The Minimax Distribution Free Procedure for an Inventory Model in Mixed Fuzzy and Stochastic Environment

This paper investigates the mixture inventory control system in which the lead time demand is a random variable with general distribution, and the defective rate of the arrived order lot is also a random variables. Furthermore, the backorder rate, setup cost, shortage penalty cost and marginal profit per unit in different cycles are iid fuzzy variables, respectively. In addition, a mathematic formulation about the expected annual total cost is presented. And then some useful properties are analyzed for establishing an efficient solution procedure. In order to search the optimal solution of the model, an iterative algorithm are designed. Finally, a numerical example is given to illustrate the procedure of searching the optimal solution.