bluuebunny/crossref_metadata_2025 huggingface dataset:
Shock models with phase type survival and shock resistance
Authors: Neuts Marcel F. , Bhattacharjee Manish C.
Published: May 2007

New closure theorems for shock models in reliability theory are presented. If the number of shocks to failure and the times between the arrivals of shocks have probability distributions of phase type, then so has the time to failure. PH‐distributions are highly versatile and may be used to model many qualitative features of practical interest. They are also well‐suited for algorithmic implementation. The computational aspects of our results are discussed in some detail.
An early‐accept modification to the test plans of military standard 781C
Authors: Butler David A. , Lieberman Gerald J.
Published: May 2007

This paper is concerned with the statistical test plans contained in Military Standard 781C, “Reliability Design Qualification and Production Acceptance Tests: Exponential Distribution” and the selection and use of these plans. Modifications to the fixed‐length test plans of MIL‐STD‐781C are presented which allow early‐accept decisions to be made without sacrificing statistical validity. The proposed plans differ from the probability ratio sequential tests in the Standard in that rejection is permitted only after a fixed number of failures have been observed.
Optimal ordering policies when anticipating parameter changes in EOQ systems
Authors: Lev B. , Weiss H. J. , Soyster A. L.
Published: May 2007

The classical Economic Order Quantity Model requires the parameters of the model to be constant. Some EOQ models allow a single parameter to change with time. We consider EOQ systems in which one or more of the cost or demand parameters will change at some time in the future. The system we examine has two distinct advantages over previous models. One obvious advantage is that a change in any of the costs is likely to affect the demand rate and we allow for this. The second advantage is that often, the times that prices will rise are fairly well known by announcement or previous experience. We present the optimal ordering policy for these inventory systems with anticipated changes and a simple method for computing the optimal policy. For cases where the changes are in the distant future we present a myopic policy that yields costs which are near‐optimal. In cases where the changes will occur in the relatively near future the optimal policy is significantly better than the myopic policy.
Postoptimality analysis in nonlinear integer programming: The right‐hand side case
Authors: Cooper Mary W.
Published: May 2007

An algorithm is presented to gain postoptimality data about the family of nonlinear pure integer programming problems in which the objective function and constraints remain the same except for changes in the right‐hand side of the constraints. It is possible to solve such families of problems simultaneously to give a global optimum for each problem in the family, with additional problems solved in under 2 CPU seconds. This represents a small fraction of the time necessary to solve each problem individually.
An iterative algorithm for the multifacility minimax location problem with euclidean distances
Authors: Charalambous Christakis
Published: May 2007

An iterative solution method is presented for solving the multifacility location problem with Euclidean distances under the minimax criterion. The iterative procedure is based on the transformation of the multifacility minimax problem into a sequence of squared Euclidean minisum problems which have analytical solutions. Computational experience with the new method is also presented.
The estimation of P(x < Y) for distributions useful in life testing
Authors: Basu A. P.
Published: May 2007

In this paper the reliability function K = P(X < Y) has been estimated when X and Y follow gamma, exponential or bivariate exponential distributions. The paper is partly expository.
Expedients for solving some specially structured mixed‐integer programs
Authors: Sherali Hanif D.
Published: May 2007

In this paper we consider dual angular and angular structured mixed integer programs which arise in some practical applications. For these problems we describe efficient methods for generating a desirable set of Benders' cuts with which one may initialize the partitioning scheme of Benders. Our research is motivated by the computational experience of McDaniel and Devine who have shown that the set of Benders' cuts which are binding at the optimum to the linear relaxation of the mixed integer program, play an important role in determining an optimal mixed integer solution. As incidental results in our development, we provide some useful remarks regarding Benders' and Dantzig‐Wolfe's decomposition procedures. The computational experience reported seems to support the expedients recommended in this paper.
Optimal control for entry of many classes of customers to an M/M/1 queue
Authors: Rue Robert C. , Rosenshine Matthew
Published: May 2007

A method is developed for determining the optimal policy for entry of customers from many independent classes of Poisson arrivals to a first‐come, first‐serve (for customers admitted to the queue) single‐server queue with exponential service times. The solution technique utilizes a semi‐Markov formulation or the decision problem.
Stochastic duels with displacements (suppression)
Authors: Williams G. Trevor , Ancker C. J.
Published: May 2007

