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.     

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.     

Mean square invariant forecasters for the weibull distribution

Many techniques of forecasting are based upon extrapolation from time series. While such techniques have useful applications, they entail strong assumptions which are not explicitly enunciated. Furthermore, the time series approach not based on an indigenous forecast principle. The first attack from the present point of view was initiated by S. S. Wilks. Of particular interest over a wide range of operational situations in reliability, for example, is the behavior of the extremes of the Weibull and Gumbel distributions. Here we formulate forecasters for the minima of various forms of these distributions. The forecasters are determined for minimization in mean square of the distance. From n original observations the forecaster provides the minimum of the next m observations when the original distribution is maintained. For each of the forecasters developed, tables of efficiency have been calculated and included in the appendix. An explicit example has been included for one of the forecasters. Its performance has been demonstrated by the use of Monte Carlo technique. The results indicate that the forecaster can be used in practice with satisfactory results.     

Armor configurations via dynamic programming

The problem of selecting materials, their thicknesses and order for armor designed for the defeat of shaped charge threats, has been formulated as a constrained optimization problem. The mathematical model provides an optimal order and thickness of each layer of material such that the resulting armor configuration will be of minimum mass per unit area subject to constraints on total thickness and shaped charge jet tip exit velocity.     

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.     

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.