bluuebunny/crossref_metadata_2025 huggingface dataset:
Analyzing availability using transfer function models and cross spectral analysis
Authors: Singpurwalla Nozer D.
Published: May 2007

If we look at the literature of reliability and life testing we do not see much on the use of the powerful methods of time series analysis. In this paper we show how the methods of multivariate time series analysis can be used in a novel way to investigate the interrelationships between a series of operating (running) times and a series of maintenance (down) times of a complex system. Specifically, we apply the techniques of cross spectral analysis to help us obtain a Box‐Jenkins type transfer function model for the running times and the down times of a nuclear reactor. A knowledge of the interrelationships between the running times and the down times is useful for an evaluation of maintenance policies, for replacement policy decisions, and for evaluating the availability and the readiness of complex systems.
Optimal admission pricing policies for M/Ek/1 queues
Authors: Anderson Michael Q.
Published: May 2007

This paper extends the Low‐Lippman M/M/1 model to the case of Gamma service times. Specifically, we have a queue in which arrivals are Poisson, service time is Gamma‐distributed, and the arrival rate to the system is subject to setting an admission fee p. The arrival rate λ(p) is non‐increasing in p. We prove that the optimal admission fee p* is a non‐decreasing function of the customer work load on the server. The proof is for an infinite capacity queue and holds for the infinite horizon continuous time Markov decision process. In the special case of exponential service time, we extend the Low‐Lippman model to include a state‐dependent service rate and service cost structure (for finite or infinite time horizon and queue capacity). Relatively recent dynamic programming techniques are employed throughout the paper. Due to the large class of functions represented by the Gamma family, the extension is of interest and utility.
Theoretical analysis of lanchester‐type combat between two homogeneous forces with supporting fires
Authors: Taylor James G.
Published: May 2007

This paper studies combat between two homogeneous forces modelled with variable‐coefficient Lanchester‐type equations of modern warfare with supporting fires not subject to attrition. It shows that this linear differential‐equation model for combat with supporting fires may be transformed into one without the supporting fires so that all the previous results for variable‐coefficient Lanchester‐type equations of modern warfare (without supporting fires) may be invoked. Consequently, new important results for representing the solution (i.e. force levels as functions of time) in terms of canonical Lanchester functions and also for predicting force annihilation are developed for this model with supporting fires. Important insights into the dynamics of combat between two homogeneous forces with such supporting fires are discussed.
On single‐machine sequencing with order constraints
Authors: Glazebrook K. D.
Published: May 2007

A collection of jobs is to be processed by a single machine. Each job has a cost function associated with it which may be either linear or exponential, costs accruing when a job is completed. The machine may be allocated to the jobs according to a precedence relation. The problem is to find a strategy for allocating the machine which minimizes the total cost and which is consistent with the precedence relation. The paper extends and simplifies some previous work done by Sidney.
Computational experience on an algorithm for the transportation problem with nonlinear objective functions
Authors: Rao Ram C. , Shaftel Timothy L.
Published: May 2007

This paper explores computational implications of allowing nonlinear objective functions in the transportation problem. Two types of nonlinearities, including polynomials, are studied. The choice of these functions resulted from our interest in models of integrated water management. Zangwill's convex simplex method and the primal method of transportation problem form the basis of our algorithm. Innovative features of our work are compact storage and efficient computation procedures. We study the effects on computation time of problem size; the density of nonlinear terms; the size of tolerances for stopping rules; and rules for choice of new variables to enter the solution. We find that problems up to 95 × 95 in size are capable of reasonably fast solution. A particularly surprising finding is that one‐dimensional search for improving solutions performs adequately, at least for the kinds of problems posed in this paper. We are encouraged by our results and believe that models involving nonlinear objective functions may be tractable even for relatively large problems, thus making possible more accurate descriptions of real situations.
Statistical analysis of a conventional fuze timer
Authors: Cohen Edgar A.
Published: May 2007

In this paper, a statistical analytic model for evaluation of the performance of a standard electric bomb fuze timer is presented. The model is based on what is called a selective design assembly, where one item, namely, a resistor, is used to time the circuit. In such an assembly, the remaining components are chosen a priori from predetermined distributions. Based on the analysis, a general numerical integration scheme is utilized for assessing performance of the timer. The results of a computer simulation are also given. In the last section of the paper, a theory for evaluation of the yield of two or more timers designed to operate in sequence is derived. To appraise such a scheme, a numerical quadrature routine is developed.
The asymptotic sufficiency of sparse order statistics in tests of fit with nuisance parameters
Authors: Weiss Lionel
Published: May 2007

