Sojourn times in G/M/1 fork‐join networks

We consider a processing network in which jobs arrive at a fork‐node according to a renewal process. Each job requires the completion of m tasks, which are instantaneously assigned by the fork‐node to m task‐processing nodes that operate like G/M/1 queueing stations. The job is completed when all of its m tasks are finished. The sojourn time (or response time) of a job in this G/M/1 fork‐join network is the total time it takes to complete the m tasks. Our main result is a closed‐form approximation of the sojourn‐time distribution of a job that arrives in equilibrium. This is obtained by the use of bounds, properties of D/M/1 and M/M/1 fork‐join networks, and exploratory simulations. Statistical tests show that our approximation distributions are good fits for the sojourn‐time distributions obtained from simulations. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A lagrangean relaxation algorithm for the constrained matrix problem

We present variants of a convergent Lagrangean relaxation algorithm for minimizing a strictly convex separable quadratic function over a transportation polytope. The algorithm alternately solves two “subproblems,” each of which has an objective function that is defined by using Lagrange multipliers derived from the other. Motivated by the natural separation of the subproblems into independent and very easily solved “subsubproblems,” the algorithm can be interpreted as the cyclic coordinate ascent method applied to the dual problem. We exhibit our computational results for different implementations of the algorithm applied to a set of large constrained matrix problems.     

The proper balancing of repair and preventive maintenance activities in the determination of coordinated shipboard allowance lists

The determination as to the cost-effective number of spares for given types of items or equipment to be carried on board various types of ships is studied. This spare pool, known as the ship's COSAL, must provide prespecified levels of protection against stockouts for all uses of that item on board the given ship. This article derives and illustrates the methodology for optimally trading off the reduction in the ship's COSAL that can be gained by improving repair/resupply capabilities or by lowering the failure rate of the equipment through more or different types of preventive maintenance. A flexible class of preventive maintenance/repair response functions to cost is studied which are nonlinear and exhibit realistic diminishing returns. Two different types of assumptions are possible regarding the interdependencies of the resupply times across different ship types. A tractable budget allocation method is presented which can be used in a multiitem, multiship, multiechelon repair environment where there is one budget to cover all spares, all repair/resupply, and preventive maintenance activities. The technique incorporates different criticalities of shortages by type of ship and item. It can be used either in a budget building mode or a budget execution mode.     

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.     

Bounds on the availability function

This paper gives bounds on the availability function for an alternating renewal process with exponential failure and general repair times. A bound on the error is also given. Several of the bounds with greatest practical consequence are worked out and illustrated. Repair distributions for which a lower bound on availability is easily computed are gamma (integer shape parameter), log normal, and Weibull. Finally, some simulation results for log normal repair versus gamma repair are given.     

An algorithm for separable piecewise convex programming problems

We present a branch and bound algorithm to solve mathematical programming problems of the form: Find x =|(x₁,…x_n) to minimize Σ?_i0(x₁) subject to x?G, l≦x≦L and Σ?_i0(x₁)≦0, j=1,…,m. With l=(l₁,…,l_n) and L=(L₁,…,L_n), each ?_ij is assumed to be lower aemicontinuous and piecewise convex on the finite interval [l_i.L_i]. G is assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C={x|l ≦ x ≦L} on the bahis of the piecewise convexity of the problem functions ?_ij. Computational considerations are discussed, and an illustrative example is presented.     

Scheduling to minimize the weighted sum of completion times with secondary criteria

A result of Smith previously published in this journal [3], on the use of secondary criteria in scheduling problems, is shown to be incorrect and a counter example is presented. Heck and Roberts [2] suggested that their paper would be extended in the same way Smith's algorithm was. A new algorithm is given that converges to a local optimum for both problems.     

Systems analysis and planning-programming-budgeting systems (PPBS) for defense decision making

Systems analysis office titles have permeated both government and business organization charts in recent years. Systems analysis as a discipline, however, even though increasingly accepted, has eluded precise definition. For the most part, it has been loosely described as “quantitative common sense” and “the general application of the scientific method.” Emphasis is placed upon the application of eclectic disciplines to a wide variety of problems. Concepts and techniques have been drawn heavily from economics, mathematics, and political science. In the Department of Defense, systems analysis has been used extensively in the evaluation of weapon systems during the last 9 years. During the 1960's, it provided the underlying concepts for the control system PPBS (Planning-Programming-Budgeting System). This article traces the origins of systems analysis within the Department of Defense and describes and analyzes the application of the technique. Although there always exists disagreement, it is generally accepted that the origin of systems analysis coincided with the inception of R. S. McNamara's administration of the Department of Defense. McNamara organized the Systems Analysis office under Mr. Charles Hitch, who had previously developed many basic systems analysis concepts at project RAND. From Hitch's basic concepts, the approach became increasingly sophisticated in evaluating complex weapons systems. Coincidently, the organizational procedures for implementing systems analysis also evolved. Under the current Department of Defense administration, the new organizational procedures emerging are contrasted with the old.     

Properties of a multifacility location problem involving euclidian distances

This paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.