The Trended Inventory Lot Sizing Problem with Shortages Under a New Replenishment Policy

In the past few years, considerable attention has been given to the inventory lot sizing problem with trended demand over a fixed horizon. The traditional replenishment policy is to avoid shortages in the last cycle. Each of the remaining cycles starts with a replenishment and inventory is held for a certain period which is followed by a period of shortages. A new replenishment policy is to start each cycle with shortages and after a period of shortages a replenishment should be made. In this paper, we show that this new type of replenishment policy is superior to the traditional one. We further propose four heuristic procedures that follow the new replenishment policy. These are the constant demand approximation method, the equal cycle length heuristic, the extended Silver approach, and the extended least cost solution procedure. We also examine the cost and computation time performances of these heuristic procedures through an empirical study. The number of test problems solved to optimality, average and maximum cost deviation from optimum were used as measures of cost performance. The results of the 10 000 test problems reveal that the extended least cost approach is most cost effective.