A three rates of EOQ/EPQ Model for Instantaneous Deteriorating Items Involving Fuzzy Parameter Under Shortages

Abstract

This paper emphasizes on developing both crisp and fuzzy (Economic ordered quantity (EOQ)/Economic production quantity(EPQ)) single commodity models with a three rates of production inventory for deteriorating items in which the demand rate is a function of both advertisement and selling price. The objective of the crisp model is to determine the optimum values of advertising cost, cycle time and selling price with the aim of maximizing the total profit. Again, in the fuzzy inventory model, fuzziness is introduced for the price rate, Triangular fuzzy number is considered to represent the fuzziness of the price rate and the total profit function is defuzzified by using the signed distance method. We develop some useful theorems for each type of models to establish the formulas for advertising cost, selling price, replenishment schedule and optimal order quantity and algorithm is designed to find the optimum solutions of both the model. Numerical examples are provided for both the models and sensitivity analyses are conducted to know the effect of changes made the values of different parameters.