In an earlier paper, it was shown that for the problem of testing that a sample comes from a completely specified distribution, a relatively small number of order statistics is asymptotically sufficient, and for all asymptotic probability calculations the joint distribution of these order statistics can be assumed to be normal. In the present paper, these results are extended to certain cases where the problem is to test the hypothesis that a sample comes from a distribution which is a member of a specified parametric family of distributions, with the parameters unspecified.
On a class of nash‐solvable bimatrix games and some related nash subsets
Authors: Isaacson Karen , Millham C. B.
Published: May 2007

This work is concerned with a particular class of bimatrix games, the set of equilibrium points of which games possess many of the properties of solutions to zero‐sum games, including susceptibility to solution by linear programming. Results in a more general setting are also included. Some of the results are believed to constitute interesting potential additions to elementary courses in game theory.
Optimality conditions for convex semi‐infinite programming problems
Authors: Ben‐Tal A. , Kerzner L. , Zlobec S.
Published: May 2007

This paper gives characterization of optimal Solutions for convex semiinfinite programming problems. These characterizations are free of a constraint qualification assumption. Thus they overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn‐Tucker theories, which give only necessary or sufficient conditions for optimality, but not both.
Sequencing independent jobs with a single resource
Authors: Baker Kenneth R. , Nuttle Henry L. W.
Published: May 2007

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well‐known results for single‐machine problems which can be applied with little or no modification to the corresponding variable‐resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.
A note on the optimal replacement time of damaged devices
Authors: Zuckerman Dror
Published: May 2007

Abdel Hameed and Shimi [1] in a recent paper considered a shock model with additive damage. This note generalizes the work of Abdel Hameed and Shimi by showing that the a‐priori restriction to replacement at a shock time made in [1] is unnecessary.
A note on the sensitivity of navy first term reenlistment to bonuses, unemployment and relative wages
Authors: Cohen Les , Reedy Diane Erickson
Published: May 2007

Multiple regression analysis of first term reenlistment rates over the period 1968–1977 confirms previous findings that reenlistment is highly sensitive to unemployment at the time of reenlistment and shortly after enlistment, almost four years earlier. Bonuses, particularly lump sum bonuses, were also shown to be a significant determinant of reenlistment.
Equalities in transportation problems and characterizations of optimal solutions
Authors: Kortanek Kenneth O. , Yamasaki Maretsugu
Published: May 2007

This paper considers the classical finite linear transportation Problem (I) and two relaxations, (II) and (III), of it based on papers by Kantorovich and Rubinstein, and Kretschmer. Pseudo‐metric type conditions on the cost matrix are given under which Problems (I) and (II) have common optimal value, and a proper subset of these conditions is sufficient for Problems (II) and (III) to have common optimal value. The relationships between the three problems provide a proof of Kantorovich's original characterization of optimal solutions to the standard transportation problem having as many origins as destinations. The result are extended to problems having cost matrices which are nonnegative row‐column equivalent.
An easy solution for a special class of fixed charge problems
Authors: McKeown Patrick G. , Sinha Prabhakant
Published: May 2007

The fixed charge problem is a mixed integer mathematical programming problem which has proved difficult to solve in the past. In this paper we look at a special case of that problem and show that this case can be solved by formulating it as a set‐covering problem. We then use a branch‐and‐bound integer programming code to solve test fixed charge problems using the setcovering formulation. Even without a special purpose set‐covering algorithm, the results from this solution procedure are dramatically better than those obtained using other solution procedures.
The M/G/1 queue with instantaneous bernoulli feedback
Authors: Disney Ralph L. , McNickle Donald C. , Simon Burton
Published: May 2007

In this paper we are concerned with several random processes that occur in M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Queue length processes embedded at various times are studied. It is shown that these do not all have the same asymptotic distribution, and that in general none of the output, input, or feedback processes is renewal. These results have implications in the application of certain decomposition results to queueing networks.
Concentrated firing in many‐versus‐many duels
Authors: Zinger A.
Published: May 2007

A simple stochastic‐duel model, based on alternate firing, is proposed. This model is shown to be asymptotically equivalent, for small hit probabilities, to other known models, such as simple and square duels. Alternate firing introduces an interaction between opponents and allows one to consider multiple duels. Conditions under which concentrated firing is better or worse than parallel firing are found by calculation and sometimes by simulation. The only parameters considered are the combat group sizes (all units within a group are assumed identical), the hit probabilities and the number of hits necessary to destroy an opposing unit.
A linear programming model for design of communications networks with time varying probabilistic demands
Authors: Kortanek K. O. , Lee D. N. , Polak G. G.
Published: May 2007

