Aggregating assignment constraints

This article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

The politics of multinational military operations

Today, few countries fight alone; most fight as allies or partners in multilateral campaigns. The end of the Cold War opened a window of opportunity for multinational military operations (MMOs). These have seen varying degrees of participation, enthusiasm, and success. This special forum is devoted to the politics of multilateral warfare including their formation, maintenance, and durability. The introduction sketches past research and derives some key questions of continuing relevance. The contributions shed light on the domestic and international politics of MMOs, focusing on the implementation of national restrictions and their repercussions for MMOs, party politics of military intervention, the conditions under which states decide to defect from military operations, and the role of junior partners in MMOs. In sum, this forum offers a fresh look at the politics of MMOs, including conceptual contributions to the study of national restrictions, domestic constraints, and coalition warfare.     

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.     

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.     

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.     

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.     

The capital supply curve in capacity expansion models: Some economic and algorithmic aspects

Capacity expansion models typically minimize the discounted cost of acquisition and operation over a given planning horizon. In this article we generalize this idea to one in which a capital supply curve replaces the usual discount rate. A capital supply curve is a means to model financial outlook, investment limits, and risk. We show that when such a curve is included in a capacity expansion model, it will, under certain conditions, provide a less capital intensive solution than one which incorporates a discount rate. In this article, we also provide an algorithm that solves capacity expansion models that incorporate a capital supply curve. The attractive feature of this algorithm is that it provides a means to utilize the “discount rate” models efficiently. Throughout, we give applications in power generation planning and computational experience for this application is also presented.