The stochastic duel is extended to include the possibility of a near‐miss on each round fired, which causes the opponent to displace. During displacement, the displacing contestant cannot return the fire but is still a target for his opponent. An alternative interpretation of this model is to consider the displacement time as the time a contestant's fire is suppressed by his opponent's fire and that he does not move, but merely ceases fire temporarily. All times are exponentially distributed.
A versatile scheme for ranking the extreme points of an assignment polytope
Authors: Bazaraa Mokhtar S. , Sherali Hanif D.
Published: May 2007

A cutting plane scheme embedded in an implicit enumeration framework is proposed for ranking the extreme points of linear assignment problems. This method is capable of ranking any desired number of extreme points at each possible objective function value. The technique overcomes storage difficulties by being able to perform the ranking at any particular objective function value independently of other objective values. Computational experience on some test problems is provided.
Exact analysis of a two‐echelon inventory system for recoverable items under batch inspection policy
Authors: Shanker Kripa
Published: May 2007

We investigate a two‐echelon (base‐depot) inventory system of recoverable (repairable) items. The arrivals of demand at the bases are in a Poisson manner and the order sizes are random. The failed units can be repaired either at the base or at the depot, and the units beyond economic repair are condemned. Inspection of the failed units is carried out in the batches they arrive, that is, arrival batches are not broken up. The exact expressions for stationary distribution of depot inventory position, and of the number of backorders, onhand inventory, in‐repair inventory at all locations are derived under the assumptions of constant repair and lead times. Special cases of complete recoverability, nonrecoverability, and of the unit order size are also discussed.
Fluctuations of the optimal advertising and inventory policy: A qualitative analysis
Authors: Balcer Yves
Published: May 2007

This paper discusses the properties of the inventory and advertising policy minimizing the expected discounted cost over a finite horizon in a dynamic nonstationary inventory model with random demand which is influenced by the level of promotion or goodwill. Attention is focused on the relation between the fluctuations over time of the optimal policies and the variations over time of the factors involved, i.e., demand distributions and various costs. The optimal policies are proved to be monotone in the various factors. Also, three types of fluctuations over time of the optimal policies are discussed according to which factor varies over time. For example, if over a finite interval, the random demand increases (stochastically) from one period to the next, reaches a maximum and then decreases, then the optimal inventory level will do the same. Also the period of maximum of demand never precedes that of maximum inventory. The optimal advertising behaves in the opposite way and its minimum will occur at the same time as the maximum of the inventory. The model has a linear inventory ordering cost and instantaneous delivery of stocks; many results, however, are extended to models with a convex ordering cost or a delivery time lag.
Minimizing costs of sequential and parallel personnel testing programs
Authors: Feigin Paul D. , Harel Gedaliahu H.
Published: May 2007

We consider groups of tests for personnel selection purposes in which each test has a known a priori probability of being failed, such failure resulting in outright rejection and termination of testing. Each test has a fixed cost and given duration. We consider the minimization of the total expected cost due to both the fixed costs and the delay costs when the tests may be conducted sequentially or in parallel. In the latter situation, a heuristic algorithm is proposed and illustrated.
Time minimizing flows in directed networks
Authors: Hinkle Robert G. , Jarvis John J.
Published: May 2007

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time‐minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time‐minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.
The hnbue and hnwue classes of life distributions
Authors: Klefsjö Bengt
Published: May 2007

Different properties of the HNBUE (HNWUE) class of life distributions (i.e.), for which \documentclass{article}\pagestyle{empty}\begin{document}$\int_t^\infty {\,\,\,\mathop F\limits^-(x)\,dx\, \le \,(\ge)\,\mu }\]$\end{document} exp(−t/μ) for t ≥ 0, where μ = \documentclass{article}\pagestyle{empty}\begin{document}$\int_t^\infty {\,\,\,\mathop F\limits^-(x)\,dx}$\end{document} are presented. For instance we characterize the HNBUE (HNWUE) property by using the Laplace transform and present some bounds on the survival function of a HNBUE (HNWUE) life distribution. We also examine whether the HNBUE (HNWUE) property is preserved under the reliability operations (i) formation of coherent structure, (ii) convolution and (iii) mixture. The class of distributions with the discrete HNBUE (discrete HNWUE) property (i.e.), for which \documentclass{article}\pagestyle{empty}\begin{document}$\sum\limits_{j=k}^\infty {\mathop{\mathop P\limits^-_{j\,\,\,}\, \le(\ge)\,\mu(1 - 1/\mu)^{^k }}\limits^{}} $\end{document} for k = 0, 1, 2, ⃛, where μ =\documentclass{article}\pagestyle{empty}\begin{document}$\sum\limits_{j=0}^\infty {\mathop {\mathop P\limits^- _{j\,\,\,\,\,}and\mathop P\limits^ - _{j\,\,\,\,\,}=}\limits^{}}\,\,\sum\limits_{k=j+1}^\infty {P_k)}$\end{document}
is also studied.
Cost analysis of pro rata and free‐replacement warranties
Authors: Mamer John W.
Published: May 2007

