The effects of learning and forgetting on the optimal production lot size for deteriorating items with time varying demand and deterioration rates

In this paper, we shall study the effects of learning and forgetting on the production lot size problems for an infinite planning horizon. Items deteriorate while they are in storage, and both demand and deterioration rates are arbitrary functions of time. The instantaneous production rate presented herein is dependent on the time required to produce the first unit at the beginning of production process, the number of units remembered, and the fixed learning slope component. The forgetting slope is represented by an approximation of the minimum break to which the manufacturer assumes total forgetting so that it allows variable total forgetting breaks. 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. A closed form for the total relevant costs is derived, and rigorous mathematical methods that guide to a minimum total cost of the underlying inventory system are introduced. Illustrative examples, which explain the applications of the theoretical results as well as their numerical verifications, are also given.