In this paper marginal investment costs are assumed known for two kinds of equipment stocks employed to supply telecommunications services: trunks and switching facilities. A network hierarchy is defined which includes important cases occurring in the field and also appearing in the literature. A different use of the classical concept of the marginal capacity of an additional trunk at prescribed blocking probability leads to a linear programming supply model which can be used to compute the sizes of all the high usage trunk groups. The sizes of the remaining trunk groups are approximated by the linear programming models, but can be determined more accurately by alternate methods once all high usage group sizes are computed. The approach applies to larger scale networks than previously reported in the literature and permits direct application of the duality theory of linear programming and its sensitivity analyses to the study and design of switched probabilistic communications networks with multiple busy hours during the day. Numerical results are presented for two examples based on field data, one of which having been designed by the multi‐hour engineering method.
Optimal maintenance models for systems subject to failure–A Review
Authors: Sherif Y. S. , Smith M. L.
Published: May 2007

This paper is a state‐of‐the‐art review of the literature related to optimal maintenance models of systems subject to failure. The emphasis is on work appearing since the 1976 survey, “A Survey of Maintenance Models: The Control and Surveillance of Deteriorating Systems,” by W.P. Pierskalla and J.A. Voelker, published in this journal.
Bounds for strength‐stress interference via mathematical programming
Authors: Kim Geung‐Ho
Published: May 2007

Problems of bounding Pr {X > Y}, when the distribution of X is subject to certain moment conditions and the distribution of Y is known to be of convexconcave type, are treated in the framework of mathematical programming. Juxtaposed are two programming methods; one is based on the notion of weak duality and the other on the geometry of a certain moment space.
Bounds and elimination in generalized markov decisions
Authors: Koehler Gary J.
Published: May 2007

In discounted Markov decision processes bounds on the optimal value function can be computed and used to eliminate suboptimal actions. In this paper we extend these procedures to the generalized Markov decision process. In so doing we forfeit the contraction property and must base our analysis on other procedures. Duality theory and the Perron‐Frobenius theorem are the main tools.
Maximal nash subsets for bimatrix games
Authors: Jansen M. J. M.
Published: May 2007

In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.
An empirical evaluation of further approximations to an approximate continuous review inventory model
Authors: Byrkett Donald L.
Published: May 2007

This paper describes an empirical evaluation of several approximations to Hadley and Whitin's approximate continuous review inventory model with backorders. It is assumed that lead time demand is normally distributed and various exponential functions are used to approximate the upper tail of this distribution. These approximations offer two important advantages in computing reorder points and reorder quantities. One advantage is that normal tables are no longer required to obtain solutions, and a second advantage is that solutions may be obtained directly rather than iteratively. These approximations are evaluated on two distinct inventory systems. It is shown that an increase in average annual cost of less that 1% is expected as a result of using these approximations. The only exception to this statement is with inventory systems in which a high shortage cost is specified and ordering costs are unusually low.
A note on optimal switching between two activities
Authors: Shreve Steven E.
Published: May 2007

Let f1 and f2 map [0, T] into the real numbers. A system is following either f1 or f2 and earning the associated reward ∫ f1 or ∫ f2, respectively. It is possible at any time to switch from fi to fj by paying a switching cost b > 0. We determine a switching policy which maximizes the total reward. Conditions which guarantee a planning horizon are established.
A two‐state system with partial availability in the failed state
Authors: Baxter Laurence A.
Published: May 2007

A generalization of the alternating renewal model of a repairable system to permit partial availability in the failed state is introduced. It is shown how, by making use of an embedded alternating renewal process, we can readily derive expressions for various measures of system availability. Expressions for the point availability of the generalized process are presented.
Analytic approximations for (s,S) inventory policy operating characteristics
Authors: Ehrhardt Richard
Published: May 2007

The operating characteristics of (s,S) inventory systems are often difficult to compute, making systems analysis a tedious and often expensive undertaking. Approximate expressions for operating characteristics are presented with a view towards simplified analysis of systems behavior.

