Fuzzy production inventory model for deteriorating items with shortages under the effect of time dependent learning and forgetting: a possibility / necessity approach

Abstract

This study investigates the effects of learning and forgetting on the production lot size problems allowing shortages for the infinite planning horizon. Items deteriorate while they are in storage, and both demand and deterioration rates are arbitrary function of time. This paper extends the work of Alamri and Balkhi (Int. J. Prod. Econ. 107:125–138, 2007) by assuming the shortages in production lot size model subject to the effects of learning and forgetting in fuzzy environment. The system is subject to learning in the production stage and to forgetting while production ceased so that the optimal manufactured quantity for any given cycle is dependent on the instantaneous production rate. All cost are taken constants or fuzzy in nature. Hence two models are introduced separately with constant and fuzzy cost. A closed form for the total relevant costs is derived, that minimizes total cost of the underlying inventory system. Model with fuzzy costs is formulated as to optimize the possibility/ necessity measure of the fuzzy goal of the objective function. When costs are imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. The models are illustrated with three examples as well as their numerical verifications are also given.