Analysis of an inventory system with discrete scheduling period, time-dependent demand and backlogged shortages

Abstract

A deterministic inventory model for goods with a power demand pattern, allowing backlogged shortages, is analyzed. The inventory cycle must be an integer multiple of a fixed time period (called basic period). Demand follows a power demand pattern during this basic time period. Demand not satisfied along the inventory cycle is fully backlogged and the stock-out period must be an integer multiple of the basic period. The goal of the inventory management is to minimize the inventory cost per unit time, considering that this inventory cost is the sum of the costs of holding, backlogging and ordering. Thus, the objective function of the inventory problem depends on two integer decision variables: the number of basic periods contained in an inventory cycle and the number of basic periods that constitute the stock-in period. The optimal inventory policy is found through a two-dimensional search method. This procedure is based on the properties of the inventory cost function. An algorithmic approach to calculate the economic order quantity and the optimal inventory cycle that minimize the total cost per unit time is proposed. The theoretical results are discussed and illustrated with some numerical examples. Finally, a sensitivity analysis of the optimal policy with respect to some parameters of the inventory model is developed.