An EOQ Model for Deteriorating Items with Fuzzy Demand and Fuzzy Partial Backlogging

Abstract

In this paper we have developed a continuous review inventory model for deteriorating items with time dependent demand rate. Deterioration rate is increasing with time. Each cycle has shortages, which have been partially backlogged. The backlogging rate is taken to be inversely proportional to the waiting time for the next replenishment. Fuzziness is introduced by considering demand rate and partial backlogging parameter to be fuzzy numbers . The maximum total profit and optimal order quantity are derived by defuzzifying the total profit through the signed distance method. Finally, the crisp model and fuzzy model are illustrated with the help of numerical example. A sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the fuzzy model.