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.     

An application of statistical techniques to estimate engineering man-hours on major aircraft programs

Data on 23 lots of various aircraft programs were gathered. Total engineering man-hours, and information on performance, weight, area, avionics systems, data, and schedule were subjected to least squares analysis. An equation is presented which indicates a relationship between total engineering manhours and a set of seven predictor variables. While the equation derived could only be used with confidence by the manufacturer whose data was analyzed, this article should be looked upon as demonstrating a method of data analysis which others may also find useful, not only for predicting engineering manhours in major aircraft programs, but also in other situations where there is an abundance of possible predictor variables, and the problem is to sort out a meaningful subset of these variables. In order to demonstrate the viability of the formula obtained, comparisons were made with various bid programs.     

Distribution of the workload in multiclass queueing systems with server vacations

The steady-state workload at an arbitrary time is considered for several single-server queueing systems with nonpreemptive services for multiple classes of customers (arriving according to Poisson processes) and server vacation (switchover) times. The distribution of the workload at an arbitrary point during the vacation period is obtained for systems with setup times, and for polling systems with exhaustive, gated, or globally gated service disciplines. From the stochastic decomposition property, this workload is added to the workload in the corresponding M/G/1 system without vacations to give the workload at an arbitrary time in vacation systems. Dependence of the workload distribution on the vacation parameters is studied.     

Evaluation of an integrated supplier-buyer quality-control system

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.     

Inference for the maximum cell probability under multinomial sampling

This article investigates inference for p_max, the largest cell probability in multinomial trials for the case of a small to moderate number of trials. Emphasis focuses on point and interval estimation. Both frequentist and Bayesian approaches are developed. The results of extensive simulation investigation are included as well as the analysis of a set of crime data for the city of New Orleans taken from the National Crime Survey.     

On the solution of a stochastic bottleneck assignment problem and its variations

In this article, we study the stochastic version of the so-called bottleneck assignment problem. Our primary objective is to maximize the probability that the bottleneck value satisfies a specified target. Under general stochastic assumptions, we show that the solution in this case is easily obtained by solving a linear assignment problem. We next examine the situation where the target is to be minimized, given that the probability of satisfying the target exceeds a specified threshold. Finally, we address extensions to the original problem where a second objective is also considered.     

A squared-euclidean distance location-allocation problem

This article is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.