time dependent demand rate under trade creditsDivyesh Solanki
 
96202108
9620210896202108
96202108IJRAT
 
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B ScenariosChapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenariositsvineeth209
 
Me 01 elasticity(3)
Me 01 elasticity(3)Me 01 elasticity(3)
Me 01 elasticity(3)ssuserafaef3
 
Concept of Demand along with its degrees
Concept of Demand along with its degreesConcept of Demand along with its degrees
Concept of Demand along with its degreesRohan Byanjankar
 
Elasticity and its application
Elasticity and its applicationElasticity and its application
Elasticity and its applicationKhalid Aziz
 
Inflationary inventory model under trade credit subject to supply uncertainty
Inflationary inventory model under trade credit subject to supply uncertaintyInflationary inventory model under trade credit subject to supply uncertainty
Inflationary inventory model under trade credit subject to supply uncertaintyIAEME Publication
 
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...11.sales forecast by taking the concept of blue ocean theory using mat lab pr...
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...Alexander Decker
 
Bba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityBba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityBhavik Panchal
 
Bba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityBba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityRai University
 
Micro Economics Elasticity
Micro Economics ElasticityMicro Economics Elasticity
Micro Economics ElasticityAvijeet Tulsiani
 
Assignment on elacticity of demand
Assignment on elacticity of demandAssignment on elacticity of demand
Assignment on elacticity of demandEHSAN KHAN
 
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...Editor IJCATR
 
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...Alexander Decker
 
Happy Hospital Statement of Financial Position As of December 31, .docx
Happy Hospital Statement of Financial Position As of December 31, .docxHappy Hospital Statement of Financial Position As of December 31, .docx
Happy Hospital Statement of Financial Position As of December 31, .docxbenjaminjames21681
 
Microeconomics Elasticity
Microeconomics ElasticityMicroeconomics Elasticity
Microeconomics ElasticityRakesh Mehta
 

Similar to Optimal Inventory Modeling of Income and Loan Elasticity Effects (20)

IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...
IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...
IRJET-Inventory Model under Trade Credit when Payment Time is Probabilistic f...
 
Bp35384385
Bp35384385Bp35384385
Bp35384385
 
study of an integrated inventory with controllable lead time
 study of an integrated inventory with controllable lead time  study of an integrated inventory with controllable lead time
study of an integrated inventory with controllable lead time
 
An eoq model with time dependent demand rate under trade credits
An eoq model with time dependent demand rate under trade creditsAn eoq model with time dependent demand rate under trade credits
An eoq model with time dependent demand rate under trade credits
 
96202108
9620210896202108
96202108
 
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B ScenariosChapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios
Chapter 12: Applications of Database Marketing in B-to-C and B-to-B Scenarios
 
Me 01 elasticity(3)
Me 01 elasticity(3)Me 01 elasticity(3)
Me 01 elasticity(3)
 
Concept of Demand along with its degrees
Concept of Demand along with its degreesConcept of Demand along with its degrees
Concept of Demand along with its degrees
 
Elasticity and its application
Elasticity and its applicationElasticity and its application
Elasticity and its application
 
Hm3312981305
Hm3312981305Hm3312981305
Hm3312981305
 
Inflationary inventory model under trade credit subject to supply uncertainty
Inflationary inventory model under trade credit subject to supply uncertaintyInflationary inventory model under trade credit subject to supply uncertainty
Inflationary inventory model under trade credit subject to supply uncertainty
 
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...11.sales forecast by taking the concept of blue ocean theory using mat lab pr...
11.sales forecast by taking the concept of blue ocean theory using mat lab pr...
 
Bba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityBba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticity
 
Bba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticityBba 1 be 1 u-2.3 elasticity
Bba 1 be 1 u-2.3 elasticity
 
Micro Economics Elasticity
Micro Economics ElasticityMicro Economics Elasticity
Micro Economics Elasticity
 
Assignment on elacticity of demand
Assignment on elacticity of demandAssignment on elacticity of demand
Assignment on elacticity of demand
 
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...
An Inventory Model with Variable Demand Rate for Deteriorating Items under Pe...
 
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...
11.[38 44]sales forecast by taking the concept of blue ocean theory using mat...
 