This article examines the short run total costs and long run average costs of products under warranty. Formulae for both consumer cost under warranty and producer profit are derived. The results in the case of the pro rata warranty correct a mistake appearing in Blischke and Scheuer [5]. We also show that expected average cost to both the producer and the consumer of a product under warranty depends on both the mean of the product lifetime distribution and on its failure rate.
Theoretical analysis of the general linear model for lanchester ‐ type combat between two homogeneous forces
Authors: Taylor James G.
Published: May 2007

This paper studies Lanchester‐type combat between two homogeneous forces modeled by the so‐called general linear model with continuous replacements/withdrawals. It demonstrates that this model can be transformed into a simpler canonical form, which is also shown to arise from fixed‐force‐level‐breakpoint battles modeled by Lanchester‐type equations for modern warfare. Analytical expressions for the force levels for the general variable coefficient linear model with continuous replacements/withdrawals are constructed out of so‐called general Lanchester functions for the model without replacements/withdrawals, for which all solutions are shown to be nonoscillatory in the strict sense. These force‐level results are unfortunately so complicated and opaque that the constant‐coefficient version of the model must be studied before any insights into the dynamics of combat may be analytically obtained. Thus, fairly complete results are given for the general linear model with constant attrition‐rate coefficients and constant rates of replacement/withdrawal. However, the expressions for the force levels are still so complicated that we have not been able to develop battle‐outcome prediction conditions directly from them alone but have had to establish general results on the qualitative behavior of solutions. A significant result (and one that greatly complicates the prediction of battle outcome) is that all solutions to the model with replacements/withdrawals are no longer necessarily nonoscillatory in the strict sense, i.e., both sides force levels can take on negative values if the force‐on‐force attrition equations are not “turned off” at the right time. Thus, this paper shows that the addition of continuous replacements/withdrawals to a Lanchester‐type model may significantly change the qualitative behavior of the force‐level trajectories. Battle‐outcome prediction conditions are nevertheless given, and important insights into the dynamics of combat are briefly indicated.
The logarithmic poisson gamma distribution: A model for leadtime demand
Authors: Nahmias Steven , Steven Demmy W.
Published: May 2007

This paper considers an inventory system in which demand occurrences arise according to a stationary Poisson process, demand sizes at each occurrence follow a logarithmic distribution, and leadtimes are random variables with the gamma distribution. Both the exact and approximate distribution for leadtime demand are derived and computations are performed which compare the approximation to the exact distribution. The results have application to both repairable and consumable item inventory systems.
The observed hazard and multicomponent systems
Authors: Brown Mark , Ross Sheldon M.
Published: May 2007

Let X denote the life of some system. We define the observed hazard rate at time t, call it R (t), as the instantaneous probability (density) of failure of X at time t given survival up to t and given a complete description of the system state at t. We conjecture that the total observed hazard—namely, σoX R(t)dt—is an exponential random variable with mean 1 and verify this for the special case when X is the distribution of system life of an n component system having an arbitrary monotone structure function.
A replacement schedule for multicomponent life‐limited parts
Authors: Epstein Sheldon , Wilamowsky Yonah
Published: May 2007

In previous papers [1], [2] the authors developed a maintenance policy for a single life‐limited part. Using an opportunistic replacement approach a scheme was devised which utilized early replacement of equipment to offset more costly future expenditures. This paper will extend the results to the multicomponent case. Examples are given illustrating the benefits of this new technique.
An efficient primal approach to bottleneck transportation problems
Authors: Russell Robert A. , Klingman Darwin D. , Partow‐Navid Parviz
Published: May 2007

