An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money

Abstract

This paper considers a general production lot size inventory model with deteriorated and imperfect products taking into account inflation and time value of money. The production, demand, and deterioration rates are known, continuous, and differentiable functions of time. Shortages are allowed, but only a fraction of the stock out is backordered, and the rest is lost. Under these general assumptions, the inventory model is formulated, and a closed form of the total relevant costs of the underlying inventory system is obtained. Sufficient conditions which lead to a minimal solution of the considered problem are derived. Then, a rigorous mathematical analysis is used to prove that such a minimal solution is unique and global-optimal. A numerical verification of the proposed model is also given.