A nonconvex max-min problem

An algorithm designed to solve a large class of nonconvex max-min problems is described. Its usefulness and applicability is demonstrated by solving an extension of a recently introduced model which optimally allocates strategic weapon systems. The extended model is shown to be equivalent to a nonconvex mathematical program with an infinite number of constraints, and hence is not solvable by conventional procedures. An example is worked out in detail to illustrate the algorithm.     

A note on the relationship between correlation and circular error probability (CEP)

This note investigates the effects of ignoring correlation (p) as is sometimes done when estimating or placing confidence intervals on circular error probability (CEP). It is shown that better estimates of CEP can be made if the axis is rotated [5] so that the estimate of p is zero. It is also shown that ignoring variability in estimating correlation can affect the confidence intervals on CEP or the placing of a lower bound on the probability content of a circle.     

Markov chain analyses of multiprogrammed computer systems

Most operating systems for large computing facilities involve service disciplines which base, to some extent, the sequencing of object program executions on the amount of running time they require. It is the object of this paper to study mathematical models of such service disciplines applicable to both batch and time-shared processing systems. In particular, Markov queueing models are defined and analyzed for round-robin and foreground-background service disciplines. With the round-robin discipline, the service facility processes each program or job for a maximum of q seconds; if the program's service is completed during this quantum, it leaves the system, otherwise it returns to the end of the waiting line to await another quantum of service. With the foreground-background discipline each new arrival joins the end of the foreground queue and awaits a single quantum of service. If it requires more it is subsequently placed at the end of the background queue which is allocated service only when the foreground queue is empty. The analysis focuses on the efficiency of the above systems by assuming a swap or set-up time (overhead cost) associated with the switching of programs on and off the processor. The analysis leads to generating functions for the equilibrium queue length probabilities, the moments of this latter distribution, and measures of mean waiting times. The paper concludes with a discussion of the results along with several examples.     

An inventory problem with obsolescence

A stochastic single product convex cost inventory problem is considered in which there is a probability, π_j, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.     

A simulated port facility in a theatre of operations

A hypothetical port facility in a theatre of operations is modeled and coded in a special purpose simulation language, for the purpose of conducting simulation experiments on a digital computer. The experiments are conducted to investigate the resource requirements necessary for the reception, discharge, and clearance of supplies at the port. Queue lengths, waiting times, facility utilizations, temporary storage levels, and ship turn-around times are analyzed as functions of transportation and cargo handling resources, using response surface methodology. The resulting response surfaces are revealing in regard to the sensitivity of port operations to transportation resource levels and the characteristics of the port facility's load factor. Two specific conclusions of significant value are derived. First, the simulation experiments clearly show that the standard procedures for determining discharge and clearance capacities take insufficient account of the effects of variability. Second, the response surfaces for ship turn-around times and temporary storage levels indicate that an extremely steep gradient exists as a function of troop levels.     

Approximate probability distributions for the extreme spread

The extreme spread, or greatest distance between all pairs of impact points on a target, is often used as a rapid measure of dispersion or precision of shot groups on a target. It is therefore desirable to know its statistical properties. Since the exact theoretical distribution has not yet been worked out, this paper examines the accuracy of several approximations which are checked against large sample monte carlo values. We find in particular that for the sample sizes considered the extreme spread can be approximated well by a Chi variate.     

The multicommodity network flow model revised to include vehicle per time period and node constraints

The minimum-cost formulation of the problem of determining multicommodity flows over a capacitated network subject to resource constraints has been treated in previobs papers. In those treatments only capacitated arcs were assumed and a uniform unit of measure like short tons was used for all commodities. This paper treats the effect of constraints on the nodes of the network, allows the commodities to be measured in their “natural” units and allows the network capacities to be expressed in vehicles per time period-in some cases giving a more accurate representation of the capacities of the network. This paper describes the solution procedure which uses the column generation technique; it also discusses computational experience.     

The economic effects of inspector error on attribute sampling plans

In this paper the effects of inspector error on a cost-based quality control system are investigated. The system examined is of a single sampling plan design involving several cost components. Both type I and type II inspector errors are considered. The model employs a process distribution, thus assuming that a stochastic process of some kind governs the quality of incoming lots. Optimal plan design is investigated under both error-free and error-prone inspection procedures and some comparisons are made.     

Least-absolute-value estimators for one-way and two-way tables

This paper concerns itself with the problem of estimating the parameters of one-way and two-way classification models by minimization of the sum of the absolute deviations of the regression function from the observed points. The one-way model reduces to obtaining a set of medians from which optimal parameters can be obtained by simple arithmetic manipulations. The two-way model is transformed into a specially structured linear programming problem, and two algorithms are presented to solve this problem. The occurrence of alternative optimal solutions in both models is discussed, and numerical examples are presented.     

The continuous multiple-modular design problem

In this article we extend our previous work on the continuous single-module design problem to the multiple-module case. It is assumed that there is a fixed cost associated with each additional module used. The Kuhn–Tucker conditions characterize local optima among which there is a global optimum. Modules are associated with partitions and a special class, guillotine partitions, are characterized. Branch-and-bound, partial enumeration, and heuristic procedures for finding optimum or good guillotine partitions are discussed and illustrated with examples.