General solution to many-on-many heterogeneous stochastic combat

Stochastic combat models are more realistic than either deterministic or exponential models. Stochastic combat models have been solved analytically only for small combat sizes. It is very difficult, if not impossible, to extend previous solution techniques to larger-scale combat. This research provides the solution for many-on-many heterogeneous stochastic combat with any break points. Furthermore, every stage in stochastic combat is clearly defined and associated aiming and killing probabilities are calculated. © 1996 John Wiley & Sons, Inc.     

Book Reviews

Patrick Finney (ed.), The Origins of the Second World War. London: Arnold, 1997. Pp.xvi + 461, index. £15.99. ISBN 0–340–67640‐X.

Maria Emilia Paz, Strategy, Security, and Spies: Mexico and the US as Allies in World War II. University Park, PA: The Pennsylvania State University Press, 1997. Pp.xii + 264, 10 illus., biblio., index. $55 (cloth); $19.95 (paper). ISBN 0–271–01665–5 and 01666–3.

Norman J.W. Goda, Tomorrow the World: Hitler, Northwest Africa and the Path toward America. College Station, Texas A&;M University Press, 1998. Pp.xxvi + 307, 2 maps, biblio., index. $39.95. ISBN 0–89096–807–1.

Michael J. Hogan, A Cross of Iron: Harry S. Truman and the Origins of the National Security State, 1945–1954. Cambridge; New York: Cambridge University Press, 1998. Pp.xii + 525, biblio., index. £25; $34.95. ISBN 0–521–64044‐X.

Stephen Van Evera, Causes of War: Power and the Roots of Conflict. Ithaca, NY: Cornell University Press, 1999. Pp.viii + 270, index. $35. ISBN 0–801403201–4.

Eric Arnett (ed.), Nuclear Weapons and Arms Control in South Asia after the Test Ban, SIPRI Research Report No.14. Oxford: Oxford University Press/Stockholm Int Peace Research Institute, 1998. Pp.viii + 98, index. £12.99. ISBN 0–19–8294115.

T.V. Paul, Richard J. Harknett and James J. Wirtz (eds.), The Absolute Weapon Revisited: Nuclear Arms and Emerging International Order. Ann Arbor, Michigan: The University of Michigan Press, 1998. Pp.vi + 312, index. $47.50/£36. ISBN 0–472–10863–8.     

Small states and their armies: Restructuring the militia framework of the Israel defense force

The British provided unprecedented shelter, training and supplies that made possible the revival of a new and better Belgian Army after the crushing German victories in 1940. Starting in Wales in 1940 as a small and disunited group, the Belgians improved more than any of the Allied exile ground forces. By 1944, their independent brigade fought well in Normandy and Belgium, restoring national pride and proving the worth of British help. The parallel and interdependent processes between the British and their Continental guests allows this analysis of the Anglo‐Belgian experience to be useful in considering British Army interactions with the other exiles as well.     

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.     

The formulation of some allocation and connection problems as integer programs

In this paper a component placement problem and a digital computer backboard wiring problem are formulated as integer linear programs. The component placement problem consists of making a unique assignment of components to column positions such that wireability is maximized. The backboard wiring problem consists of three interrelated subproblems, namely, the placement, the connection, and the routing problems. The placement and connection problems are combined and solved as one, thereby giving the optimal circuit connections as well as minimizing the total lead length. It is shown that under certain assumptions, the number of inequalities and variables in the problem can be greatly reduced. Further simplifying assumptions lead to a near optimal solution. Examples of other allocation problems to which the models presented here are applicable are given. The following concepts are formulated as linear inequalities: (1) the absolute magnitude of the difference between two variables; (2) minimize the minimum function of a set of functions; and (3) counting the number of (0, 1) adjacent component pairs in a vector.     

On some stocxastic tactical antisubmarine games

Mathematical models of tactical problems in Hntisubmarine Warfare (ASW) are developed. Specifically, a game of pursuit between a hunter-killer force. player 1, and a possible submarine, player 2 is considered. The game consists of a sequence of moves and terminates when player 2 is tcaught or evades player 1. When the players move they observe the actual tactical configuration of the forces (state) and each player choosa-s a tactical plan from a finite collection. This joint choice of tactical plans determines an immediate payoff and a transition probability distribution over the states. Hence an expected payoff function is defined, Formally this game is a Terminating Stochastic Game (TSG). Shapley demonstrated the existence of a value and optimal strategies (solution), An iterative technique to approximate the solution to within desired accuracy is proposed. Each iteration of the technique is obtained by solving a set of linear programs. To introduce more realism into the game several variations of the TSG are also considered. One variation is a finite TSG and linear programming techniques are employed to find the solution.     

Comparative evaluation of prior versus progressive articulation of preference in bicriterion optimization

Procedures for solving multiple criteria problems are receiving increasing attention. Two major solution approaches are those involving prior articulation and progressive articulation of preference information. A progressive articulation (interactive) optimization approach, called the Paired Comparison Method (PCM) is compared to the prior articulation approach of a priori utility function measurement in a quality control decision environment from the perspective of the decision maker. The three major issues investigated included: (1) the ease of use of each method, (2) the preferences of solutions obtained, and (3) the insight provided by the methodology into the nature and structure of the problem. The problem setting involved management students who were rquired to determine an acceptance sampling plan using both methods. The PCM provided the most preferred solutions and was considered easier to use and understand. The prior articulation of preference method was found to give more insight into the problem structure. The results suggest that a hybrid approach, combining both prior preference assessment and an interactive procedure exploiting the advantages of each, should be employed to solve multiple criteria problems.