Fuzzy EOQ model for deteriorating items with price dependent demand and time-varying holding cost

In this paper, a fuzzy economic order quantity (EOQ) model is formulated for single deteriorating item considering price dependent demand and time dependent holding cost. Shortages are allowed and partially backlogged with a variable rate dependent on the length of the waiting time for the next replenishment. For the Fuzzification of model, the demand, holding cost, unit purchase cost, deterioration rate, ordering cost, shortage cost and cost of lost sale are assumed to be trapezoidal fuzzy numbers. As a result, the profit function will be derived in fuzzy sense in order to obtain the optimal cycle length and the selling price. The graded mean integration method is used to defuzzify the profit function. Then, to illustrate the model as well as to test the validity of the model a numerical example is considered and solved. Finally, to study the effect of changes of different parameters on the average profit, order quantity, cycle length and selling price, sensitivity analysis are performed.