A probabilistic inventory model with deterioration factor and continuous discount function

Abstract

In this paper we develop a mathematical model for probabilistic inventory system by considering deterioration factor and continuous discount function. We consider a perpetual inventory system where demands follow certain continuous distribution. It is realized that a quantity discount function (QDF) has not widely used in practice compared to all-units discount and incremental discount to purchase product in a larger quantity. However, usually discount offered by the supplier comes in a discrete form, and in the model this is approximated by a continuous function called QDF. By employing a QDF, a firm can evaluate the amount of discount received for all purchase quantity. In general, our model will determine the optimal order quantity that minimize total inventory cost that consists of purchasing cost, ordering cost, holding cost, deterioration cost and shortage cost. We also develop an algorithm to find the optimal solution. Numerical example is given and analysis for several demand distributions from the family of Gamma distribution will also be provided.