Inventory Policy with Stock, Price and Credit-Linked Demand: A Fuzzy Genetic Algorithm Approach

Inventory Policy with Stock, Price and Credit-Linked Demand: A Fuzzy Genetic Algorithm Approach

Partha Guchhait (Vidyasagar University, India), Pravash Kumar Giri (Vidyasagar University, India), Manas Kumar Maiti (Mahishadal Raj College, India) and Manoranjan Maiti (Vidyasagar University, India)
Copyright: © 2012 |Pages: 19
DOI: 10.4018/jsds.2012040104
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Abstract

An inventory control problem under two-level trade-credit policy with fuzzy inventory costs is proposed where supplier provides not only a credit-period for settling account but also a cash discount to the retailers. Due to this advantage the retailer also offers a fixed credit period to all its customers to boost the demand. Demand also depends on stock and selling price. A Genetic Algorithm (GA) with chromosome’s life-time dependent varying population size is used to solve the model where, at the time of generation of initial population, diversity in the population is maintained using information entropy theory. In the algorithm crossover probability of a pair of parents is a function of their age-type (young, middle-aged, old, etc.) and is obtained using a fuzzy rule base and possibility theory. A fuzzy possibility/necessity based evolution process is proposed to deal with fuzzy objective function.
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1. Introduction

In the last two decades, the models for inventory replenishment policies under the trade credit have been widely studied by several researchers. However the extant papers tacitly assumed that the supplier allows a certain fixed credit period to settle the account for stimulating retailer’s demand. During this credit period the retailer can start to accumulate revenues on the sales and earn interest on that revenue, but beyond this period the supplier charges interest. Hence, paying later indirectly reduces the cost of holding stock. On the other hand, trade credit offered by the supplier encourages the retailer to buy more and it is also a powerful promotional tool that attracts new customers, who consider it as an alternative incentive policy to quantity discounts. Owing to this fact, during the past few years, many articles dealing with various inventory models under trade credit have appeared in various research journals (Goyal, 1985; Aggarwal & Jaggi, 1995; Chang et al., 2001; Dye, 2002; Chang et al., 2004; Goyal et al., 2007; Valliathal & Uthayakumar, 2010; Jaggi & Kausar, 2010, 2011; Jaggi & Goel, 2011).

All the aforementioned inventory models implicitly assumed that the customer would pay for the items as soon as the items are received from the retailer. But, in most business transactions, this assumption is unrealistic and usually the supplier offers a credit period to the retailer and the retailer, in turn, passes on this credit period to his/her customers. Huang (2007) presented an inventory model assuming that the retailer also offers a credit period to his/her customer which is shorter than the credit period offered by the supplier, in order to stimulate the demand. Jaggi et al. (2008) developed an inventory model incorporating credit-linked demand under permissible delay in payments. Recently, Mahata and Mahata (2011) published an inventory model for deteriorating item under retailer’s partial trade credit Policy. But none has considered inventory model incorporating the influence of credit period, stock level and selling price together on demand. Though impact of any one of these factors on demand have been studied by several researchers (Chang et al., 2001; Dye, 2002; Huang, 2007; Jaggi, 2008; Chen, 2009; Khanra et al., 2010). Again in some situations, the supplier also offers a cash discount to encourage retailer to pay for his purchase quickly (Ouyang, 2005).

In recent years inventory control problems are rapidly developing in fuzzy environment (Cassone, 2010; Saha & Soni, 2011; Valliathal & Uthayakumar, 2011). One should estimate the parameters as stochastic when sufficient past data are available. But in the case when sufficient past data are not available, estimation of fuzzy parameters are done by expert’s opinion. So when past data is insufficient one has to depend on fuzzy parameters.

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