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.     

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.     

Minimal disconnecting sets in directed multi-commodity networks

The problem of finding minimal disconnecting sets for multi-commodity directed networks may be solved using an arc-path formulation and Gomory's all-integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.     

Expectation of contract incentives

The application of statistical expectation to risk density functions and fee/incentive-element relationships is shown to be useful in structuring contract incentives. A mathematical procedure for calculating the expected value of fee for a given risk/incentive arrangement is described along with cost examples and related sensitivity analyses. The structuring of equivalent incentives is demonstrated by the use of the contracting procedure used for procuring the C-5A aircraft.     

On the equivalence between the Node-ARC and ARC-Chain formulations for the multi-commodity maximal flow problem

The purpose of this article is to formulate the multi-commodity maximal flow problem into a node-arc form and to show that when decomposition is applied to this form the resulting master and subproblems become precisely those described by Ford & Fulkerson [3] using the arc-chain formulation. A generalization to the problem is then considered which can potentially speed its convergence.     

Sequencing many jobs on a multi-purpose facility

Suppose a given set of jobs has to be processed on a multi-purpose facility which has various settings or states. There is a choice of states in which to process a job and the cost of processing depends on the state. In addition, there is also a sequence-dependent changeover cost between states. The problem is then to schedule the jobs, and pick an optimum setting for each job, so as to minimize the overall operating costs. A dynamic programming model is developed for obtaining an optimal solution to the problem. The model is then extended using the method of successive approximations with a view to handling large-dimensioned problems. This extension yields good (but not necessarily optimal) solutions at a significant computational saving over the direct dynamic programming approach.     

A model for manpower productivity during organization growth

A mathematical model is developed that enables organization and manpower planners to quantify the inefficiencies involved in rapid buildups of organizations, such as is frequently found in the aerospace industry shortly after the award of a major contract. Consideration is given to the time required to train, indoctrinate, and familiarize new workers with their jobs and the general program aspects. Once trained, workers are assumed to be productive. If the ratio of untrained to trained workers exceeds a critical value, called the buildup threshold, then the performance of the trained workers is degraded to the extent that they are no longer 100 percent efficient until this ratio returns to a value less than the threshold. The model is sufficiently general to consider an arbitrary manpower plan with more than one peak or valley. The model outputs are functions of real time and consist of the fraction of the total labor force which is productive, the fraction of the total labor units expended for nonproductive effort, the cumulative labor costs for productive effort, and the cumulative labor cost for all effort.     

An acceptance life test for high-reliability products

This article introduces a replacement life-test procedure for the exponential failure rate: Failure-free operation of a unit for at least t_k consecutive time units is designated a “success”; the acceptance test is passed if and only if the first success is encountered before k unit failures have been recorded. Test plans are presented and the test is compared with the usual time-truncated test and to the truncated sequential probability ratio test. It is shown that this new test has smaller expected test time than the time truncated test when the true failure rate is small relative to the null hypothesized failure rate. Consistency and unbiasedness are proved and methods for making inferences on failure rate are described.