The operating characteristics under consideration are the expected values of: total cost per period, period‐end inventory, period‐end stockout quantity, replenishment cost per period, and backlog frequency. The approximations are obtained by a two step procedure. First, exact expressions for the operating characteristics are approximated by simplified functions. Then the approximations are used to design regression models which are fitted to the operating characteristics of a large number of inventory items with diverse parameter settings. Accuracy to within a few percent of actual values is typical for most of the approximations.
Counterexamples to optimal permutation schedules for certain flow shop problems
Authors: Panwalkar S. S. , Smith M. L. , Woollam C. R.
Published: May 2007

It is well known that a minimal makespan permutation sequence exists for the n × 3 flow shop problem and for the n × m flow shop problem with no inprocess waiting when processing times for both types of problems are positive. It is shown in this paper that when the assumption of positive processing times is relaxed to include nonnegative processing times, optimality of permutation schedules cannot be guaranteed.
A new bivariate negative binomial distribution
Authors: Mitchell C. R. , Paulson A. S.
Published: May 2007

A new bivariate negative binomial distribution is derived by convoluting an existing bivariate geometric distribution; the probability function has six parameters and admits of positive or negative correlations and linear or nonlinear regressions. Given are the moments to order two and, for special cases, the regression function and a recursive formula for the probabilities. Purely numerical procedures are utilized in obtaining maximum likelihood estimates of the parameters. A data set with a nonlinear empirical regression function and another with negative sample correlation coefficient are discussed.
Minimax inspection strategies for single unit systems
Authors: Beichelt F.
Published: May 2007

A model for proper scheduling of inspections is considered, if system failures can be detected only by checking. Two cases are analyzed: replacement and no replacement of a failed system. On condition that no or only partial information on the lifetime distribution of the system is available, minimax inspection strategies are obtained with respect to cost criterions.
A differential equation model of search for randomly arriving and departing targets
Authors: Chelst Kenneth R.
Published: May 2007

In this paper we analyze optimal search strategies in an environment in which multiple, independent targets arrive and depart at random. The analysis revolves around a continuous time differential equation model which captures the time dependent nature of the search process. We explore the impact on optimal strategies of nonzero travel times between regions as well as differing target arrival rates. We derive simple closed form expressions for determining if only one region should be searched.
Optimal stopping problems for differential equations perturbed by a poisson process
Authors: Wickwire K. H.
Published: May 2007

We investigate a class of optimal stopping problems for dynamical systems described by one‐dimensional differential equations with an additive Poisson disturbance. The rate of the disturbance may depend upon the current state of the system. A dynamic programming equation for the optimal stopping cost is derived along with conditions which must be met at the boundary of the optimal stopping set. These boundary conditions depend upon whether or not the stopping set may be entered by smooth motion.
Optimal control of price through restricted production
Authors: Lippman Steven A. , Winston Wayne L.
Published: May 2007

Consider a regulated monopolist whose current profits would be maximized if they could charge a price p̄, where p̄ exceeds the current market price. By reducing production below current consumer demand the monopolist can create an illusion of a shortage and induce the regulator to allow a price increase. Conditions are given for which the production rate that maximizes the monopolist's expected discounted profits over an infinite horizon will have the property that the amount of unsatisfied consumer demand will be a non‐increasing function of current market price.
Estimation in single server queues
Authors: Basawa I. V. , Prabhu N. U.
Published: May 2007

Moment and maximum likelihood estimates (m.l.e.'s) arc investigated for nonparametric and parametric models for a single server queue observed over a random time horizon, namely, up to the nth departure epoch. Also. m.l.e's of the mean interarrival time and mean service time in anM/M/1 queue observed over a fixed time‐interval are studied Limit distributions of these estimates are obtained Without imposing steady state assumptions on the queue‐size or waiting time processes.
On the optimal allocation of crewmen aboard a warship
Authors: Zuidweg J. K. , Van Dam J.
Published: May 2007

In the temporarily isolated situation in which a warship finds itself during a mission. not only spare parts, but also “spare” crewmen in various categories of specialization must he on board.

Mathematical models for the probabilities of mission survival for personnel and for personnel and materiel jointly are proposed. A practical example is worked out: the optimal allocation of spare crewmen to different categories of specialization is calculated.
A primal‐dual cutting‐plane algorithm for all‐integer programming
Authors: Ghandforoush Parviz , Austin Larry M.
Published: May 2007

The integer programming literature contains many algorithms for solving all‐integer programming problems but, in general, existing algorithms are less than satisfactory even in solving problems of modest size. In this paper we present a new technique for solving the all‐integer, integer programming problem. This algorithm is a hybrid (i.e., primal‐dual) cutting‐plane method which alternates between a primal‐feasible stage related to Young's simplified primal algorithm, and a dual‐infeasible stage related to Gomory's dual all‐integer algorithm. We present the results of computational testing.
Computing the discounted return in markov and semi‐markov chains
Authors: Porteus Evan L.
Published: May 2007

