Fuzzy Random EOQ Model with Defective Items and Shortages

This paper develops an economic order quantity (EOQ) model for the inventory decision problem with defective items and shortages in fuzzy random environment. It is assumed that the percentage of defective items is a random variable, and the defective items contain imperfect-quality items and scrap items, but the rate of scrap items in defective items is a fuzzy variable. Also the holding cost and backorder cost are characterized as fuzzy variables since they are hard to express accurately. Then a mathematic formulation about the expected average profit is presented, and the concave property of the objective function is analyzed for obtaining the closed-form solutions. Finally, the sensitivities to parameters are discussed and an illustrated numerical example is presented.