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.
A method for reducing coefficients in integer linear inequalities
Authors: Wilson J. M.
Published: May 2007

Approaches are considered for the reduction of coefficients in linear integer inequalities. It is shown that coefficients may be reduced easily in many practical examples. The (0‐1) problem is also reconsidered and certain areas of exploration developed.
An advanced dual algorithm with constraint relaxation for all‐integer programming
Authors: Austin Larry M. , Ghandforoush Parviz
Published: May 2007

In this article we present an all‐integer cutting plane algorithm called the Reduced Advanced Start Algorithm (RASA). The technique incorporates an infeasible advanced start based on the optimal solution to the LP relaxation, and initially discards nonbinding constraints in this solution. We discuss the results of computational testing on a set of standard problems and illustrate the operation of the algorithm with three small examples.
Assessment of hazardous‐inspection policies
Authors: Chou Chung‐Kuang , Butler David A.
Published: May 2007

Inspection procedures may at times pose a hazard to the system being monitored. In this article, a simple hazardous‐inspection model is considered. The character of the optimal ongoing inspection policy (for inspections subsequent to the first) is reviewed, and the possible forms of the optimal initiation policy are established. Efficient computational procedures are developed for calculating optimal policies. Some discussion is included of the counterintuitive nature of some of the results.
Solvable cases of the flow‐shop problem without interruptions in job processing
Authors: Szwarc Wlodzimierz
Published: May 2007

This article examines solvable cases of the flow‐shop problem without interruptions in job processing where the completion time is being minimized. All those cases utilize Gilmore‐Gomory's algorithm. A lower completion time bound is also provided.
Multiple resource leveling in construction systems through variation of activity intensities
Authors: Leachman Robert C.
Published: May 2007

The resource leveling problem for a construction system producing a stream of output units is considered. The system is modeled using a critical‐path‐analysis activity network, from which an extended network is developed for an integrated planning effort of all output units. Activity intensity variables are defined which measure activity demand rates for resources and consequent activity durations for the production of each output unit. A heuristic approach consisting of an iterative nonlinear programming procedure is presented which computes activity durations (intensities) for the minimization of resource capacity costs subject to meeting construction due dates. The application to a major ship overhaul project is described, in which the procedure was used to level workloads of the various labor–trade shops.
Optimal control of entry to an M/Ek/1 queue serving several classes of customers
Authors: Rue Robert C. , Rosenshine Matthew
Published: May 2007

The individual and social optimum control policies for entry to an M/M//1 queue serving several classes of customers have been shown to be control‐limit policies. The technique of policy iteration provides the social optimum policy for such a queue in a straightforward manner. In this article, the problem of finding the optimal control policy for the M/Ek/1 system is solved, thereby expanding the potential applicability of the solutions developed. The Markovian nature of the queueing system is preserved by considering the service as having k sequential phases, each with independent, identically distributed, exponential service times, through which a customer must pass to be serviced. The optimal policy derived by policy iteration for such a system is likely to be difficult to use because it requires knowledge of the number of phases rather than customers in the system when an arrival occurs. To circumvent this difficulty, a heuristic is used to find a good usable (implementable) solution. In addition, a mixed‐integer program is developed which yields the optimal implementable solution when solved.
Optimal admission pricing and service rate control of an M[x]/M/s queue with reneging
Authors: Anderson Michael Q.
Published: May 2007

In this article we consider the optimal control of an M[X]/M/s queue, s ≧ 1. In addition to Poisson bulk arrivals we incorporate a reneging function. Subject to control are an admission price p and the service rate μ. Thus, through p, balking response is induced. When i customers are present a cost h(i,μ,p) per unit time is incurred, discounted continuously. Formulated as a continuous time Markov decision process, conditions are given under which the optimal admission price and optimal service rate are each nondecreasing functions of i. In Section 4 we indicate how the infinite state space may be truncated to a finite state space for computational purposes.
A note on first passage times in birth and death and nonnegative diffusion processes
Authors: Derman Cyrus , Ross Sheldon M. , Schechner Zvi
Published: May 2007

