An EOQ model with defective items and shortages in fuzzy sets environment

Abstract

The basic assumption of the classical inventory (EOQ/EPQ) models is that %100 of items ordered/produced are perfect. However, in most of the production processes, it is unavoidable that the items ordered or produced are defective. This study developes a fuzzy economic order quantity model with defective items and shortages. In this model, the demand, defective rate, ordering cost, unit cost, disposal cost,  holding cost, backordering cost and screening cost are expressed as trapezoidal and triangular fuzzy numbers. Moreover, the Graded Mean Integration Representation method is applied to defuzzify the total profit function in fuzzy sense, and then the optimal policy for the model is determined. The results between crisp case and fuzzy case are compared with the help of numerical examples. Finally, sensitivity analysis is carried out to find the effect of changes in the values of selling prices of good-and imperfect quality items, screening rate and percentage of scrap items on optimal solutions. 

Keywords

• Economic Order Quantity,Defective Items,Backorder,Graded Mean Integration Representation Method,Trapezoidal/Triangular Fuzzy Numbers