Optimal multicommodity network flows with resource allocation

The problem of determining multicommodity flows over a capacitated network subject to resource constraints may be solved by linear programming; however, the number of potential vectors in most applications is such that the standard arc-chain formulation becomes impractical. This paper describes an approach—an extension of the column generation technique used in the multicommodity network flow problem—that simultaneously considers network chain selection and resource allocation, thus making the problem both manageable and optimal. The flow attained is constrained by resource availability and network capacity. A minimum-cost formulation is described and an extension to permit the substitution of resources is developed. Computational experience with the model is discussed.     

On constraint qualifications in nonlinear programming

In this paper we examine the relationship between two constraint qualifications developed by Abadie and Arrow, Hurwicz, and Uzawa. A third constraint qualification is discussed and shown to be weaker than either of those mentioned above.     

A linear programming model for minimum-cost procurement and operation of marine corps training aircraft

In military situations of sharply increasing combat activity the Marine Corps is faced with training problems in its expanding aviator corps. Additional training aircraft are required, and procurement decisions must be made. In view of the significant costs involved in procurement and operation of new high performance aircraft, it is very desirable to buy and operate an efficient mix of aircraft necessary for training the pilots to make the Marine Aircraft Wings essentially 100-percent tactically qualified. The mathematical model presented here enables computation of a least-cost mix of training aircraft which satisfies certain specified training requirements. The basic element allowing tradeoffs is the commonality of training available in the F4, RF4, A6, and EA6 types of aircraft. Both airframe oriented and mission oriented training are necessary, but the airframe oriented training can be conducted in either of the aircraft possessing the commonality. Training requirements over a five year period are considered, and the mix of training aircraft has the minimum five year procurement and operating cost.     

Minimum cost sampling plans using bayesian methods

This article considers a general method for acceptance/rejection decisions in lot-by-lot sampling situations. Given arbitrary cost functions for sampling, accepting, and rejecting (where the cost can depend on the quality of the item) and a prior distribution on supplier quality, formulas are derived that lead to the minimal cost single-staged inspection plan. For the Bernoulli case, where each item is classified as acceptable or defective, the formulas simplify immensely. A computer code for solving the Bernoulli case is given.     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

A (Q,R) inventory model with lost sales and erlang-distributed lead times

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.     

An efficient heuristic for large set covering problems

A heuristic solution procedure for set covering is presented that works well for large, relatively dense problems. In addition, a confidence interval is established about the unknown global optimum. Results are presented for 30 large randomly generated problems.     

The two-on-one stochastic duel

The one-on-one stochastic duel is extended to the general two-on-one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.     

Testing goodness of fit to the increasing failure rate family

One branch of the reliability literature is concerned with devising statistical procedures with various nonparametric “restricted family” model assumptions because of the potential improved operating characteristics of such procedures over totally nonparametric ones. In the single-sample problem with unknown increasing failure rate (IFR) distribution F, (1) maximum-likelihood estimators of F have been calculated, (2) upper or lower tolerance limits for F have been determined, and (3) tests of the null hypothesis that F is exponential have been constructed. Barlow and Campo proposed graphical methods for assessing goodness of fit to the IFR model when the validity of this assumption is unknown. This article proposes several analytic tests of the IFR null hypothesis based on the maximum distance and area between the cumulative hazard function and its greatest convex minorant (GCM), and the maximum distance and area between the total time on test statistic and its GCM. A table of critical points is provided to implement a specific test having good overall power properties.