Happy Hospital Statement of Financial Position As of December 31, .docx
Happy Hospital Statement of Financial Position As of December 31, .docxHappy Hospital Statement of Financial Position As of December 31, .docx
Happy Hospital Statement of Financial Position As of December 31, .docx
 
Microeconomics Elasticity
Microeconomics ElasticityMicroeconomics Elasticity
Microeconomics Elasticity
 

More from IJRES Journal

Exploratory study on the use of crushed cockle shell as partial sand replacem...
Exploratory study on the use of crushed cockle shell as partial sand replacem...Exploratory study on the use of crushed cockle shell as partial sand replacem...
Exploratory study on the use of crushed cockle shell as partial sand replacem...IJRES Journal
 
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...IJRES Journal
 
Review: Nonlinear Techniques for Analysis of Heart Rate Variability
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityReview: Nonlinear Techniques for Analysis of Heart Rate Variability
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityIJRES Journal
 
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...IJRES Journal
 
Study and evaluation for different types of Sudanese crude oil properties
Study and evaluation for different types of Sudanese crude oil propertiesStudy and evaluation for different types of Sudanese crude oil properties
Study and evaluation for different types of Sudanese crude oil propertiesIJRES Journal
 
A Short Report on Different Wavelets and Their Structures
A Short Report on Different Wavelets and Their StructuresA Short Report on Different Wavelets and Their Structures
A Short Report on Different Wavelets and Their StructuresIJRES Journal
 
A Case Study on Academic Services Application Using Agile Methodology for Mob...
A Case Study on Academic Services Application Using Agile Methodology for Mob...A Case Study on Academic Services Application Using Agile Methodology for Mob...
A Case Study on Academic Services Application Using Agile Methodology for Mob...IJRES Journal
 
Wear Analysis on Cylindrical Cam with Flexible Rod
Wear Analysis on Cylindrical Cam with Flexible RodWear Analysis on Cylindrical Cam with Flexible Rod
Wear Analysis on Cylindrical Cam with Flexible RodIJRES Journal
 
DDOS Attacks-A Stealthy Way of Implementation and Detection
DDOS Attacks-A Stealthy Way of Implementation and DetectionDDOS Attacks-A Stealthy Way of Implementation and Detection
DDOS Attacks-A Stealthy Way of Implementation and DetectionIJRES Journal
 
An improved fading Kalman filter in the application of BDS dynamic positioning
An improved fading Kalman filter in the application of BDS dynamic positioningAn improved fading Kalman filter in the application of BDS dynamic positioning
An improved fading Kalman filter in the application of BDS dynamic positioningIJRES Journal
 
Positioning Error Analysis and Compensation of Differential Precision Workbench
Positioning Error Analysis and Compensation of Differential Precision WorkbenchPositioning Error Analysis and Compensation of Differential Precision Workbench
Positioning Error Analysis and Compensation of Differential Precision WorkbenchIJRES Journal
 
Status of Heavy metal pollution in Mithi river: Then and Now
Status of Heavy metal pollution in Mithi river: Then and NowStatus of Heavy metal pollution in Mithi river: Then and Now
Status of Heavy metal pollution in Mithi river: Then and NowIJRES Journal
 
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...IJRES Journal
 
Experimental study on critical closing pressure of mudstone fractured reservoirs
Experimental study on critical closing pressure of mudstone fractured reservoirsExperimental study on critical closing pressure of mudstone fractured reservoirs
Experimental study on critical closing pressure of mudstone fractured reservoirsIJRES Journal
 
Correlation Analysis of Tool Wear and Cutting Sound Signal
Correlation Analysis of Tool Wear and Cutting Sound SignalCorrelation Analysis of Tool Wear and Cutting Sound Signal
Correlation Analysis of Tool Wear and Cutting Sound SignalIJRES Journal
 
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...IJRES Journal
 
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...IJRES Journal
 
A novel high-precision curvature-compensated CMOS bandgap reference without u...
A novel high-precision curvature-compensated CMOS bandgap reference without u...A novel high-precision curvature-compensated CMOS bandgap reference without u...
A novel high-precision curvature-compensated CMOS bandgap reference without u...IJRES Journal
 
Structural aspect on carbon dioxide capture in nanotubes
Structural aspect on carbon dioxide capture in nanotubesStructural aspect on carbon dioxide capture in nanotubes
Structural aspect on carbon dioxide capture in nanotubesIJRES Journal
 
Thesummaryabout fuzzy control parameters selected based on brake driver inten...
Thesummaryabout fuzzy control parameters selected based on brake driver inten...Thesummaryabout fuzzy control parameters selected based on brake driver inten...
Thesummaryabout fuzzy control parameters selected based on brake driver inten...IJRES Journal
 

More from IJRES Journal (20)

Exploratory study on the use of crushed cockle shell as partial sand replacem...
Exploratory study on the use of crushed cockle shell as partial sand replacem...Exploratory study on the use of crushed cockle shell as partial sand replacem...
Exploratory study on the use of crushed cockle shell as partial sand replacem...
 