This paper addresses the problem of computing the expected discounted return in finite Markov and semi‐Markov chains. The objective is to reveal insights into two questions. First, which iterative methods hold the most promise? Second, when are interative methods preferred to Gaussian elimination? A set of twenty‐seven randomly generated problems is used to compare the performance of the methods considered. The observations that apply to the problems generated here are as follows: Gauss‐Seidel is not preferred to Pre‐Jacobi in general. However, if the matrix is reordered in a certain way and the author's row sum extrapolation is used, then Gauss‐Seidel is preferred. Transforming a semi‐Markov problem into a Markov one using a transformation that comes from Schweitzer does not yield improved performance. A method analogous to symmetric successive overrelaxation (SSOR) in numerical analysis yields improved performance, especially when the row‐sum extrapolation is used only sparingly. This method is then compared to Gaussian elimination and is found to be superior for most of the problems generated.
A branch‐and‐bound algorithm for solving fixed charge problems
Authors: McKeown Patrick G.
Published: May 2007

Numerous procedures have been suggested for solving fixed charge problems. Among these are branch‐and‐bound methods, cutting plane methods, and vertex ranking methods. In all of these previous approaches, the procedure depends heavily on the continuous costs to terminate the search for the optimal solution. In this paper, we present a new branch‐and‐bound algorithm that calculates bounds separately on the sum of fixed costs and on the continuous objective value. Computational experience is shown for various standard test problems as well as for randomly generated problems. These test results are compared to previous procedures as well as to a mixed integer code. These comparisons appear promising.
Minimizing the average deviation of job completion times about a common due date
Authors: Kanet John J.
Published: May 2007

This paper considers a single‐machine scheduling problem in which penalities occur when a job is completed early or late. The objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions for jobs. A procedure is presented for finding an optimal schedule.
A mathematical model for generating the area of a drainage basin
Authors: Robinson R. T.
Published: May 2007

This paper presents a mathematical model that yields the area drained by a naturally‐occurring network of streams. The model is based on empirically derived relationships in the field of quantitative geomorphology and an assumption concerning the probabilistic nature of stream system formation. A wide range of model solutions is indicated, and the model is validated by comparing the results to statistics from actual stream systems.
A note on the flow‐shop problem without interruptions in job processing
Authors: Szwarc Wlodzimierz
Published: May 2007

This paper deals with a flow‐shop problem where the n jobs are being processed uninterrupted by m machines. A comprehensive theory based on “an earliest starting time of a job” concept produced the most efficient solution method for a variety of optimization criteria. The paper also rectifies several known results in this area.
A note on two IFR systems
Authors: Schechner Zvi
Published: May 2007

We present probabilistic proofs for the following two facts: (i) A k out of n system of i.i.d (independent identically distributed). IFR (increasing failure rate) components has an IFR life distribution. (ii) A compound Poisson process with nonnegative i.i.d jumps with PF2 distribution is IFR.
Optimal strategies in a game of economic survival
Authors: Borch Karl
Published: May 2007

The games of economic survival introduced by Shubik and Thompson seem tailor‐made for the analysis of some problems in insurance and have found many applications in this industry. The optimal strategy in such games may be a so‐called “band strategy.” This result seems counter‐intuitive and has caused some puzzlement. This paper gives sufficient conditions so that the optimal strategy will be of a simpler form, and it is argued that these conditions are satisfied in most applications to insurance.
Diagnostic analysis of inventory systems: An optimization approach
Authors: Bitran Gabriel R. , Hax Arnoldo C. , Valor‐Sabatier Josep
Published: May 2007

The objective of a diagnostic analysis is to provide a measure of performance of an existing system and estimate the benefits of implementing a new one, if necessary. Firms expect diagnostic studies to be done promptly and inexpensively. Consequently, collection and manipulation of large quantities of data are prohibitive. In this paper we explore aggregate optimization models as tools for diagnostic analysis of inventory systems. We concentrate on the dynamic lot size problem with a family of items sharing the same setup, and on the management of perishable items. We provide upper and lower bounds on the total cost to be expected from the implementation of appropriate systems. However, the major thrust of the paper is to illustrate an approach to analyze inventory systems that could be expanded to cover a wide variety of applications. A fundamental by‐product of the proposed diagnostic methodology is to identify the characteristics that items should share to be aggregated into a single family.
The class of mifra lifetimes and its relation to other classes
Authors: Block Henry W. , Savits Thomas H.
Published: May 2007

In a previous paper, the authors have introduced a class of multivariate lifetimes (MIFRA) which generalize the univariate lifetimes with increasing failure rate average (IFRA). They have also shown that this class satisfies many fundamental properties. In this paper it is shown that other concepts of multivariate IFRA do not satisfy all of these properties. Relationships between MIFRA and these other concepts are given. Finally, positive dependence implications with respect to these classes are also discussed.
Remarks on a univariate shock model with some bivariate generalizations
Authors: Griffith William S.
Published: May 2007

