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This paper examines the system fill-rate of a one-warehouse N-identical retailer distribution system as a function of warehouse and retailer safety stock. Using the approximation model of Deuermeyer and Schwarz (Deuermeyer, B. L., L. B. Schwarz. 1981. A model for the analysis of system service level in warehouse/retailer distribution systems: the identical retailer case. Chapter 8 in Multi-Level Production/Inventory Control Systems: Theory and Practice. North-Holland, Amsterdam.) we examine the problem of maximizing system fill-rate subject to a constraint on system safety stock. Optimal safety stock policy is characterized to be the intersection of a fill-rate policy line and the safety stock budget line. Properties of fill-rate policy lines are given. These properties may be used to provide managerial insight into system optimization and as the basis for heuristics. One heuristic, the vertical heuristic, based on the corresponding deterministic version of the problem, yields trivially simple and near-optimal policies.

This paper considers the problem of sequencing the installation of replacement parts for the repeated repair of a machine consisting of two working parts. A finite inventory of spares is initially available for each type of part. Each spare has a known (deterministic) field life, and spares of each type may have different field lives. The inventories are eventually depleted since no replacement or repairs of parts occur. The primary objective is to obtain a sequencing policy which minimizes the total number of installations (replacements). This problem is a special case of many opportunistic replacement problems and is called a “build” problem. The motivation for this work is based on the maintenance of modular gas turbine aircraft engines used by domestic airlines and the U.S. Air Force. We show this build problem is NP-hard which indicates the necessity of efficient heuristic solution procedures. This paper considers several “greedy” type algorithms based on grouping parts according to exact matching of field lives. Then, a generalization is presented which allows approximate matches. The focus of the analysis is to obtain tight worst case bounds on the number of replacements obtained by each of the greedy algorithms.

This paper develops a one-period model for investigating the properties of the optimal production policy for a system composed of two production processes called types A and B. These in turn produce two perishable stock items called products 1 and 2, having independent random demands and different lifetimes. Type A produces both products in amounts governed by a fixed set of production coefficients. Type B can be used only to manufacture product 2. The optimal starting inventory level is characterized for the one-period problem using the criterion of minimized expected total cost. The optimal production levels are characterized in terms of the starting inventory levels. Results show that the decision space is partitioned into four distinct regions whose boundaries are defined by a point and four hypersurfaces.

This paper considers the optimal control of a production system which is composed of two distinct production processes, types A and B, that produce two different products, 1 and 2, having distinct random demands. Production type A produces both products in amounts determined by a fixed set of production coefficients. Type B can only be used to make product 2. Costs consist of linear production costs and convex holding and shortage costs. Each period, the optimal production level of each type must be determined. The criterion is the minimum expected discounted total cost. Results show that the decision space of each period is partitioned into four regions by three monotone functions and a point. Extensions include capacitated production, nonstationary costs, lost sales, fixed lead times aid the general m process-n product system.inventory/production, inventory/production: stochastic models