Optimal policy for multi-item systems with stochastic demands, backlogged shortages and limited storage capacity

Abstract

In this paper, an inventory model for multiple products with stochastic demands is developed. The scheduling period or inventory cycle is known and prescribed. Demands are independent random variables and they follow power patterns throughout the inventory cycle. For each product, an aggregate cycle demand is realized first and then the demand is released to the inventory system gradually according to power patterns within a cycle. These demand patterns express different ways of drawing units from inventory and can be a good approach to modelling customer demands in inventory systems. Shortages are allowed and they are fully backlogged. It is assumed that the warehouse where the items are stored has a limited capacity. For this inventory system, we determine the inventory policy that maximizes the expected profit per unit time. An efficient algorithmic approach is proposed to calculate the optimal inventory levels at the beginning of the inventory cycle and to obtain the maximum expected profit per unit time. This inventory model is applicable to on-line sales of a wide variety of products. In this type of sales, customers do not receive the products at the time of purchase, but sellers deliver goods a few days later. Also, this model can be used to represent inventories of products for in-shop sales when the withdrawal of items from the inventory is not at the purchasing time, but occurs in a period after the sale of the products. This inventory model extends various inventory systems studied by other authors. Numerical examples are introduced to illustrate the theoretical results presented in this work.