On the output of parallel exponential service channels

The paper treats the output process of a service center that has a large number of independent exponential channels in parallel. Initially all channels are working and there is a fixed backlog of items awaiting service. The moments are derived and central limit theorems are developed. Problems of computation are discussed and suitable formulae are developed. The joint distribution of the output of the center with the center's total busy time and total idle time are derived. Normal approximations to these distributions are presented.     

An operator theory of parametric programming for the generalized transportation problem: I. Basic theory

This paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph-theoretic approach is utilized to define the basis as a one-forest consisting of one-trees (a tree with an extra edge). Algorithmic development of the pivot-step is presented by the representation of a two-tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers we will present additional results on the operator theory for the generalized transportation problem based on the results in the present paper.     

A computation procedure for the exact solution of location-allocation problems with rectangular distances

A method is presented to locate and allocate p new facilities in relation to n existing facilities. Each of the n existing facilities has a requirement flow which must be supplied by the new facilities. Rectangular distances are assumed to exist between all facilities. The algorithm proceeds in two stages. In the first stage a set of all possible optimal new facility locations is determined by a set reduction algorithm. The resultant problem is shown to be equivalent to finding the p-median of a weighted connected graph. In the second stage the optimal locations and allocations are obtained by using a technique for solving the p-median problem.     

On the treatment of force-level constraints in times-equential combat problems

The treatment of force-level constraints in time-sequential combat optimization problems is illustrated by further studying the fire-programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire-distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire-programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time-sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.     

Pseudo-monotonic interval programming

A pseudo-monotonic interval program is a problem of maximizing f(x) subject to x ε X = {x ε Rⁿ | a < Ax < b, a, b ε R^m} where f is a pseudomonotonic function on X, the set defined by the linear interval constraints. In this paper, an algorithm to solve the above program is proposed. The algorithm is based on solving a finite number of linear interval programs whose solutions techniques are well known. These optimal solutions then yield an optimal solution of the proposed pseudo-monotonic interval program.     

Refined prediction for linear regression models

Adequate prediction of a response variable using a multiple linear regression model is shown in this article to be related to the presence of multicollinearities among the predictor variables. If strong multicollinearities are present in the data, this information can be used to determine when prediction is likely to be accurate. A region of prediction, R, is proposed as a guide for prediction purposes. This region is related to a prediction interval when the matrix of predictor variables is of full column rank, but it can also be used when the sample is undersized. The Gorman-Toman ten-variable data is used to illustrate the effectiveness of the region R.     

An easy solution for a special class of fixed charge problems

The fixed charge problem is a mixed integer mathematical programming problem which has proved difficult to solve in the past. In this paper we look at a special case of that problem and show that this case can be solved by formulating it as a set-covering problem. We then use a branch-and-bound integer programming code to solve test fixed charge problems using the setcovering formulation. Even without a special purpose set-covering algorithm, the results from this solution procedure are dramatically better than those obtained using other solution procedures.     

The bounded interval generalized assignment model

The bounded interval generalized assignment model is a “many-for-one” assignment model. Each task must be assigned to exactly one agent; however, each agent can be assigned multiple tasks as long as the agent resource consumed by performing the assigned tasks falls within a specified interval. The bounded interval generalized assignment model is formulated, and an algorithm for its solution is developed. Algorithms for the bounded interval versions of the semiassignment model and sources-to-uses transportation model are also discussed.     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.     

Another manifestation of cyber conflict: attaining military objectives through cyber avenues of approach

Cyberspace is an avenue of approach through which a military force can attain objectives of value. Through these cyber avenues of approach, military forces can engage, vet, organize, and direct human agents to accomplish specific activities. Although the objectives of these activities could differ from traditional military objectives, they still have military relevance. This particular manifestation of cyber conflict is neither a new domain of war nor something outside of warfare. Rather, it can be viewed as an emerging avenue of approach in the larger context of military operations, auguring benefits in the integration of cyber activities with operations.