Consider a birth and death process starting in state 0. Keilson has shown by analytical arguments that the time of first passage into state n has an increasing failure rate (IFR) distribution. We present a probabilistic proof for this. In addition, our proof shows that for a nonnegative diffusion process, the first passage time from state 0 to any state x is IFR.
A branch‐and‐bound‐based heuristic for solving the quadratic assignment problem
Authors: Bazaraa M. S. , Kirca O.
Published: May 2007

In this article a branch‐and‐bound algorithm is proposed for solving the quadratic assignment problem. Using symmetric properties of the problem, the algorithm eliminates “mirror image” branches, thus reducing the search effort. Several routines that transform the procedure into an efficient heuristic are also implemented. These include certain 2‐way and 4‐way exchanges, selective branching rules, and the use of variable upper‐bounding techniques for enhancing the speed of fathoming. The computational results are quite encouraging. As an exact scheme, the algorithm solved the 12‐facility problem of Nugent et al. and the 19‐facility problem of Elshafei. More importantly, as a heuristic, the procedure produced the best known solutions for all well‐known problems in the literature, and produced improved solutions in several cases.
Minimax and maximin facility location problems on a sphere
Authors: Drezner Zvi , Wesolowsky George O.
Published: May 2007

The problem dealt with in this article is as follows. There are n “demand points” on a sphere. Each demand point has a weight which is a positive constant. A facility must be located so that the maximum of the weighted distances (distances are the shortest arcs on the surface of the sphere) is minimized; this is called the minimax problem. Alternatively, in the maximin problem, the minimum weighted distance is maximized. A setup cost associated with each demand point may be added for generality. It is shown that any maximin problem can be reparametrized into a minimax problem. A method for finding local minimax points is described and conditions under which these are global are derived. Finally, an efficient algorithm for finding the global minimax point is constructed.
Stochastic duels with multiple hits and limited ammunition supply
Authors: Kwon Tai Young , Bai Do Sun
Published: May 2007

Ancker's stochastic duels with limited ammunition supply are extended to cases where a kill is obtained through repetitive multiple hits with two firing modes, single‐shot firing and pattern firing. Examples with negative exponential firing time and geometric ammunition supply are given.
The truncated normal–gamma mixture as a distribution for lead time demand
Authors: Ord J. K. , Bagchi U.
Published: May 2007

A central problem in inventory control concerns the statistical description of total demand during the lead time between placement and receipt of an order. Since both the demand per unit time and the lead time are random variables, the distribution of lead time demand is formulated as a mixture. In application, one or both components of the mixture are often assumed to be normally distributed despite their nonnegativity. In practice, this assumption is taken to imply that a normal curve, truncated at zero, is a valid description. Several approximations to the true tail area probabilities (given truncation) are examined. In turn, this leads to an improved and simpler expression for the normal–gamma mixture. Some numerical results are also presented.
Parameter estimation for the EOQ lot‐size model: Minimax and expected value choices
Authors: Lowe Timothy J. , Schwarz Leroy B.
Published: May 2007

This article provides formulas for estimating the parameters to be used in the basic EOQ lot‐size model. The analysis assumes that the true values of these parameters are unknown over known ranges and perhaps nonstationary over time. Two measures of estimator “goodness” are derived from EOQ sensitivity analysis. Formulas are given for computing the minimax choice and the minimum expected value choice for the parameter estimates using both measures of estimator “goodness”. A numerical example is included.
Optimal replacement under additive damage in randomly varying environments
Authors: Waldmann K.‐H.
Published: May 2007

A system is subject to a sequence of randomly occurring shocks. Each shock causes a random amount of damage which accumulates additively. Any of the shocks might cause the system to fail. The shock process is in some sense related to an environmental process in order to describe randomly varying external factors of an economical and/or technical nature as well as internal factors of a statistical nature. A discrete time formulation of the problem is given. Sufficient conditions are found for optimality of a generalized control‐limit rule with respect to the total cost criterion: Whenever the accumulated damage s is not less than a specified critical number t(i), depending on the environmental state i, replace the system by a new one; otherwise do not replace it. Moreover, bounds are given for these critical numbers.
An optimality condition for a nondifferentiable convex program
Authors: Wolkowicz Henry
Published: May 2007

An optimality condition for the ordinary convex programming problem which utilizes the directional derivatives of the constraints is studied.
The effect of stochastic time delays on the reliability of isolated impulse systems
Authors: Bendell A.
Published: May 2007

