An Optimal Inventory Model for a Retailer with Price Dependent Demand and Unavailability Supply
Today many retailers face high competition, therefore they have to operate in an efficient way. One aspect of efficiency is inventory. Many research on inventory is conducted intensively to get more realistic inventory model. In this paper, an inventory model was developed by considering pricing. Many retailers try to increase their profit by setting the best price for a single item, especially for some items that have high price-dependent demand. The customer demand depends on the price such household items. In the other side, some retailers face supply problems. Supplier often cannot supply products when the products needed on time. There is delay time between customer demand and products arrive at retailer warehouse. The retailer should determine the optimal price and replenishment time. There are some assumptions are used for the model. The first assumption, the demand is known and has constant elasticity. Second, there is stochastic replenishment period and demand that are not filled are lost sales. The model is developed mathematically and a numerical example is conducted to show how the model works. A sensitivity analysis is accomplished to get some management insight and some interesting result are derived.
Keywords: deteriorating inventory model; genetic algorithm; stochastic time
 Teng JT, Chang CT. Economic production quantity models for deteriorating items with price- and stock-dependent demand. Computers & Operations Research 2005; 32(2):297–308. https://www.sciencedirect.com/science/article/abs/pii/S0305054803002375
 Das D, Roy A, Kar S. Improving production policy for deteriorating item under permissible delay in payments with stock-dependent demand rate. Computers and Mathematics with Applications 2010; 60(7):1973–1985. https://www.sciencedirect.com/science/article/pii/S0898122110005237
 Teng JT, Cardenas-Barron LE, Chang HJ, Wu J, Hu Y. Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Applied Mathematical Modelling 2016; 40(19–20):8605– 8616. https://www.sciencedirect.com/science/article/abs/pii/S0307904X16302724
 Banerjee S, Agrawal S. Inventory model for deteriorating items with freshness and price dependent demand: Optimal discounting and ordering policies. Applied Mathematical Modelling 2017; 52:53–64. https://www.sciencedirect.com/science/article/abs/pii/S0307904X17304584
 Tiwari S, Cardenas-Baron LE, Goh M, Shaikh AA. Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. International Journal of Production Economics 2018; 200:16–36. https://www.sciencedirect.com/science/article/abs/pii/S0925527318301233
 Liuxin C, Xian C, Keblis FM, Gen L. Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand. Computers & Industrial Engineering 2019; 135:1294–1299. https://www.sciencedirect.com/science/article/abs/pii/ S0360835218302778
 Duan Y, Cao Y, Huo J. Optimal pricing, production, and inventory for deteriorating items under demand uncertainty: The finite horizon case. Applied Mathematical Modelling 2018; 58:331–348. https://www.sciencedirect.com/science/article/abs/pii/S0307904X1830074X
 Hsieh TP, Dye CY. Pricing and lot-sizing policies for deteriorating items with partial backlogging under inflation. Expert Systems with Applications 2010; 37(10):7234–7242. https://www.sciencedirect.com/ science/article/pii/S0957417410002757
 Yang PC. Pricing strategy for deteriorating items using quantity discount when demand is price sensitive. European Journal of Operational Research 2004; 157(2):389–397.
 San-Jose LA, Sicilia J, Alcaide-Lopez-de-Pablo D. An inventory system with demand dependent both time and price assuming backlogged shortages. European Journal of operational Research 2018; 270(3):889–897. https://www.sciencedirect.com/science/article/abs/pii/S0377221717309554