Properties of an approximate hazard transform

The calculation of the exact reliability of complex systems is a difficult and tedious task. Consequently simple approximating techniques have great practical value. The hazard transform of a system is an invertible transformation of its reliability function which is convenient and useful in both applied and theoretical reliability work. A simple calculus for finding an approximate hazard transform for systems formed by series and parallel combinations of components is extended so that it can be used for any coherent system. The extended calculus is shown to lead to conservative approximations. A first order version of the extended calculus is also discussed. This method of approximation is even more simple to use, but is not always conservative. Examples of its application indicate that it is capable of giving quite accurate results.     

Three ways of obtaining the average cost expression in a problem related to joint replenishment inventory control

This paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem. The same “average cost per unit time” expression is developed by three quite different procedures. This variety of approaches, as well as the recounting of the author's chronological efforts to solve the problem, should be of interest to the reader. The specific inventory problem studied is one where the controller of an item is faced with random opportunities for replenishment at a reduced setup cost; the problem is an integral component of the broader problem of inventory control of a group of items whose replenishments are coordinated to reduce the costs of production, procurement, and/or transportation.     

An explicit general solution in linear fractional programming

A complete analysis and explicit solution is presented for the problem of linear fractional programming with interval programming constraints whose matrix is of full row rank. The analysis proceeds by simple transformation to canonical form, exploitation of the Farkas-Minkowki lemma and the duality relationships which emerge from the Charnes-Cooper linear programming equivalent for general linear fractional programming. The formulations as well as the proofs and the transformations provided by our general linear fractional programming theory are here employed to provide a substantial simplification for this class of cases. The augmentation developing the explicit solution is presented, for clarity, in an algorithmic format.     

Sequential bid selection by stochastic approximation

Suppose that a contractor is faced with a sequence of “minimum bid wins contract” competitions. Assuming that a contractor knows his cost to fulfill the contract at each competition and that competitors are merely informed whether or not they have won, bids may be selected sequentially via a tailored stochastic approximation procedure. The efficacy of this approach in certain bidding environments is investigated.     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

Optimal material control in an assembly system with component commonality

Allocation of scarce common components to finished product orders is central to the performance of assembly systems. Analysis of these systems is complex, however, when the product master schedule is subject to uncertainty. In this paper, we analyze the cost—service performance of a component inventory system with correlated finished product demands, where component allocation is based on a fair shares method. Such issuing policies are used commonly in practice. We quantify the impact of component stocking policies on finished product delays due to component shortages and on product order completion rates. These results are used to determine optimal base stock levels for components, subject to constraints on finished product service (order completion rates). Our methodology can help managers of assembly systems to (1) understand the impact of their inventory management decisions on customer service, (2) achieve cost reductions by optimizing their inventory investments, and (3) evaluate supplier performance and negotiate contracts by quantifying the effect of delivery lead times on costs and customer service. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:409–429, 2001     

Applying a bootstrap approach for setting reorder points in military supply systems

This paper develops and applies a nonparametric bootstrap methodology for setting inventory reorder points and a simple inequality for identifying existing reorder points that are unreasonably high. We demonstrate that an empirically based bootstrap method is both feasible and calculable for large inventories by applying it to the 1st Marine Expeditionary Force General Account, an inventory consisting of $20–30 million of stock for 10–20,000 different types of items. Further, we show that the bootstrap methodology works significantly better than the existing methodology based on mean days of supply. In fact, we demonstrate performance equivalent to the existing system with a reduced inventory at one‐half to one‐third the cost; conversely, we demonstrate significant improvement in fill rates and other inventory performance measures for an inventory of the same cost. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 459–478, 2000