A fuzzy imperfect quality inventory model with proportionate discount under learning effect

Abstract

The present article establishes both crisp and fuzzy economic order quantity (EOQ) models with proportionate discount for items with imperfect quality under learning effect in a finite time horizon. The objective of the crisp model is to determine the optimal order lot size to maximise the total profit where the demand rate is constant and the defective items follow a learning curve. Then, we discussed on two different cases of fuzzy inventory models. Case-1: Defective rate follows a learning curve and the demand rate assumed to be a triangular fuzzy number. Case-2: Defective rate, fixed ordering cost and holding cost follow the learning curve and the demand rate taken to be a triangular fuzzy number. The objective of the fuzzy models is to estimate the maximum total profit per unit time in fuzzy sense and then to derive formula of the optimal lot size for each case and the corresponding total profit functions are defuzzified by using signed distance method. Numerical examples are provided to demonstrate the developed models. Sensitivity analysis is conducted both for crisp and fuzzy models to examine the effect of number of shipments on the order quantity and total profits under various conditions.