In a 1973 paper J. D. Esary, A. W. Marshall, and F. Proschan [5] considered a shock model giving rise to various nonparametric classes of life distributions of interest in reliability theory. A number of authors have extended these results in a variety of directions. In this paper, alternative proofs of the increasing failure rate (IFR) and decreasing mean residual life (DMRL) results are given which do not make use of the theory of total positivity. Some bivariate extensions are then obtained using a shock model similar to that originally used by H. W. Block, A. S. Paulson, and R. C. Kohberger [2] to unify various bivariate exponential distributions.
Asymptotic joint normality of an increasing number of multivariate order statistics and associated cell frequencies
Authors: Weiss Lionel
Published: May 2007

Take n independent identically distributed (IID) observations from a continuous r‐variate population, and choose some order statistics from each of the r variates. These order statistics are used to construct a grid in r‐dimensional space. Under certain conditions, it is shown that as n increases we can choose an increasing number of order statistics in such a way that the asymptotic joint distribution of the chosen order statistics and of the frequencies of sample points falling in the cells of the grid can be assumed to be a normal distribution. An application to testing independence of random variables is given.
Reformulating zero‐sum games with multiple goals
Authors: Hannan Edward L.
Published: May 2007

This paper investigates the two‐person zero‐sum multiple payoff game in which the objective is to minimize a player's total underachievement from a fixed set of goals. It is demonstrated that a previous formulation of this problem can be substantially simplified.
On a generalized bin‐packing problem
Authors: Lewis R. T. , Parker R. G.
Published: May 2007

In this paper we address a bin‐packing problem which possesses a variety of modifications of the classic theme. Among these are bin‐dependent chip weights, bin costs, and bin‐dependent penalties for unused capacity. Lagrangian relaxations are employed in the context of a branch‐and‐bound framework in order to solve the problem after which substantial computational experience is provided.
A note on solving multifacility location problems involving euclidean distances
Authors: Juel Henrik
Published: May 2007

This note considers a recently proposed solution method for a multifacility location problem. It is shown that the method does not always produce an optimal solution.
A combined approach to solve binary multicriteria problems
Authors: Bitran Gabriel R. , Rivera Jorge M.
Published: May 2007

An implicit enumeration algorithm is developed to determine the set of efficient points in zero‐one multiple criteria problems. The algorithm is specialized for the solution of a particular class of facility location problems. The procedure is complemented with the use of the utility function of the decision maker to identify a subset of efficient point candidates for the final selection. Computational results are provided and discussed.
The discrete search problem and the construction of optimal allocations
Authors: Wegener Ingo
Published: May 2007

Suppose one object is hidden in the k‐th of n boxes with probability p(k). The boxes are to be searched sequentially. Associated with the j‐th search of box k is a cost c(j,k) and a conditional probability q(j,k) that the first j ‐ 1 searches of box k are unsuccessful while the j‐th search is successful given that the object is hidden in box k.

The problem is to maximize the probability that we find the object if we are not allowed to offer more than L for the search. We prove the existence of an optimal allocation of the search effort L and state an algorithm for the construction of an optimal allocation. Finally, we discuss some problems concerning the complexity of our problem.
Search techniques for a nonlinear multiprocessor scheduling problem
Authors: Price Camille C. , Pooch Udo W.
Published: May 2007

The problem of assigning computer program modules to functionally similar processors in a distributed computer network is investigated. The modules of a program must be assigned among processors in such a way as to minimize interprocessor communication while taking advantage of affinities of certain modules to particular processors. This problem is formulated as a zero‐one quadratic programming problem, but is more conveniently modeled as a directed acyclic search graph. The model is developed and a backward shortest path labeling algorithm is given that produces an assignment of program modules to processors. A non‐backtracking branch‐and‐bound algorithm is described that uses a local neighborhood search at each stage of the search graph.
Least‐absolute‐deviations position finding
Authors: Book Stephen A.
Published: May 2007

Position finding has historically been carried out by calculating the coordinates of the mean position via a least‐squares procedure based on the distance of the position from several direction lines. It has been suggested that the least‐squares procedure assigns too much weight to outliers among the set of direction lines, outliers which may actually be associated with objects other than the one being located. In this paper, a method of using least‐absolute deviations, which yields a more outlier‐resistant median estimate of the position instead of the least‐squares mean estimate, is presented.
Production‐location problems
Authors: Hurter Arthur P. , Venta Enrique R.
Published: May 2007

