The lower bounded and partial upper bounded distribution model

This paper pruvides a smaller equivalelnt bounded variable transportation problem than that in Charnes, Glover, and Klingman [1] for the lower bounded and partial upper bounded distribution model.     

The single server queue in discrete time-numerical analysis II

This paper deals with the numerical problems arising in the computation of higher order moments of the busy period for certain classical queues of the M|G|I type, both in discrete and in continuous time The classical functional equation for the moment generating function of the busy period is used. The higher order derivatives at zero of the moment generating function are computed by repeated use of the classical differentiation formula of Fá di Bruno. Moments of order up to fifty may be computed in this manner A variety of computational aspects of Fá di Bruno's formula, which may be of use in other areas of application, are also discussed in detail.     

An algorithm for separable piecewise convex programming problems

We present a branch and bound algorithm to solve mathematical programming problems of the form: Find x =|(x₁,…x_n) to minimize Σ?_i0(x₁) subject to x?G, l≦x≦L and Σ?_i0(x₁)≦0, j=1,…,m. With l=(l₁,…,l_n) and L=(L₁,…,L_n), each ?_ij is assumed to be lower aemicontinuous and piecewise convex on the finite interval [l_i.L_i]. G is assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C={x|l ≦ x ≦L} on the bahis of the piecewise convexity of the problem functions ?_ij. Computational considerations are discussed, and an illustrative example is presented.     

Total optimality of incrementally optimal allocations

This paper considers the problem of finding optimal solutions to a class of separable constrained extremal problems involving nonlinear functionals. The results are proved for rather general situations, but they may be easily stated for the case of search for a stationary object whose a priori location distribution is given by a density function on R, a subset of Euclidean n-space. The functional to be optimized in this case is the probability of detection and the constraint is on the amount of effort to be used Suppose that a search of the above type is conducted in such a manner as to produce the maximum increase in probability of detection for each increment of effort added to the search. Then under very weak assumptions, it is proven that this search will produce an optimal allocation of the total effort involved. Under some additional assumptions, it is shown that any amount of search effort may be allocated in an optimal fashion.     

Allocation of resources to offensive strategic weapon systems

In this paper a very versatile game model is developed for use in the long range planning of our strategic force posture. This highly aggregate model yields optimal force mixes for the triad (land- and sea-based missile systems and bombers) under a variety of constraints. The model described here is a survivability model; however, it is shown how the model can still be used as a measure of overall system effectiveness. Constraints imposed on the problem include both SALT and budget limitations.     

The bilinear programming problem

The paper deals with bilinear programming problems and develops a finite algorithm using the “piecewise strategy” for large-scale systems. It consists of systematically generating a sequence of expanding polytopes with the global optimum within each polytope being known. The procedure then stops when the final polytope contains the feasible region.     

Confidence bounds and propagation of uncertainties in system availability and reliability computations

This paper develops bounds on the uncertainties in system availabilities or reliabilities which have been computed from structural (series, parallel, etc.) relations among uncertain subsystem availabilities or reliabilities. It is assumed that the highly available (reliable) subsystems have been tested or simulated to determine their unavailabilities (unreliabilities) to within some small percentages of uncertainty. It is shown that series, parallel and r out of n structures which are nominally highly available will have unavailability uncertainties whose percentages errors are of the same order as the subsystem uncertainties. Thus overall system analysis errors, even for large systems, are of the same order of magnitude as the uncertainties in the component probabilities. Both systematic (bias type) uncertainties and independent random uncertainties are considered.     

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.     

Landmarks in defense literature

Strategy, Politics and Defense Budgets. By Warner R. Schilling, Paul Y. Hammond and Glenn H. Snyder. Columbia University Press, New York (1962)