An optimal inventory model for a deteriorating item with multivariate demand function

Abstract

Managing the inventory of perishable items is a vital task in the supply chain. The demand for some deteriorating items is influenced by many factors that make their management a complicated task. Therefore, it is important to take multiple key factors into account to develop a more realistic model. In this paper, an inventory model for non-instantaneous deteriorating items is proposed, for the case where the quality and quantity of the item decrease over time. The demand is an additive, continuous, and differentiable function of price, stock level, and also age of the product. The deterioration starts after a fixed period with a constant rate and the shortage is not allowed. Permissible delay in payment and time value of money are also considered in the model. First, we formulate the problem in a piecewise mixed-integer nonlinear programming model. We then propose an algorithm to solve a number of examples.