A Fuzzy Two-Echelon Supply Chain Model for Deteriorating Items with Time Varying Holding Cost Involving Lead Time as a Decision Variable

Abstract

In this paper, we have developed a two-stage supply chain production-inventory model for deteriorating product with time-dependent demand under fuzzy environment. Here we describe an EOQ model with changeable lead time and time-dependent holding cost. This situation is very common in the market, once an enterprise has some key technology or product that others have not, as a supplier, it can decide the prices and lead time of the technology or product to the buyers or retailers according to its need. Then the retailer determines his optimal order strategy, i.e., decides on the quantity of products to order from the suppliers. Under this circumstance, the problem that lead time, as a controllable variable of the supplier, and how it affects the cost to the supplier, retailer and whole supply chain is very important to the supplier and retailer because double-win benefits is a base of existence for the supply chain. In reality it is seen that we cannot define all parameters precisely due to imprecision or uncertainty in the environment. So we have defined the inventory parameters, such as set up cost, stock-out cost, and deterioration cost as triangular fuzzy numbers. The signed distance method and graded mean integration method have been used for defuzzification. To illustrate the proposed model a numerical example and sensitivity analysis with respect to different associated parameters has been presented.