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...
 
Review: Nonlinear Techniques for Analysis of Heart Rate Variability
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityReview: Nonlinear Techniques for Analysis of Heart Rate Variability
Review: Nonlinear Techniques for Analysis of Heart Rate Variability
 
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...
 
Study and evaluation for different types of Sudanese crude oil properties
Study and evaluation for different types of Sudanese crude oil propertiesStudy and evaluation for different types of Sudanese crude oil properties
Study and evaluation for different types of Sudanese crude oil properties
 
A Short Report on Different Wavelets and Their Structures
A Short Report on Different Wavelets and Their StructuresA Short Report on Different Wavelets and Their Structures
A Short Report on Different Wavelets and Their Structures
 
A Case Study on Academic Services Application Using Agile Methodology for Mob...
A Case Study on Academic Services Application Using Agile Methodology for Mob...A Case Study on Academic Services Application Using Agile Methodology for Mob...
A Case Study on Academic Services Application Using Agile Methodology for Mob...
 
Wear Analysis on Cylindrical Cam with Flexible Rod
Wear Analysis on Cylindrical Cam with Flexible RodWear Analysis on Cylindrical Cam with Flexible Rod
Wear Analysis on Cylindrical Cam with Flexible Rod
 
DDOS Attacks-A Stealthy Way of Implementation and Detection
DDOS Attacks-A Stealthy Way of Implementation and DetectionDDOS Attacks-A Stealthy Way of Implementation and Detection
DDOS Attacks-A Stealthy Way of Implementation and Detection
 
An improved fading Kalman filter in the application of BDS dynamic positioning
An improved fading Kalman filter in the application of BDS dynamic positioningAn improved fading Kalman filter in the application of BDS dynamic positioning
An improved fading Kalman filter in the application of BDS dynamic positioning
 
Positioning Error Analysis and Compensation of Differential Precision Workbench
Positioning Error Analysis and Compensation of Differential Precision WorkbenchPositioning Error Analysis and Compensation of Differential Precision Workbench
Positioning Error Analysis and Compensation of Differential Precision Workbench
 
Status of Heavy metal pollution in Mithi river: Then and Now
Status of Heavy metal pollution in Mithi river: Then and NowStatus of Heavy metal pollution in Mithi river: Then and Now
Status of Heavy metal pollution in Mithi river: Then and Now
 
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...
 
Experimental study on critical closing pressure of mudstone fractured reservoirs
Experimental study on critical closing pressure of mudstone fractured reservoirsExperimental study on critical closing pressure of mudstone fractured reservoirs
Experimental study on critical closing pressure of mudstone fractured reservoirs
 
Correlation Analysis of Tool Wear and Cutting Sound Signal
Correlation Analysis of Tool Wear and Cutting Sound SignalCorrelation Analysis of Tool Wear and Cutting Sound Signal
Correlation Analysis of Tool Wear and Cutting Sound Signal
 
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...
 
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...
 
A novel high-precision curvature-compensated CMOS bandgap reference without u...
A novel high-precision curvature-compensated CMOS bandgap reference without u...A novel high-precision curvature-compensated CMOS bandgap reference without u...
A novel high-precision curvature-compensated CMOS bandgap reference without u...
 
Structural aspect on carbon dioxide capture in nanotubes
Structural aspect on carbon dioxide capture in nanotubesStructural aspect on carbon dioxide capture in nanotubes
Structural aspect on carbon dioxide capture in nanotubes
 
Thesummaryabout fuzzy control parameters selected based on brake driver inten...
Thesummaryabout fuzzy control parameters selected based on brake driver inten...Thesummaryabout fuzzy control parameters selected based on brake driver inten...
Thesummaryabout fuzzy control parameters selected based on brake driver inten...
 

