Stochastic duels with displacements (suppression)

The stochastic duel is extended to include the possibility of a near-miss on each round fired, which causes the opponent to displace. During displacement, the displacing contestant cannot return the fire but is still a target for his opponent. An alternative interpretation of this model is to consider the displacement time as the time a contestant's fire is suppressed by his opponent's fire and that he does not move, but merely ceases fire temporarily. All times are exponentially distributed.     

Diagnostic analysis of inventory systems: An optimization approach

The objective of a diagnostic analysis is to provide a measure of performance of an existing system and estimate the benefits of implementing a new one, if necessary. Firms expect diagnostic studies to be done promptly and inexpensively. Consequently, collection and manipulation of large quantities of data are prohibitive. In this paper we explore aggregate optimization models as tools for diagnostic analysis of inventory systems. We concentrate on the dynamic lot size problem with a family of items sharing the same setup, and on the management of perishable items. We provide upper and lower bounds on the total cost to be expected from the implementation of appropriate systems. However, the major thrust of the paper is to illustrate an approach to analyze inventory systems that could be expanded to cover a wide variety of applications. A fundamental by-product of the proposed diagnostic methodology is to identify the characteristics that items should share to be aggregated into a single family.     

A heuristic routine for solving large loading problems

The loading problem involves the optimal allocation of n objects, each having a specified weight and value, to m boxes, each of specified capacity. While special cases of these problems can be solved with relative ease, the general problem having variable item weights and box sizes can become very difficult to solve. This paper presents a heuristic procedure for solving large loading problems of the more general type. The procedure uses a surrogate procedure for reducing the original problem to a simpler knapsack problem, the solution of which is then employed in searching for feasible solutions to the original problem. The procedure is easy to apply, and is capable of identifying optimal solutions if they are found.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.     

Some constraints on shipping in linear programming models

This note describes some constraints that may be applied to shipping models structured as linear programming problems. These constraints defining port-throughput capability have proven useful in applications of linear programming by the author and provide additional realism in problems of vessel allocation and ship design selection. Increase in model size through the use of the constraints is in general mode rate.     

Toward a multi-stage information conversion model of the research and development process

Research and development activities in a business firm or government laboratory are portrayed as a multi-stage information generation and conversion process. A “basic research” phase generates opportunities, in the form of findings in a set of scientific disciplines, which are available for subsequent exploitation. It is assumed that increments to information in a subject area are stochastic, proportional to the amount of knowledge which already exists in the area, and have values which are randomly distributed. An “exploratory development” phase is viewed as a process of selecting a subset of alternative research opportunities, improving each opportunity in the direction of its applications, estimating the value of the improved opportunity and using these estimates to choose the exploratory development results to be implemented in engineering development. The “engineering development” phase makes the value of exploratory results realizable without changing value or risk. Engineering development costs are assumed to increase as value increases. If exploratory development is not successful, additional costs in engineering development must be incurred to bring the design up to a minimum desirable level. The model is intended as a step toward formulating and analyzing problems in management planning and control of the several interrelated stages of the research and development process.     

Fitting Lanchester equations to the battles of Kursk and Ardennes

Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding of how well various parameter combinations explain the battles. It turns out that a variety of Lanchester models fit the data about as well. This explains why previous studies on Ardennes, using different minimization techniques and data formulations, have found disparate optimal fits. We also find that none of the basic Lanchester laws (i.e., square, linear, and logarithmic) fit the data particularly well or consistently perform better than the others. This means that it does not matter which of these laws you use, for with the right coefficients you will get about the same result. Furthermore, no constant attrition coefficient Lanchester law fits very well. The failure to find a good‐fitting Lanchester model suggests that it may be beneficial to look for new ways to model highly aggregated attrition. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.