Minimal disconnecting sets in directed multi-commodity networks

The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.     

Equivalent knapsack-type formulations of bounded integer linear programs: An alternative approach

In this paper we show that every bounded integer linear program can be transformed into an integer program involving one single linear constraint and upper and lower bounds on the variables, such that the solution space of the original problem coincides with that one of the equivalent knapsack-type problem.     

Expectation of contract incentives

The application of statistical expectation to risk density functions and fee/incentive-element relationships is shown to be useful in structuring contract incentives. A mathematical procedure for calculating the expected value of fee for a given risk/incentive arrangement is described along with cost examples and related sensitivity analyses. The structuring of equivalent incentives is demonstrated by the use of the contracting procedure used for procuring the C-5A aircraft.     

A mixed optimization technique for the generalized machine replacement problem

A mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models. Optimal purchase, maintenance and sale of a given machine between any two given points in time is treated as a subproblem, which one may choose to solve via control theory, dynamic programming, or practical engineering considerations. (A control theory formulation is used in the paper as an illustration.) These subproblem solutions are then incorporated into a Wagner-Whitin formulation for solution of the full problem. The technique is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change. A simple numerical example is solved in the Appendix.     

Systems analysis and planning-programming-budgeting systems (PPBS) for defense decision making

Systems analysis office titles have permeated both government and business organization charts in recent years. Systems analysis as a discipline, however, even though increasingly accepted, has eluded precise definition. For the most part, it has been loosely described as “quantitative common sense” and “the general application of the scientific method.” Emphasis is placed upon the application of eclectic disciplines to a wide variety of problems. Concepts and techniques have been drawn heavily from economics, mathematics, and political science. In the Department of Defense, systems analysis has been used extensively in the evaluation of weapon systems during the last 9 years. During the 1960's, it provided the underlying concepts for the control system PPBS (Planning-Programming-Budgeting System). This article traces the origins of systems analysis within the Department of Defense and describes and analyzes the application of the technique. Although there always exists disagreement, it is generally accepted that the origin of systems analysis coincided with the inception of R. S. McNamara's administration of the Department of Defense. McNamara organized the Systems Analysis office under Mr. Charles Hitch, who had previously developed many basic systems analysis concepts at project RAND. From Hitch's basic concepts, the approach became increasingly sophisticated in evaluating complex weapons systems. Coincidently, the organizational procedures for implementing systems analysis also evolved. Under the current Department of Defense administration, the new organizational procedures emerging are contrasted with the old.     

A network isolation algorithm

A set of edges D called an isolation set, is said to isolate a set of nodes R from an undirected network if every chain between the nodes in R contains at least one edge from the set D. Associated with each edge of the network is a positive cost. The isolation problem is concerned with finding an isolation set such that the sum of its edge costs is a minimum. This paper formulates the problem of determining the minimal cost isolation as a 0–1 integer linear programming problem. An algorithm is presented which applies a branch and bound enumerative scheme to a decomposed linear program whose dual subproblems are minimal cost network flow problems. Computational results are given. The problem is also formulated as a special quadratic assignment problem and an algorithm is presented that finds a local optimal solution. This local solution is used for an initial bound.     

Stochastic duels with nonrepairable weapons

This paper examines the effect of limitation, regarding weapons that are likely to fail during the period of deployment, on the final outcome in a stochastic duel model. Inter-firing times as well as inter-failure times have been assumed to be exponentially distributed.     

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.