Recently uploaded

Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...
Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...
Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...Alkin Tezuysal
 
Time Series Foundation Models - current state and future directions
Time Series Foundation Models - current state and future directionsTime Series Foundation Models - current state and future directions
Time Series Foundation Models - current state and future directionsNathaniel Shimoni
 
Top 10 Hubspot Development Companies in 2024
Top 10 Hubspot Development Companies in 2024Top 10 Hubspot Development Companies in 2024
Top 10 Hubspot Development Companies in 2024TopCSSGallery
 
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...itnewsafrica
 
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...Nikki Chapple
 
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptxUse of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptxLoriGlavin3
 
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptx
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptxThe Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptx
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptxLoriGlavin3
 
QCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesQCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesBernd Ruecker
 
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security ObservabilityGlenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security Observabilityitnewsafrica
 
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better StrongerModern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better Strongerpanagenda
 
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptxMerck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptxLoriGlavin3
 
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfConnecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfNeo4j
 
React Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkReact Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkPixlogix Infotech
 
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024BookNet Canada
 
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxThe Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxLoriGlavin3
 
Potential of AI (Generative AI) in Business: Learnings and Insights
Potential of AI (Generative AI) in Business: Learnings and InsightsPotential of AI (Generative AI) in Business: Learnings and Insights
Potential of AI (Generative AI) in Business: Learnings and InsightsRavi Sanghani
 
How to write a Business Continuity Plan
How to write a Business Continuity PlanHow to write a Business Continuity Plan
How to write a Business Continuity PlanDatabarracks
 
Moving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdfMoving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdfLoriGlavin3
 
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptx
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptxPasskey Providers and Enabling Portability: FIDO Paris Seminar.pptx
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptxLoriGlavin3
 
Generative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfGenerative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfIngrid Airi González
 

Recently uploaded (20)

Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...
Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...
Unleashing Real-time Insights with ClickHouse_ Navigating the Landscape in 20...
 
Time Series Foundation Models - current state and future directions
Time Series Foundation Models - current state and future directionsTime Series Foundation Models - current state and future directions
Time Series Foundation Models - current state and future directions
 
Top 10 Hubspot Development Companies in 2024
Top 10 Hubspot Development Companies in 2024Top 10 Hubspot Development Companies in 2024
Top 10 Hubspot Development Companies in 2024
 
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...Abdul Kader Baba- Managing Cybersecurity Risks  and Compliance Requirements i...
Abdul Kader Baba- Managing Cybersecurity Risks and Compliance Requirements i...
 
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...
Microsoft 365 Copilot: How to boost your productivity with AI – Part one: Ado...
 
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptxUse of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
Use of FIDO in the Payments and Identity Landscape: FIDO Paris Seminar.pptx
 
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptx
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptxThe Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptx
The Fit for Passkeys for Employee and Consumer Sign-ins: FIDO Paris Seminar.pptx
 
QCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architecturesQCon London: Mastering long-running processes in modern architectures
QCon London: Mastering long-running processes in modern architectures
 
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security ObservabilityGlenn Lazarus- Why Your Observability Strategy Needs Security Observability
Glenn Lazarus- Why Your Observability Strategy Needs Security Observability
 
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better StrongerModern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
 
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptxMerck Moving Beyond Passwords: FIDO Paris Seminar.pptx
Merck Moving Beyond Passwords: FIDO Paris Seminar.pptx
 
Connecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdfConnecting the Dots for Information Discovery.pdf
Connecting the Dots for Information Discovery.pdf
 
React Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkReact Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App Framework
 
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
New from BookNet Canada for 2024: Loan Stars - Tech Forum 2024
 
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptxThe Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
The Role of FIDO in a Cyber Secure Netherlands: FIDO Paris Seminar.pptx
 
Potential of AI (Generative AI) in Business: Learnings and Insights
Potential of AI (Generative AI) in Business: Learnings and InsightsPotential of AI (Generative AI) in Business: Learnings and Insights
Potential of AI (Generative AI) in Business: Learnings and Insights
 
How to write a Business Continuity Plan
How to write a Business Continuity PlanHow to write a Business Continuity Plan
How to write a Business Continuity Plan
 
Moving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdfMoving Beyond Passwords: FIDO Paris Seminar.pdf
Moving Beyond Passwords: FIDO Paris Seminar.pdf
 
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptx
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptxPasskey Providers and Enabling Portability: FIDO Paris Seminar.pptx
Passkey Providers and Enabling Portability: FIDO Paris Seminar.pptx
 
Generative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfGenerative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdf
 