This article concerns the effect of stochastic time delays in the operation of components upon system reliability for isolated impulse systems, for which component delays have hitherto been treated as deterministic. These are systems, such as automatic protective devices, which remain idle for most of their lives but which are required to respond with the utmost speed to input signals arising at arbitrary isolated time instants. System failure can arise from components failing to operate, or from being too slow to operate so that the systems operation is too slow to meet requirements. During operation components are usually subjected to greater stresses than during idling, so that it is assumed that components are subjected to increased failure tendencies during the time it takes them to perform their functions. The effect of stochastic time delays on the evaluation of systems reliability is considered, and a hierarchy of complexity associated with the physical nature of the delays in series and redundant configurations is exposed. Some simple exponential illustrations are presented.
The proper balancing of repair and preventive maintenance activities in the determination of coordinated shipboard allowance lists
Authors: Landsdowne Zachary F. , Morey Richard C.
Published: May 2007

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.
A transportation problem with competition
Authors: Marchi Ezio , Tarazaga Pablo
Published: May 2007

The classic transportation problem can be generalized with many carriers and one owner. From the formulation the competition in sense of game theory naturally appears. Here we present and solve this problem using a generalized n‐person game. Besides the same composition properties about solutions and regarding zones, related results are considered. Finally, the problem in which there is a modification of the set of destinations assigned to the carriers is also studied.
Armed services recruiting research: Issues, findings, and needs
Authors: Morey Richard C. , McCann John M.
Published: May 2007

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.
On a rational stopping rule for facilities location algorithms
Authors: Juel Henrik
Published: May 2007

In the multifacility location problem, a number of new facilities are to be located so as to minimize a sum of weighted distances. Recently, a lower bound on the optimal value was developed, for use in deciding when to stop an iterative solution procedure. We develop a stronger bound that allows some computational savings.
Some branch‐and‐bound procedures for fixed‐cost transportation problems
Authors: Cabot A. Victor , Erenguc S. Selcuk
Published: May 2007

In this article we present three properties that will improve the performance of branch‐and‐bound algorithms for fixed‐cost transportation problems. By applying Lagrangian relaxation we show that one can develop stronger up and down penalties than those traditionally used and also develop a strengthened penalty for nonbasic variables. We also show that it is possible to “look ahead” of a particular node and determine the solution at the next node without actually calculating it. We present computational evidence by comparing our developments with existing procedures.
A characterization of the wald distribution
Authors: Ahsanullah M. , Kirmani S. N. U. A.
Published: May 2007

SupposeXis a random variable having an absolutely continuous distribution functionF(x). We assume thatF(x) has the Wald distribution. A relation between the probability density function ofX−1with that ofXis used to characterize the Wald distribution.
On efficient salvo policies
Authors: Gould Jerren
Published: May 2007

This article demonstrates that whenever the probability of single‐shot kill is nondecreasing (from one salvo to the next), then the sequence of salvo sizes which minimizes the expected number of shots used is also nondecreasing.
An efficient heuristic for large set covering problems
Authors: Vasko Francis J.
Published: May 2007

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.
On the optimal policies of an exponential machine repair problem
Authors: Lehtonen Tapani
Published: May 2007

We consider an exponential repair model with s machines and one repairman. The machines' failure rates are equal but the repair rate may change from machine to machine. The repairman repairs the failed machines one at a time and in the course of his work he may even interrupt repairing one machine and start another. We compare repair policies and prove an optimality result by means of stochastic order. The proof is based on representing the compared models simultaneously in a special way and comparing then the sample paths of the interesting stochastic processes.
Disaggregation in economic models
Authors: Tiplitz Charles
Published: May 2007

This article illustrates numerically that the adjustment path of the economy will not show how a national policymaker may be misled by overaggregation until it is too late for correction. Labor and other resources are overaggregated in the equilibrating mechanism of most economic models, tending to mislead policymakers regarding both the amount and direction of change of important variables. Overaggregation also hides important constraints and tradeoffs which masks opportunities to use slack resources. In turn, this creates unnecessary dilemmas, such as that between inflation and unemployment which plagued the progress of the Humphrey‐Hawkins Bill. The article first illustrates the hypothesis using simple models. Then its relevance to current analysis and planning is discussed.
A family of games on 1,∞)2 with payoff a function of y/x
Authors: Heuer G. A.
Published: May 2007

