A finite-range distribution of failure times

Properties of a finite-range failure-time distribution, that includes the exponential as a particular case, have been studied. The distribution is IFR when the shape parameter exceeds unity, but is IFRA always. For a given value of the shape parameter, the distribution is NBUE over a segment of its range. Estimators of parameters have been derived. Distributions of two-component series, parallel, and standby system lives have also been worked out.     

Armed services recruiting research: Issues,findings, and needs

Manning the nation's armed services will continue to be a crucial issue for the remainder of the 1980s. With the projected growth of the services during this decade, the downturn in the 17–21-year-old male population, and the possible upturn in the economy, the ability of the services to meet their respective quality and quantity recruiting goals becomes of central concern. The accurate estimation of the supply for various types of recruits becomes especially important when one views the nearly $1 billion budgeted annually for recruiting and the impact that any military pay raises can have on the DOD's manpower costs of over $40 billion annually. In addition, perceived difficulties in recruiting can impact on weapon systems design decisions, authorized manning levels, and exacerbate the debate concerning the draft; hence, it is clear that few issues today warrant more attention than improving the efficiency and effectiveness of military recruiting. This article provides an introduction and review of some of the key issues involved in modeling and estimating the supply of military recruits. It summarizes and compares the findings of selected econometric models, all of which are based on enlistment experience since the introduction of the All-Volunteer Force in 1973. It also presents some new insights and directions for research dealing with simultaneity, validation, generation of rigorous confidence intervals, and data base selection. It concludes by listing some of the research needs to be addressed in the future.     

An efficient primal approach to bottleneck transportation problems

This article addresses bottleneck linear programming problems and in particular capacitated and constrained bottleneck transportation problems. A pseudopricing procedure based on the poly-ω procedure is used to facilitate the primal simplex procedure. This process allows the recent computational developments such as the Extended Threaded Index Method to be applied to bottleneck transportation problems. The impact on problem solution times is illustrated by computational testing and comparison with other current methods.     

The knapsack problem: A survey

A unifying survey of the literature related to the knapsack problem; that is, maximize \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {v_i x_{i,} } $\end{document}, subject to \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_j {w_i x_i W} $\end{document} and x_i ? 0, integer; where v_i, w_i and W are known integers, and w_i (i = 1, 2, …, N) and W are positive. Various uses, including those in group theory and in other integer programming algorithms, as well as applications from the literature, are discussed. Dynamic programming, branch and bound, search enumeration, heuristic methods, and other solution techniques are presented. Computational experience, and extensions of the knapsack problem, such as to the multi-dimensional case, are also considered.     

Exact first and second order moments of order statistics from the truncated exponential distribution

Exact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances-covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.     

Scheduling jobs,with exponentially distributed processing times,on two machines of a flow shop

This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.     

Structured markovian decision problems

Structured finite action-finite state space discounted Markovian decision problems are analyzed. Any problem of a general class is shown to be equivalent to a “separated” problem with decomposable problem structure. A modified policy iteration approach is developed for this decomposable reformulation. Both analytic and computer evaluations of the decomposition algorithm's effectiveness are presented.     

Concave minimization over a convex polyhedron

A general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed-charge problem, the separable concave programming problem, the quadratic problem, and the 0-1 mixed integer problem are discussed. Computer results for the fixed-charge problem are also presented.     

Allocation of resources to offensive strategic weapon systems

In this paper a very versatile game model is developed for use in the long range planning of our strategic force posture. This highly aggregate model yields optimal force mixes for the triad (land- and sea-based missile systems and bombers) under a variety of constraints. The model described here is a survivability model; however, it is shown how the model can still be used as a measure of overall system effectiveness. Constraints imposed on the problem include both SALT and budget limitations.     

A survey of maintenance models: The control and surveillance of deteriorating systems

The literature on maintenance models is surveyed. The focus is on work appearing since the 1965 survey, “Maintenance Policies for Stochastically Failing Equipment: A Survey” by John McCall and the 1965 book, The Mathematical Theory of Reliability, by Richard Barlow and Frank Proschan. The survey includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.