A bounded dual (all-integer) integer programming algorithm with an objective cut

In this article, we describe a new algorithm for solving all-integer, integer programming problems. We generate upper bounds on the decision variables, and use these bounds to create an advanced starting point for a dual all-integer cutting plane algorithm. In addition, we use a constraint derived from the objective function to speed progress toward the optimal solution. Our basic vehicle is the dual all-integer algorithm of Gomory, but we incorporate certain row- and column-selection criteria which partially avoid the problem of dual-degenerate iterations. We present the results of computational testing.     

A note on allocating jobs to two machines

A recent article in this journal by Mehta, Chandrasekaran, and Emmons [1] described a dynamic programming algorithm for assigning jobs to two identical parallel processors in a way that minimizes the average delay of these jobs. Their problem has a constraint on the sequence of the jobs such that any group of jobs assigned to a processor must be processed in the order of the sequence. This note has two purposes. First, we wish to point out a relationship between this work and some prior work [2]. Second, we wish to point out that Mehta, Chandrasekaran, and Emmons formulation, slightly generalized, can be used to find the optimum assignment of jobs to two machines in a more general class of problems than they considered including a subclass in which the jobs are not constrained to be processed in a given sequence.     

Landmarks in defense literature

Strategy, Politics and Defense Budgets. By Warner R. Schilling, Paul Y. Hammond and Glenn H. Snyder. Columbia University Press, New York (1962)     

Optimal admission pricing policies for M/Ek/1 queues

This paper extends the Low-Lippman M/M/1 model to the case of Gamma service times. Specifically, we have a queue in which arrivals are Poisson, service time is Gamma-distributed, and the arrival rate to the system is subject to setting an admission fee p. The arrival rate λ(p) is non-increasing in p. We prove that the optimal admission fee p^* is a non-decreasing function of the customer work load on the server. The proof is for an infinite capacity queue and holds for the infinite horizon continuous time Markov decision process. In the special case of exponential service time, we extend the Low-Lippman model to include a state-dependent service rate and service cost structure (for finite or infinite time horizon and queue capacity). Relatively recent dynamic programming techniques are employed throughout the paper. Due to the large class of functions represented by the Gamma family, the extension is of interest and utility.     

Bicriteria product design optimization: An efficient solution procedure using AND/OR trees

Competitive imperatives are causing manufacturing firms to consider multiple criteria when designing products. However, current methods to deal with multiple criteria in product design are ad hoc in nature. In this paper we present a systematic procedure to efficiently solve bicriteria product design optimization problems. We first present a modeling framework, the AND/OR tree, which permits a simplified representation of product design optimization problems. We then show how product design optimization problems on AND/OR trees can be framed as network design problems on a special graph—a directed series‐parallel graph. We develop an enumerative solution algorithm for the bicriteria problem that requires as a subroutine the solution of the parametric shortest path problem. Although this parametric problem is hard on general graphs, we show that it is polynomially solvable on the series‐parallel graph. As a result we develop an efficient solution algorithm for the product design optimization problem that does not require the use of complex and expensive linear/integer programming solvers. As a byproduct of the solution algorithm, sensitivity analysis for product design optimization is also efficiently performed under this framework. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 574–592, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10031     

Analysis of artillery shoot‐and‐scoot tactics

Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.     

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