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An EOQ model for perishable products with discounted selling price and stock dependent demand

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Abstract

A single item economic order quantity model is considered in which the demand is stock dependent. After a certain time the product starts to deteriorate and due to visualization effect and other aspects of deterioration the demand becomes constant. In that situation a discount on selling price provides significant increment in demand rate. In this paper we investigate how much discount on selling price may be given during deterioration to maximize the profit per unit time and whether a pre-deterioration discount affects the unit profit or not. A mathematical model is developed incorporating both pre- and post deterioration discounts on unit selling price, where analytical results reveal some important characteristics of discount structure. A numerical example is presented and sensitivity analysis of the model is carried out.

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Abbreviations

C 0 :

set up cost

S :

constant selling price of the product per unit

r 1 :

discount offer per unit before deterioration

r 2 :

discount offer per unit after deterioration

h :

holding cost per unit per unit time

d :

disposal cost per unit

c :

per unit purchase cost of the product

Q 1 :

order level for pre- and post deterioration discount on selling price

Q 2 :

order level for only post deterioration discount on selling price

Q 3 :

order level for no discount on selling price

Q 4 :

order level for post deterioration discount on selling price with instant deterioration

Q 41 :

order level for no discount on selling price with instant deterioration

Q 5 :

order level for pre-deterioration discount on selling price for fixed life time product

Q 51 :

order level for no discount on selling price for fixed life time product

T 1 :

cycle length for pre- and post deterioration discount on selling price

T 2 :

cycle length for only post deterioration discount on selling price

T 3 :

cycle length for no discount on selling price

T 4 :

cycle length for post deterioration discount on selling price with instant deterioration

T 41 :

cycle length for no discount on selling price with instant deterioration

T 5 :

cycle length for post deterioration discount on selling price for fixed life time product

T 51 :

cycle length for post deterioration discount on selling price for fixed life time product

t 1 :

a decision variable representing the time from which pre-deterioration discount starts

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Authors and Affiliations

  1. Department of Mathematics, Bengal Institute of Technology, 1.no. Govt. Colony, Kolkata, 700150, West Bengal, India

    S. Panda

  2. Department of Mathematics, University of Kalyani, Kalyani, 741235, West Bengal, India

    S. Saha & M. Basu

Authors
  1. S. Panda
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  2. S. Saha
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  3. M. Basu
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Correspondence to S. Panda.

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Panda, S., Saha, S. & Basu, M. An EOQ model for perishable products with discounted selling price and stock dependent demand. Cent Eur J Oper Res 17, 31–53 (2009). https://doi.org/10.1007/s10100-008-0073-z

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