A two‐parameter class of games on 1,∞)2 is studied. The games may be regarded as analogs of Silverman games, having continuous payoff function in place of a step function of y/x. This change is motivated by a desire to move toward a model for competitive situations where the penalty for overspending increases with the amount of overspending. There are some similarities to games with bell‐shaped kernel. For most of the region considered in the plane of the two parameters there are solutions of finite type, which are obtained explicitly. There are, however, pockets in this plane where no optimal strategies have been found and possibly where none of finite type exist.
Scheduling stochastic jobs on a single machine subject to breakdowns
Authors: Glazebrook K. D.
Published: May 2007

A single machine is available to process a collection of stochastic jobs. There may be technological constraints on the job set. The machine sometimes breaks down. Costs are incurred and rewards are earned during processing. We seek strategies for processing the jobs which maximize the total expected reward earned.
Continuous‐time markov decision processes with nonzero terminal reward
Authors: Jo Kyung Y.
Published: May 2007

In this article we consider a continuous‐time Markov decision process with a denumerable state space and nonzero terminal rewards. We first establish the necessary and sufficient optimality condition without any restriction on the cost functions. The necessary condition is derived through the Pontryagin maximum principle and the sufficient condition, by the inherent structure of the problem. We introduce a dynamic programming approximation algorithm for the finite‐horizon problem. As the time between discrete points decreases, the optimal policy of the discretized problem converges to that of the continuous‐time problem in the sense of weak convergence. For the infinite‐horizon problem, a successive approximation method is introduced as an alternative to a policy iteration method.
The stochastic duel with time‐dependent hit probabilities
Authors: Ancker C. J.
Published: May 2007

The fundamental stochastic duel considers two opponents who fire at each other at either random continuous or fixed‐time intervals with a constant hit probability on each round fired. Each starts with an unloaded weapon, unlimited ammunition, and unlimited time. The first to hit wins. In this article we extend the theory to the case where hit probabilities are functions of the time since the duel began. First, the marksman firing at a passive target is considered and the characteristic function of the time to a hit is developed. Then, the probability of a given side winning the duel is derived. General solutions for a wide class of hit probability functions are derived. Specific examples of both the marksman and the duel problem are given.
Hu's precedence tree scheduling algorithm: A simple proof
Authors: McHugh James A. M.
Published: May 2007

This article presents a simple proof of Hu's algorithm for scheduling in minimum time a set of tasks constrained by precedence tree constraints, each task requiring a unit time to complete, and where m processors are available.
Quadratic forms in spherical random variables: Generalized noncentral x2 distribution
Authors: Cacoullos T. , Koutras M.
Published: May 2007

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi‐square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.
Estimating the common location parameter of exponential distributions with censored samples
Authors: Chiou Wen‐Jau , Cohen Arthur
Published: May 2007

Consider the problem of estimating the common location parameter of two exponential distributions when censored samples are taken. The unique minimum variance unbiased estimator (UMVUE) is found along with an expression for its variance. The asymptotic distribution is given for a special case and a generalized Bayes property is exhibited. Extensions include the case of k > 2 populations. Also the UMVUE is found for P(Y > X) and certain reliability functions.
Optimal policy of continuous and discrete replacement with minimal repair at failure
Authors: Nakagawa Toshio
Published: May 2007

This article considers combined continuous and discrete replacement with minimal repair at failure, in which a unit is replaced at time T or at number N of uses. Both optimal time T* and number N* to minimize the expected cost rate are discussed. They are found by unique solutions of equations when the hazard rates are monotonously increasing. A numerical example is given.
Application of disjunctive programming to the linear complementarity problem
Authors: Ramarao B. , Shetty C. M.
Published: May 2007

In this article we address the question of developing deep cuts for disjunctive programs using rectilinear distance measures. The method is applied to linear complementarity problems where the matrix M need not be copositive plus. Some modifications that are needed as a computational expediency are discussed. The computation results for matrix M of size up to 30 × 30 are discussed.
Layered defense of deceptively based ICBMs
Authors: Bracken Jerome
Published: May 2007

