Note--Optimal Heuristic Decisions for the s, S Inventory Policy

Heuristic decision rules for the s, S policy in probabilistic inventory systems are proposed. The rules require only the knowledge of the mean and standard deviation of demand, probability of no demand, carrying and replenishing costs, desired availability, and leadtime. Numerical results are given to illustrate the application of the rules.

On the Equivalence of Some Inventory Systems

In an earlier paper ("Some Models of Inventory and an Application", Management Science, Vol. 2, No. 4, July, 1956) the author analyzed four inventory systems which were referred to as Models I, II, III, IV. In the present paper the notion of equivalence of inventory systems is introduced and it is shown that Models I and II are equivalent and so are models III and IV. The results are also extended to systems with non-zero leadtime. In all cases considered it is shown that the total expected costs of the systems (with or without leadtime) can be expressed in the form

Some Models of Inventory and an Application

This paper is concerned with two topics: (1) the development of mathematical models for several simple inventory situations, and (2) an industrial application of a mathematical model of inventory. Because T. M. Whitin has described in detail in this journal the present state of research in inventory control (Whitin, T. M. 1954. Inventory control research. Management Sci. I (November).), no attempt will be made to provide a review here. This paper is not an attempt to solve the "general inventory problem." On the contrary, the object is to deal with specific situations, and with an illustrative industrial application. The emphasis is on methodology of approach rather than on a general solution.

Note--Sensitivity to Distributions in Inventory Systems

The optimal decisions and costs of several inventory systems with the s, S policy are presented showing how they are affected by different distributions of demand, different shortage costs and different leadtimes. The numerical results seem to imply that in many cases the optimal decisions depend on the means and standard deviations of demand but not on the specific forms of the distributions.inventory/production: parametric analysis

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.