Optimal multicommodity network flows with resource allocation

The problem of determining multicommodity flows over a capacitated network subject to resource constraints may be solved by linear programming; however, the number of potential vectors in most applications is such that the standard arc-chain formulation becomes impractical. This paper describes an approach—an extension of the column generation technique used in the multicommodity network flow problem—that simultaneously considers network chain selection and resource allocation, thus making the problem both manageable and optimal. The flow attained is constrained by resource availability and network capacity. A minimum-cost formulation is described and an extension to permit the substitution of resources is developed. Computational experience with the model is discussed.     

An alternative proof of the IFRA property of some shock models

Let , where A (t)/t is nondecreasing in t, {P(k)^1/k} is nonincreasing. It is known that H(t) = 1 — H (t) is an increasing failure rate on the average (IFRA) distribution. A proof based on the IFRA closure theorem is given. H(t) is the distribution of life for systems undergoing shocks occurring according to a Poisson process where P (k) is the probability that the system survives k shocks. The proof given herein shows there is an underlying connection between such models and monotone systems of independent components that explains the IFRA life distribution occurring in both models.     

Book reviews

Use of Force: The Practise of States by A. Mark Weisburd, Penn: Penn State Press, University Park, 1997, ISBN 0-271-01679-5 (hbk), $65.00/£58.00, ISBN 0-271-01680-9 (pbk), $25.00/£22.50

Late Breaking Foreign Policy: the News Media's Influence on Peace Operations by Warren P. Strobel, Washington DC: United States Insititute of Peace Press, 1997, ISBN 1-878379-68-2 (hbk), £23.25, ISBN 1-878379-67-4 (pbk)

The Reluctant Sheriff: The United States After the Cold War by Richard N. Haass, New York: Council on Foreign Relations, 1997, 148pp, index, ISBN 0-87609-201-6 (hbk), $24.95

The UN, Peace and Force edited by Michael Pugh, London: Frank Cass, 1997, ISBN 0-7146-4795-4 (hbk), £29.50, ISBN 0-7146-4320-3 (pbk), £15.00

Confidence-Building in South East Asia by Malcolm Chalmers, Oxford: Westview Press, 1996, ISBN 1-85143-116-0 (pbk), £19.95

Britain's Strategic Nuclear Deterrent: From Before the V-Bomber to Beyond Trident by Robert H. Paterson, London: Frank Cass, 1997, ISBN 0-7146470-3 (hbk), £35.00, ISBN 0-7146-4297-5 (pbk) £18.00

OSS in China: Prelude to Cold War by Maochun Yu, London: Yale University Press, 1997, ISBN 0 300 06698-8 (hbk), £25.00

Preventing Violent Conflicts: A Strategy for Preventive Diplomacy by Michael S. Lund, Washington DC: US Institute of Peace Press, 1996, ISBN 1-878379-52-6 (pbk), £11.75     

Estimating negative binomial demand for retail inventory management with unobservable lost sales

The importance of effective inventory management has greatly increased for many major retailers because of more intense competition. Retail inventory management methods often use assumptions and demand distributions that were developed for application areas other than retailing. For example, it is often assumed that unmet demand is backordered and that demand is Poisson or normally distributed. In retailing, unmet demand is often lost and unobserved. Using sales data from a major retailing chain, our analysis found that the negative binomial fit significantly better than the Poisson or the normal distribution. A parameter estimation methodology that compensates for unobserved lost sales is developed for the negative binomial distribution. The method's effectiveness is demonstrated by comparing parameter estimates from the complete data set to estimates obtained by artificially truncating the data to simulate lost sales. © 1996 John Wiley & Sons, Inc.     

Multiperiod allocation of limited resources: A minimax approach

We consider a multiperiod model in which limited resources are allocated among competing activities in each period. The objective is to minimize the maximum weighted deviation of the cumulative activity levels from the cumulative demands among all activities at all periods. All resources are assumed to be storable; that is, surpluses at one period can be used later on. This model is useful, for example, in multiperiod production planning for high-technology industries that assemble a large variety of circuit boards using numerous electronic components. The model is formulated with a minimax objective. We develop an efficient algorithm that can solve large-scale problems very quickly. At each iteration, the algorithm makes use of the solution to a relaxed problem to identify activities that should be permanently set to zero, as well as groups of activities that should have the same value.     

Arms export controls and emerging domestic producers†

The possibility of domestic production raises a difficulty for arms export control measures, since embargoes, by raising the effective price of imports, increase the incentive for domestic production. We address this issue by developing a partial equilibrium model of the international arms market We compare three arms export regimes involving the exporters of high‐technology arms, with a particular focus on the effect of emerging domestic production: laissez‐faire trade, the uncoordinated regulation of exports and a producer cartel consisting of coordinated regulation. The main conclusion is that the possibility of domestic production significantly changes the nature of these stylized export regimes.     

A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Review of the ordered and proportionate flow shop scheduling research

Ordered flow shop models have appeared in the literature since the mid‐1970s and proportionate flow shop models have appeared since the early 1980s. We provide a detailed review of these models along with some analysis and potential topics for future research. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Algorithms for solving the conditional covering problem on paths

Consider the conditional covering problem on an undirected graph, where each node represents a site that must be covered by a facility, and facilities may only be established at these nodes. Each facility can cover all sites that lie within some common covering radius, except the site at which it is located. Although this problem is difficult to solve on general graphs, there exist special structures on which the problem is easily solvable. In this paper, we consider the special case in which the graph is a simple path. For the case in which facility location costs do not vary based on the site, we derive characteristics of the problem that lead to a linear‐time shortest path algorithm for solving the problem. When the facility location costs vary according to the site, we provide a more complex, but still polynomial‐time, dynamic programming algorithm to find the optimal solution. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Optimal maintenance models for systems subject to failure–A Review

This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.