The basing of ICBMs is a fundamental problem of defense analysis. Deceptive basing and antiballistic missile defense are two of the methods available to attempt to insure that there are ICBMs surviving after undergoing an attack. This article treats tradeoffs among missiles, silos or shelters, exoatmospheric interceptors, and endoatmospheric interceptors. Most of the analysis deals with 200 missiles, the number of MX missiles which were recommended to be moved among the 4600 shelters of the Multiple Protective Shelter (MPS) deployment, though some variants in the number of missiles (from 115 to 400) are also treated here. The basic reference point of the analysis is the provision of 1000 ICBM warheads delivered in a second strike. The combination of exoatmospheric interceptors and endoatmospheric interceptors is referred to as “layered defense.” Warheads are destroyed by interceptors after the warheads separate from the missile which carries them. Exoatmospheric interceptors are assumed to achieve a non‐nuclear kill, while endoatmospheric interceptors are assumed to achieve either a non‐nuclear or nuclear kill, depending on the technology available to both sides. Exoatmospheric interceptors may be capable of protecting value targets against the warheads of a second strike. To the extent that this can be achieved, they facilitate a first strike with relative impunity and hence are destabilizing. This article explores various layered defense topics.
Multistate reliability models
Authors: Ebrahimi Nader
Published: May 2007

Most of the reliability literature deals with binary systems of binary components in which the only two states are functioning or failed. In this article two types of multistate coherent system (MCS) have been introduced. Various properties of our definitions are studied. The relationship between our definitions of MCS and other definitions of MCS in the literature are discussed.
Some pros and cons of MIL‐STD‐414
Authors: Perry Darrell D.
Published: May 2007

MIL‐STD‐414 has been in existence in its original form since 1957. Obviously, there are some things that are right about 414. But there are some changes to the standard that are long overdue. This article presents some pros and cons of 414 and a recommendation that it be replaced by a MIL‐STD‐414A. Two concerns regarding ANSI/ASQC Z1.9 are discussed.
Minimum cost sampling plans using bayesian methods
Authors: Lorenzen Thomas J.
Published: May 2007

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.
Bilateral phase‐type distributions
Authors: Shanthikumar J. G.
Published: May 2007

In this article we define a class of distributions called bilateral phase type (BPH), and study its closure and computational properties. The class of BPH distributions is closed under convolution, negative convolution, and mixtures. The one‐sided version of BPH, called generalized phase type (GPH), is also defined. The class of GPH distributions is strictly larger than the class of phase‐type distributions introduced by Neuts, and is closed under convolution, negative convolution with nonnegativity condition, mixtures, and formation of coherent systems. We give computational schemes to compute the resulting distributions from the above operations and extend them to analyze queueing processes. In particular, we present efficient algorithms to compute the steady‐state and transient waiting times in GPH/GPH/1 queues and a simple algorithm to compute the steady‐state waiting time in M/GPH/1 queues.
A finite algorithm for concave minimization over a polyhedron
Authors: Benson Harold P.
Published: May 2007

We present a new algorithm for solving the problem of minimizing a nonseparable concave function over a polyhedron. The algorithm is of the branch‐and‐bound type. It finds a globally optimal extreme point solution for this problem in a finite number of steps. One of the major advantages of the algorithm is that the linear programming subproblems solved during the branch‐and‐bound search each have the same feasible region. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some preliminary computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several bilinear programming problems with the code.
Three‐machine flowshop stochastic scheduling to minimize distribution of schedule length
Authors: Frostig E. , Adiri I.
Published: May 2007

This article studies a special case of stochastic three‐machine, permutation flowshop scheduling. It is proved that a sequence where processing times on the first and third machines are in a monotone nondecreasing and nonincreasing order of the likelihood ratio, respectively, and on the second machine are equally distributed, minimizes distribution of schedule length.
Sensitivity analysis of the optimal location of a facility
Authors: Drezner Zvi
Published: May 2007

We perform a sensitivity analysis of the Euclidean, single‐facility minisum problem, which is also known as the Weber problem. We find the sensitivity of the optimal site of the new facility to changes in the locations and weights of the demand points. We apply these results to get the optimal site if some of the parameters in the problem are changed. We also get approximate formulas for the set of all possible optimal sites if demand points are restricted to given areas, and weights must be within given ranges, which is a location problem under conditions of uncertainty.