Optimal Integrated Inventory Policy for Deteriorating Units Under Selling-Price-Dependent Demand When Holding Cost Is Capacity-Utilization Dependent

Optimal Integrated Inventory Policy for Deteriorating Units Under Selling-Price-Dependent Demand When Holding Cost Is Capacity-Utilization Dependent

Ishaben Talati (Pandit Deendayal Petroleum University, India) and Poonam Prakash Mishra (Pandit Deendayal Petroleum University, India)
DOI: 10.4018/978-1-5225-3232-3.ch005

Abstract

Conventional EOQ models always discussed profit maximization for one player at a time. But modern approach of supply chain suggests that growing and sustainable supply chain is possible only when benefits of all members of chain are protected. This chapter proposes an integrated model of supply chain where units in inventory are subjected to time dependent deterioration. Since demand is inversely proportional to selling price of the item, it is assumed selling price dependent. To make it more practical and feasible permissible delay on payments is offered only on purchase of a certain amount of quantity. This chapter helps to offer an algorithm to attain optimal number of orders, quantity, selling price and trade credit to maximize the joint profit of supply chain. Isolated profit of supply chain is compared with overall system profit. Results are validated by numerical examples and further sensitivity analyses of important parameters are discussed. Conclusion obtained from the chapter is useful to supply chains involved with FMCGs, Drugs, Fashion goods and home decor textile.
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Introduction

Conventional inventory models focuses on profit of one player at a time. They also consider settlement of accounts as early as lot is received. These assumptions are not practical so, as trade credit offered by manufacturer to retailer increases demand as well as reduces inventory carrying cost of manufacturer. On the other hand integrated models helps to attain a long term sustainable relationship. Researchers have studied and offered different models under trade credit since some years. Goyal (1977) proposed an integrated model. Later Banerjee (1986) extended Goyal’s work for an EOQ model. Goyal & Gupta (1989) discussed integrated inventory models with buyer – vendor coordination to attain joint profit. Further Hu (2011) discussed an integrated model for price-and-credit-linked demand, Giri & Maiti (2013) extended for two level trade credit. Shah (2015) extended with profit sharing contract. Shah et al. (2014) discussed integrated model for price sensitive demand.

Goyal (1985) proposes an EOQ model with trade credit for constant time. Kouja & Mehrez (1996) developed the inventory policies for lot size dependent trade credit. Shinn & Hwang (2003) developed for retailer. Chang et al. (2004) extended the above model with subject to deterioration. Jaggi et al. (2008) developed for retailer subject to replenishment decisions. Shah et al. (2010) gave an up to date review of trade credit. The research articles by Annadurai (2013), Ouyang et al. (2013), Daniel et al. (2013), Shah et al. (2015) discussed different inventory models with order quantity linked trade credit.

On the other hand, in the classical inventory models the replenishment rate or production rate is often assumed to be constant. However, it has been observed that the production rate is flexible in many practical situations. Silver (1990) discussed the effects of slowing down production rate in saving potential costs under controllable production rates. Bhunia & Maiti (1997) presented two inventory models in which the production rate depends upon the on-hand inventory for the first model and upon the demand for the second one. Manna & Chaudhuri (2001) discussed an EOQ model with deteriorating items in which the production rate is proportional to the time dependent demand rate. Chang et al. (2009) discussed it for integrated inventory. Shah et al. (2013) took production rate is Price Sensitive Stock-Dependent Demand; Shah et al. (2013) extended it for deteriorating units.

A number of authors have derived the EOQ formula for special distributions of deteriorating items, where deterioration is defined as decay, damage or spoilage that prevents the item from being used for its original purpose. Ghare & Schrader (1963) assumed a constant rate of deterioration. Richard et al (1973) formulated model for Weibull distribution. Further Philip (1973) generalized that model. Goyal & Giri (2001) gave review on deteriorating items. It’s extended by Bakker et al. (2012) and then by Janssen et al. (2016).

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