The joint problems of determining the optimal plant location and optimal input mix and plant size are addressed. The interrelationship between input substitutability and plant location is stressed. Conditions under which the location problem can be separated from the determination of the optimal input mix are developed for a number of problem variations. The stability of the optimal location in the face of changes in problem parameters is also discussed. It is demonstrated that consideration of input substitutability often makes the resulting problem no more difficult to solve than problem formulations in which the inherent input substitutability is ignored.
Econometric forecasting via discounted least squares
Authors: Agnew Robert A.
Published: May 2007

Simple direct smoothing formulas are derived for updating coefficient estimates and forecasts in a discounted least squares model. These formulas are the natural extensions of R. G. Brown's well‐known smoothing formulas to a general econometric setting with arbitrary explanatory time series. The recursive updating process and its forecast error properties are illustrated via a simple, yet realistic numerical example.
Spares stocking policies for repairable items with dependent repair times
Authors: Scudder Gary D. , Hausman Warren H.
Published: May 2007

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.
The outfit planning problem: Production planning in shipbuilding
Authors: Graves R. J. , McGinnis L. F.
Published: May 2007

Shipbuilding as currently practiced in U.S. commercial shipyards employs little quantitative modeling or analysis in production planning. This paper presents a brief discussion of the shipbuilding process and focuses on one major component which is referred to as outfitting. The outfit planning problem is described in detail and then formally modeled as a generalization of the resource constrained project scheduling problem. The value of the approach as well as barriers to its adoption are also discussed.
Selecting among weibull, lognormal and gamma distributions using complete and censored smaples
Authors: Siswadi  , Quesenberry C. P.
Published: May 2007

In a recent paper, Kent and Quesenberry [19] considered using certain optimal invariant statistics to select the best fitting member of a collection of probability distributions using complete samples of life data. In the present work extensions of this approach in two directions are given. First, selection for complete samples based on scale and shape invariant statistics is considered. Next, the selection problem for type I censored samples is considered, and both scale invariant and maximum likelihood selection procedures are studied. The two‐parameter (scale and shape) Weibull, lognormal, and gamma distributions are considered and applications to real data are given. Results from a (small) comparative simulation study are presented.
A time series analysis of some interrelated logistics performance variables
Authors: Singpurwalla Nozer D. , Talbott Carlos M.
Published: May 2007

This paper is a case study. We show how the powerful methods of time series analysis can be used to investigate the interrelationships between Alert Availability, a logistics performance variable, and Flying Hours, an operational requirement, in the presence of a major change in operating procedures and using contaminated data. The system considered is the fleet of C‐141 aircraft of the U.S. Air Force. The major change in operating procedures was brought about by what is known as Reliability Centered Maintenance, and the contaminated data were due to anomalies in reporting procedures. The technique used is a combination of transfer function modeling and intervention analysis.
Application of level crossing analysis to discrete state processes in queueing systems
Authors: Shanthikumar J. G. , Chandra M. Jeya
Published: May 2007

In this paper we introduce a discrete state level crossing analysis and present some basic results and a key theorem of level crossings. We illustrate the fertility of the discrete state level crossing analysis by applying it to queueing systems with (i) bulk arrival, (ii) instantaneous feedback, (iii) limited waiting space, and (iv) to machine interference problems.
Equivalence relations in the theory of repetitive consumption
Authors: Balintfy Joseph L. , Melachrinoudis Emmanuel S.
Published: May 2007

Preference for food in the function of the time since last consumption and total preference in the function of eating frequency are equivalent mathematical representations of attitudes governing food consumption. The observed and postulated properties of these functions imply a formal correspondence between preference maximizing and variety seeking behavior.
A sampling procedure and public policy
Authors: Lieberman G. J. , Olkin I. , Riddle F.
Published: May 2007

This paper describes the background of the Office of Management Budget Circular A‐21, “Principles for Determining Costs Applicable to Grants, Contracts, and Other Agreements with Educational Institutions,” that describes the requirement for effort reporting. A sampling procedure is proposed as an alternative to 100% reporting.
Some limiting distributions associated with sequences of multinomial trials
Authors: Arnold B. C. , Angus J. E.
Published: May 2007

A series of independent trials is considered in which one of k ≥ 2 mutually exclusive and exhaustive outcomes occurs at each trial. The series terminates when m outcomes of any one type have occurred. The limiting distribution (as m → ∞) of the number of trials performed until termination is found with particular attention to the situation where a Dirichlet distribution is assigned to the k vector of probabilities for each outcome. Applications to series of races involving k runners and to spares problems in reliability modeling are discussed. The problem of selecting a stopping rule so that the probability of the series terminating on outcome i is k−1 (i.e., a “fair” competition) is also studied. Two generalizations of the original asymptotic problem are addressed.
Computing demand properties at the wholesale warehouse level
Authors: Schultz Carl R.
Published: May 2007

