Optimal and Heuristic Decisions in Single-and Multi-Item Inventory Systems

A comparison of optimal solutions of single-item inventory systems for the three classical policies tZ, sq, and sZ shows that the optimal order levels in the tZ and sZ policies are usually the same, and so are the optimal reorder points in the sq and sZ policies. The total cost for each of the three policies can be expressed as that of a fundamental model using an appropriate equivalent distribution. The fundamental model can be analyzed with ease. It also provides closed-form results for the normal distribution. Heuristic rules are presented allowing the analysis of inventory systems on the basis of their average demand, standard deviation of demand, probability of no demand, lead-time, carrying cost, replenishing cost, and an availability index. Compared with the optimal decisions and costs for identical inventory systems, in which the probability distribution of demand is known, the heuristic rules give excellent results. The optimal and heuristic decisions are extended to multi-item systems in which there is a cost for placing and receiving an order for a family of items every reviewing period. An algorithm is presented for finding the optimal reviewing period and the corresponding decisions and costs. The heuristic decisions compare very favorably with the optimal ones.