Optimal Inventory Modeling of Income and Loan Elasticity Effects

  • 1. The present paper considers the effect of income and loan elasticity on demand and determines the buyers’ optional special order, quantity as well as the optimal time. When the supplier reduces his sale price, the buyer can offer a discount to push his sale, so as to increase the profit margin. The paper introduces income and loan availability elasticity effect in inventory management. The gain equation has been derived to find out the optimal special order quantity and profit associated with it under two different conditions i.e. when the remnant inventory is zero and when the remnant inventory is finite. . ABSTRACT: An Optimal Inventory Model : Income and Loan Availability Elasticity Dr.J.K.Mantri Deptt of Comp.Application North Orissa University jkmantri@gmail.com Keywords: Elasticity,Inventory model,Profit,Loan 39 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 2. INTRODUCTION The elasticity of demand is an economic terms which refers to the responsiveness of demand to the change in price. When the demand is not elastic, the drastic change in price may not affect the demand, for example a fall in price or rise in price does not change the demand of essential commodities. In case of a fall in price tends to reduce demand and rise in price tends to extend demand. But in case of the articles, which are sensitive to the change in price, the demand increases or decreases, such goods or product are price responsive. The present paper is devoted to introduce a new concept i.e. income and loan availability elasticity vis-à-vis inventory models. Income and loan availability elasticity may be defined as: E1 = Proportionate change in demand / Proportionate change in (income + loan availability). The optional policies for no buyers discount and constant demand are derived in [1]. Optional ordering policies in response to permanent price increase when demand is assumed to be constant have been well documented by [2], [3], [4] and [5]. A model to determine the optional ordering policies for a finite horizon consisting of two distinct time intervals characterized by different inventory parameters is presented by [6]. Models which determine the optimal special order quantity when supplier reduces his price temporarily, assume that the reduced price is in effect buyer’s replenishment time and the demand rate remains constant [1], [7] and [8]. In most cases a price discount results in an increase in demand. Ardalan [9] relaxes demand assumption made in most inventory system with price change. Ardalan[9] presents a procedure to include any relationship between price and demand to determine the combined to optimal price and optimal order quantity. The present paper considers the effect of income and loan availability elasticity on demand and determines the buyer’s optimal special order quantity and optimal time. When supplier reduces the price temporarily, the buyer may offer a discount to his customers to push his sale and increase his profit margin. This paper brings in to picture income and loan availability demand relationship, which deals with classification of products into essential and non-essential goods. For non-essential goods like Luxuries the 40 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 3. income and loan availability demand relationship is considerable. We introduce the income and loan availability elasticity effect in to inventory analysis and obtain the gain equation to find optimal special order quantity under two conditions i.e. when there is finite remnant inventory and when it is zero. We also determine optimal time for placing order quantity when there is finite remnant inventory and extend it to find the optimal time for placing such an order. We further modify our model to find cost of saving of special purchase when supplier announces to increase his sale price by some amount from a specified date. Finally an optimal ordering policy is determined to get profit maximization. MODEL ASSUMPTIONS The present paper consider the effect of income and loan availability elasticity because of the fact that in the current liberalized market and consumerism, the financial institutions are very much liberal in financing consumer loans at very low percentage of interest, the low rate loan availability can be considered