Computational formulas are given for the mean, variance, and autocorrelation function of the demand process at an upper‐echelon facility (warehouse). The demand process at the warehouse is induced by the aggregated inventory replenishment processes of N independently operated lower‐echelon facilities (stores) in parallel. Each store, we assume, employs an (s,S) inventory replenishment policy with complete backlogging to satisfy its own random, independently and identically distributed demand. The formulas result from an analysis of the stochastic replenishment process at a single store. Examples of the properties of the demand process at the upper‐echelon facility are presented for several lower‐echelon environments.
Approximate decision rules for continuous review inventory systems
Authors: Gardner Everette S.
Published: May 2007

Constrained multi‐item inventory models have long presented signifcant computational problems. This article presents a general algorithm to obtain simultaneous solutions for order quantities and safety stocks for each line item in an inventory, while satisfying constraints on average inventory investment and reordering workload. Computational experience is presented that demonstrates the algorithm's efficiency in handling large‐scale applications. Decision rules for several customer service objectives are developed, with a discussion of the characteristics of the inventory systems in which each objective would be most appropriate. The decision rules are approximations, based on the assumptions commonly used in practice.
The traveling salesman problem: An update of research
Authors: Parker R. G. , Rardin R. L.
Published: May 2007

During the course of the last few years, attacks on the traveling salesman problem have resulted in a variety of often innovative and rather powerful computational procedures. In this article, we present a review of these results for problems defined on weighted and unweighted graphs. Some account of computational behavior for exact algorithms is provided; however, the primary coverage deals with the strategy of particular procedures. In addition, we include some aspects of nonexact algorithms with major interest confined to the establishment of worst‐case bounds.
A multifacility capacity expansion model with joint expansion set‐up costs
Authors: Luss Hanan
Published: May 2007

This article describes a multifacility capacity expansion model in which the different facility types represent different quality levels. These facility types are used to satisfy a variety of deterministic demands over a finite number of discrete time periods. Applications for the model can be found in cable sizing problems associated with the planning of communication networks. It is assumed that the cost function associated with expanding the capacity of any facility type is concave, and that a joint set‐up cost is incurred in any period in which one or more facilities are expanded. The model is formulated as a network flow problem from which properties associated with optimal solutions are derived. Using these properties, we develop a dynamic programming algorithm that finds optimal solutions for problems with a few facilities, and a heuristic algorithm that finds near‐optimal solutions for larger problems. Numerical examples for both algorithms are discussed.
“simple‐approximate” battle‐outcome‐prediction conditions for variable‐coefficient lanchester‐type equations of modern warfare
Authors: Taylor James G.
Published: May 2007

This article considers combat between two homogeneous forces modeled by variable‐ coefficient Lanchester‐type equations of modern warfare and develops new “simple‐approximate” battle‐outcome‐prediction conditions for military engagements terminated by two different types of prescribed conditions being met (fixed‐force‐level‐breakpoint battles and fixed‐force‐ratio‐breakpoint battles). These battle‐outcome‐prediction conditions are sufficient (but not necessary) to determine the outcome of battle without having to explicitly compute the force‐level trajectories, and they are characterized by their simplicity, requiring no advanced mathematical knowledge or tabulations of “special functions” for their application. Integrability properties of the Lanchester attrition‐rate coefficients figure prominently in their results, and involved in their development is a generalization of Lanchester's famous square law to variable‐coefficient Lanchester‐type combat and several other novel mathematical developments for the analysis of ordinary differential equations. Examples are given, with the attack of a mobile force against a static defensive position (both sides armed with weapons whose firepower is range dependent) being examined in detail.
Multivariate dependent relevations with applications, and related topics
Authors: Johnson Norman L. , Kotz Samuel
Published: May 2007

“Relevation” is the name given by Krakowski to the distribution of failure time of a replacement from an aging stock. The present authors have extended this concept to include (i) hierarchal replacement systems and (ii) dependence between lifetimes of original and replacement items. In this article, we present some further developments, including first steps toward a synthesis of (i) and (ii).
The continuous multiple‐modular design problem
Authors: Shaftel Timothy L. , Thompson Gerald L.
Published: May 2007

In this article we extend our previous work on the continuous single‐module design problem to the multiple‐module case. It is assumed that there is a fixed cost associated with each additional module used. The Kuhn–Tucker conditions characterize local optima among which there is a global optimum. Modules are associated with partitions and a special class, guillotine partitions, are characterized. Branch‐and‐bound, partial enumeration, and heuristic procedures for finding optimum or good guillotine partitions are discussed and illustrated with examples.