A Fuzzy Inventory Model for Weibull Deteriorating Items with Price-Dependent Demand and Shortages under Permissible Delay in Payment

1. Introduction

Demand is always one of the most influential factors in the decision making relating to inventory policy. In the existing literature of inventory control theory, it is observed that various forms of demand (like constant demand, price dependent demand etc.) have been studied by several researchers. In this connection, one may refer to the works of constant demand (Padmanabhan & Vrat, 1990), price dependent demand (Abad, 1996, 2001), time dependent demand (Sachan, 1984), and time and price dependent demand (Wee, 1995). Inventory model for ameliorating items for price dependent demand rate was proposed by (Mondal et al., 2003) and inventory model with price and time dependent demand was developed by (You, 2005). Covert and Philip (1973) developed an inventory model for deteriorating items with Weibull distribution by using two parameters.

In the most of business communications, the supplier allows a specific credit period to the retailer for payment without penalty in order to stimulate the demand of his products. Before the end of the trade credit period, the retailer can sell all the goods and accumulate revenue and earn interest. A higher rate of interest is charged if the payment is not settled by the end of the trade credit period. Goyal (1985) formulated an EOQ model under some conditions of permissible delay in payment. Hwang and Shinn (1997) determined lot-sizing policy for exponential demand when delay in payment is permissible. Aggarwal and Jaggi (1995) developed an ordering policy for deteriorating items under the condition of permissible delay in payment without shortages after that Jamal et al. (1997) extended their model with the consideration of shortages. Jaggi et al. (2008) determined a retailer’s optimal replenishment decisions with trade credit-linked demand under permissible delay in payments. Soni et al. (2010) summarized the work on permissible delay in payment. Recently, Tripathi and Misra (2010) developed EOQ model credit financing in economic ordering policies of non- deteriorating items with time- dependent demand rate in the presence of trade credit using a discounted cash-flow (DCF) approach.