as an aid to buying capacity so we find a heavy demand on non essential goods such as luxury items Automobiles, Ornaments etc. As for example this above effect has an impact not only on the “Growth Rates of Industrial production of India but also on the globalization of Indian economy”. The structure of interest (loan) rates and the growth rates of industrial production in India are cited in Table (1). The models developed in this paper has taken care of the simultaneous effect of income change and; loan facilities on classical inventory models. This concept has very much importance to the stockiest to go for a better margin of profit and improvement in their sale. If E1 is the income and loan availability Elasticity, then from its definition. E1 = Proportionate change in demand/ Proportionate change in (Income + loan availability) D = Buyer ‘s annual demand; D1 = Buyer’s annual demand after discount to customer. D2 =Buyer’s new annual demand after the effect of income and loan availability elasticity. Thus, New annual demand = Old demand (Change in income + loan availability) 41 Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 4. D2 = D1 + (E1 × proportionate change in (income + Loan availability) /100) D1 D2 = D1 [1+ E1 × proportionate change in (income + Loan availability) /100] D2 = D1 (1+Y+L) where L = (E1 × proportionate change in loan availability /100) Where Y = (E1 × proportionate change in income/100) (1) P = Suppliers regular price per unit; P1 = Buyer’s regular price per unit; P2 = Buyer’s sale (reduced) price per unit; C = ordering cost per order, H = PF = Holding cost per unit per year; F = Annual holding cost as a fraction of unit cost (carry cost parameters); E.O.Q. = the size of an order that minimizes the total inventory cost is known as economic order quantity. Q = Lot size or order quantity in units (a special order quantity); Tc = Total annual cost Qr = Regular optimal order quantity = √(2CD/PF) (2) Further if, ‘d’ is the amount which supplier offers on his sale price and Qd is regular optimal order quantity using the reduced price. If income and loan availability elasticity effect is there, then Qd = [2D2 C/(p-d) F] ½ = [2D1 (1+Y+L) C/(P – d) F] ½ (3) If however the income and loan availability elasticity effect is not there then Y = 0; Qd = [2D1C/(P – d) F] ½ (4) Q0 = Special optimal order quantity when remnant inventory is zero. Qq = Special optimal order quantity when remnant inventory is not zero. Gr = Gain associated with regular policy during Ts; Gs = Gain associated with special order during TS . TS = The time interval between the time the buyer receives the special order of size “Q” and his next replenishment time. 42 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 5. Optimal Special Order Quantity when Remnant Inventory is zero and effect of income and loan Availability Elasticity is significant. Suppose D2 is the buyer’s new annual demand after change in income and loan availability elasticity of the customer. At replenishment time buyer places an order of Q units at reduced price (offered by supplier). So the buyer too offers a discount to his customers on all the Q units. TS is the time interval after which the suppliers reduced price is not available and buyer reverts to his usual ordering policy. Now the gain associated within the time interval TS Gs = [P2 – (P-d)] Q – [Q2 (P – d) F]/[2D1 (1+Y+L)] –C (5) If suppliers reduced price and buyers discount were permanent then classical inventory formula of E.O.Q could be used to determine optimal order quantity. As a result these are temporary business manoeuvirs and so this cannot be used, but these can be taken as rudimentary tool to obtain optimal policy for special order Qd. If ‘d’ be the discount offered on Qd units then purchase cost of these Qd units would be (P – d) Qd. The number of units bought at usual regular price during Ts = [D/D1 (1+Y+L)](Q – Qd) (6) Therefore, the total buying cost is (P – d) Qd+[PD/D1 (1+Y+L)](Q-Qd) (7) The holding cost of the first order is Qd2 (P-d) F/2D1 (1+Y+L) (8) The holding cost during the rest of Ts is [Qr(Q-Qd)PF]/[2D1 (1+Y+L)] (9) The total holding cost during Ts is [Qd2 (P-d) F]/[2D1(1+Y+L)]+[Qr(Q-Qd)PF]/[2D1 (1+Y+L)] (10) The number of orders placed during Ts is (1+D (Q-Qd)/D1 (1+Y+L) Qr] (11) The ordering cost associated with this order will be given by