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.     

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.     

Adaptive forecasting of the size of a work force subject to random withdrawals

Adaptive forecasting procedures are developed for predicting the size of a work force which is subject to random withdrawals. The procedures are illustrated using Marine Corps data in which four stages of service for incoming cohorts are distinguished. Using these data, three forecasting procedures—conditional maximum likelihood estimation of prediction intervals; tolerance intervals; and Bayes prediction intervals—are compared.     

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.     

Optimum sequential search with discrete locations and random acceptance errors

Much work has been done in search theory; however, very little effort has occurred where an object's presence at a location can be accepted when no object is present there. The case analyzed is of this type. The number of locations is finite, a single object is stationary at one location, and only one location is observed each step of the search. The object's location has a known prior probability distribution. Also known are the conditional probability of acceptance given the object's absence (small) and the conditional probability of rejection given the object's presence (not too large); these Probabilities remain fixed for all searching and locations. The class of sequential search policies which terminate the search at the first acceptance is assumed. A single two-part optimization criterion is considered. The search sequence is found which (i) minimizes the probability of obtaining n rejections in the first n steps for all n, and (ii) maximizes the probability that the first acceptance occurs within the first n steps and occurs at the object's location for all n. The optimum sequential search policy specifies that the next location observed is one with the largest posterior probability of the object's presence (evaluated after each step from Bayes Rule) and that the object is at the first location where acceptance occurs. Placement at the first acceptance seems appropriate when the conditional probability of acceptance given the object's absence is sufficiently small. Search always terminates (with probability one). Optimum truncated sequential policies are also considered. Methods are given for evaluating some pertinent properties and for investigating the possibility that no object occurs at any location.     

Large deviation probabilities for order statistics

Asymptotic representations are found for the large deviation probabilities that the nα-th order statistic exceeds δ, where δ>α. The probabilities are first expressed in terms of the empirical distribution function, and then the 1960 theorem of Bahadur and Ranga Rao is applied. The result is then shown to be more precise than a logarithmic statement in a 1969 paper of Sievers dealing with the asymptotic relative efficiency of the sample median test.     

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.