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

In this paper the full transmission of learning for the general production lot size problem with an infinite planning horizon is studied under the following assumptions: (1) Items deteriorate while they are produced or stored. (2) Both demand and deterioration rates are (known) functions of time. (3) Shortages are allowed, but are partially backordered. (4) The production rate is defined as the number of units produced per unit time. A closed form for the total relevant cost as well as a rigorous mathematical method that leads to a minimum total cost of the underlying inventory system are introduced. An illustrative example which explains the applications of the theoretical results as well as its numerical verification are also given