C[1+D(Q-Qd)/D1 (1+Y+L)Qr] (12) 43 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 6. The gain associated with the usual (regular) ordering policy during Ts is given by: Gr=[P2 –(P-d)]Qd+(P1-P)D(Q-Qd)/D1 (1+Y+L)-(P-d)FQd2 /2D1 (1+Y+L) -Qr(Q-Qd)PF/2D1(1+Y+L)-C[1+D(Q-Qd)/D1(1+Y+L)Qr] (13) In order to maximize gain the difference between Gr and Gs should be maximized. G = [P2 –(P-d)] Q-Q2 (P-d) F/2D1(1+Y+L)-C -[P2 (P-d)]Qd-(P1-P)D(Q-Qd)/D1 (1+Y+L)+(P-d)F Qd2 /2D1(1+Y+L) +Qr(Q-Qd)PF/2D1(1+Y+L)+C[1+D(Q-Qd)/D1 (1+Y+L)Qr] (14) Differentiating G with respect to Q and equating dG/dQ = 0, we get Q0 = [D1 (1+Y+L) (P2 -P+d)-(P1 -P) D]/[(P-d) F]+[Qr P/(P-d)] Putting Q0 in Equation (14) to get the optimal value of G = C (Q0- Qd) 2 /Qd2 Optimal Special Order Quantity when Remnant Inventory is not zero and Effect of Income and Loan Availability Elasticity are significant. If effect of income and loan availability elasticity is considerable and there is sufficient remnant inventory, then buyer has two options either to buy at the reduced price of supplier and subsequently offer discount to his customer or just avoid the business ploy and follow his usual optimal order policy. If ‘q’ be the level of remnant inventory then to determine special order quantity the difference between Gr and Gs should be maximized. If per capita income rised and loan availability rises increase in purchasing power of customer, the gain associated with special order quantity (Gs) and gain associated with usual ordering policy (Gr) is expressed as - Gs=Q(P2–P+d)–q2 PF/2D–qQ(P-d)F/D-[(p-d)FQ2 ]/[2D1 (1+Y+L)]–C (15) Gr=[DQ(P1 -P)/D1(1+Y+L)-(q2 PF/2D)] -(QrQPF/2D1(1+Y+L)]-[DQC/D1 (1+Y+L)Qr] (16) The increase in gain due to special order is G = Gs – Gr. G=Q(P2-P+d)-q2 PF/2D-qQ(p-d)F/D-(p-d)FQ2 /2D1 (1+Y+L)-C –DQ(P1 -P)/D1(1+Y+L)+q2 PF/2D+QrQPF/2D1(1+Y+L)+DQC/D1 (1+Y+L)Qr (17) 44 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 7. To maximize profit differentiating G with respect to Q and equating dG/dQ = 0 ⇒Qq=[(P2 -P+d)D1(1+Y+L)-D(P1-P)]/[(P-d)F] +QrP/(P-d)-qD1(1+Y+L)/D (18) ⇒Qq=Qo-[qD1 (1+Y+L)/D] (19) To determine the optimal time for placing special order Qq, a theorem is deduced: - Theorem – 1. Higher the income and loan availability elasticity smaller the level of remnant inventory and it determines the optimal time for placing optimal special order. Proof : When remnant inventory is ‘q’ the special order quantity is ‘Qq’ When remnant inventory is ‘q-1 ’ the optimal order is given by Qq+D1 (1+Y+L)/D. If Ei is income and loan availability elasticity then new demand due to it is D2 given by D2 = D1(1+Y+L). Using the gain equation 17, putting Q=Qq when remnant inventory is q units and gain G as Gq and Q = Qq -1 when remnant inventory is (q-1) units and gain G as Gq -1 . Where Qq -1 = Qq+[D1(1+Y+L)/D] Equation 17 ⇒ Gq= Qq(P2-P+d) –qQq(P-d)F/D - (P-d)FQq2 /2D1 (1+Y+L) –C-DQq(P1-P) /D1(1+Y+L)+QrQqPF/2D1(1+Y+L)+DQqC/D1(1+Y+L)Qr (20) For remnant inventory (Qq-1) Equation 17 ⇒ Gq -1 = Qq -1 (P2 -P+d)-(q-1)Qq -1 (P-d)F/D- (p-d)F(Qq-1)2 /2D1 (1+Y+L) +QrQq -1 PF/2D1 (1+Y+L)+DQq -1 C/D1 (1+Y+L)Qr - DQq (P1-P)/D1 (1+Y+L) -C (21) Here we need to Prove Gq-1 > Gq i.e. Gq -1 –Gq = positive. Gq -1 –Gq = D1(1+Y+L) (P2 -P+d)/D-D1 (1+Y+L)q (P-d)F/D2 +D1(1+Y+L)(P-d)F/2D2 -P1+P+QrPF/2D+C/Qr (22) Using equation (18) in equation (22) we get [Gq -1 –Gq ][D/(P-d)F]=Qq+D1(1+Y+L)/2D (23) Which is a positive value, this proves the theorem. (Proved) 45 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 8. Theorem –2 Higher the income and loan availability elasticity larger the level of remnant inventory and higher is the cost of saving when price rise is imminent. Proof: If the supplier changes his sale policy and he stops the discount given to customer and announces a new increased sale price. Let P be the amount by which supplier tends to increase his sale price at some date ti. The units purchased before ti will cost ‘p’ but purchase after ti will cost (P+p). If D be the annual demand and Ei be the income and loan availability elasticity and ‘q’ be level of remnant inventory. New demand due to income and loan availability elasticity = Old demand +change in demand D * =D(1+Y+L) (24) The optimal order quantity before price increase Qr=(2CD*/PF) ½ =[2CD(1+Y+L)/PF] ½ (25) The optimal order quantity after the price rise will be: Qr*=[2CD*/(P+p)F]½=[2CD(1+Y+L)/(P+p)F] ½ (26) To obtain optimal special order size, it is necessary to maximize the cost difference during td – tr with and without special time order. Total cost = Purchased cost+ Holding cost + Ordering cost Tcr=PQs+[QsPFq/D(1+Y+L)]+Qs2 PF/2D(1+Y+L)]+[q2 PF/2D(1+Y+L)]+C (27) If no special order is placed prior to ti the total cost of the system during tr to td when several purchases of Qr* are made at new price (P+p) Tcs =(P+p)Qs+ (Qr* /2)(P+p)F(Qs/D*)+(q/2)PF(q/D*)+(Qs/Qr*)C Using equation (24) and Equation (26) Tcs = (P+p)Qs+( ½) [2CD(1+Y+L)/(P+p)F] ½ (P+p) F[Qs/D(1+Y+L)]+q2 PF/2D(1+Y+L)+(Qs/Qr*)C (28) To find the optimal order size the difference between Tcr and Tcs should be minimized G = Tcs-Tcr ⇒G=Qs[p+C[F(P+p)/2D(1+Y+L)]½ -PFq/D(1+Y+L)- [PFQs2 /2D(1+Y+L)]-C (29) 46 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 9. Differentiating with respect to Qs and putting dG/dQs = 0, we get optimal special order quantity Qso. Qso=Qr*/2+p/2PF[2D(1+Y+L)+Qr*F]-q (30) This is optimal special order size, putting equation 30 in equation 29 we get the optimal cost of saving associated with Qso G⇒Qso[p+[CF+(P+p)/2D(1+Y+L)]1/2 –PFq/D(1+Y+L)]- PFQso2 /2D(1+Y+L)]-C Theorem 3: If tf <tr the optimal ordering policy is (i) To order Qq at ‘tf’ if Qq > Qd otherwise (ii) Order Qr at ‘tr’ Proof: The value of the remnant inventory Qr for which Gr and Gs are equal can be determined by equating equation 15 and 16. Q(P2 -p+d)-q2 PF/2D-qQ(P-d)F/D-[(P-d)FQ2 ]/[2D1 (1+Y+L)]-C =[DQ(P1 -P)/D1(1+Y+L)]-[q2 PF/2D]-[QrQPF/2D1(1+Y+L)]-[DQC/D1(1+Y+L)Qr] Simplifying and putting Q=Qq and q=qc using equation (18) we get Qq/2=Qd2 /2Qq=Qq2 =Qd2 (31) Since Gs> Gr for any Qq> Qd as long as Equation 31 holds good and optimal order size Qq at ‘tf’ would maximize the gain. Otherwise the usual (regular) ordering policy will be optimal. 47 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 10. Conclusions When a supplier reduces his sale price temporarily, then buyer might follow a policy which increases his demand. However due to income and loan availability elasticity effect, the change in demand may be much greater than expected. In fact income and elasticity brings product classification, which is an important economic consideration. The mathematical treatment of influence of income elasticity of a buyer’s policy is discussed. We determine the case of finding optimal order quantity and profit when supplier reduced his sale price in both situation i.e. with/without remnant inventory. The special cost of saving is determined when rise in price is imminent and finally ordering policy is discussed. 48 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org
  • 11. REFERENCES 1. Ardalan A. 1967, “Optimal Ordering Policies in Response to sale” IIE Trans. 20 192-194 2. Ardalan A, 1991 “Combined Optimal Price and Optimal inventory Replenishment Policies When a Sale Results in increase in Demand” Computers Ops. , Res. Vol.18, No. 18. 3. Bhandari M.R. and Sharma P.K., 1998, ‘Journal of public Budgeting, Accounting and financial Management”, Spring, Volume X. 4. Brown R.G., “Decision Rules for inventory Management” Holt, Reinchart & Winston, pp. 21-203, New York. 5. Carlsson C.and Fuller Rs., 1995, “Multiple Criteria Decision Making the Case for interdependence” Computers Ops. Rs. Vol22,No.3. 6. Dewett K.K and Chand, A., 1996 “Modern Economic Theory” S. Chand. 7. Lev. B. et a, 1981 “Optimal Ordering policies when Anticipating parameter changes in ECQ systems” Res. Logist Q. 8. Naddor, E., 1996, “ Inventory System”, Wiley, New York. 9. Petterson, R. and Silver, E.A., “Decision system for inventory Management and Production Planning” Wiley, New York. 10. 10.Raman, A. and Fisher, M., 1996 “Reading the cost of demand Uncertainty Through Accurate Response to Early Sales” Os. Res. Vol. 44, No.1. 11. Song, J.H. and Zipkin, 1993 “ Inventory Control in Fluctuating Demand Environment” Ops, Res., Vol.41, No.2. 12. Taylor S.H. and Bradley, C.E., 1985, “ Optimal Ordering Strategies for Announced Price Increase” Ops., Res. 13. Tersine R.J. (ed), 1998, “Principles of Inventory and Materials Management” North Holland, New York. 14. Tersine, R.J. and Grasso, E.T., 1998, “ Forward Buying in Response to Announced Price Increase” J. Purchase, Mater Mgmt. 49 | Page International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 3 Î July 2013 Î PP.39-49 www.ijres.org