bluuebunny/crossref_metadata_2025 huggingface dataset:
Estimating Need and Demand for Prehospital Care
Authors: Kamenetzky Ricardo D. , Shuman Larry J. , Wolfe Harvey
Published: November 2008

Models estimating demand and need for emergency transportation services are developed. These models can provide reliable estimates which can be used for planning purposes, by complementing and/or substituting for historical data. The model estimating demand requires only four independent variables, population in the area, employment in the area, and two indicators of socioeconomic status which can be obtained from census data. The model can be used to estimate demand according to 4 operational categories and 11 clinical categories. The parameters of the model are calibrated with 1979 data from 82 ambulance services covering over 200 minor civil divisions in Southwestern Pennsylvania. This model was tested with data from another 55 minor civil divisions, also in Southwestern Pennsylvania, and it provided good estimates of total demand. The model to estimate need evolves from the demand model. It enables planners to estimate unmet need occurring in the region. The effect of emergency transportation service (ETS) provider characteristics on demand was also investigated. Statistical tests show that, for purposes of forecasting demand, when the sociodemographic factors are taken into account, provider characteristics are not significant.
An Outer Approximation Algorithm for Solving General Convex Programs
Authors: Fukushima Masao
Published: November 2008

A new outer approximation algorithm is proposed for solving general convex programs. A remarkable advantage of the algorithm over existing outer approximation methods is that the approximation of the constraint set is not cumulative. That is, the algorithm solves at each iteration a quadratic program whose constraints depend only on the current estimate of an optimal solution. Convergence of the algorithm is proved and possible applications are discussed.
System Balance for Extended Logistic Systems
Authors: Graves Stephen C. , Keilson Julian
Published: November 2008

An extended logistic system is a well-defined configuration of complex equipment, supporting inventory levels of components and modules, supporting maintenance facilities, supporting transportation system between local and remote inventory and maintenance sites, and procedures governing the allocation and shipment of components from remote and local sites. Examples of extended logistic systems are aircraft programs, radar systems, or networks of communication satellites. For each of these systems, the basic unit of interest (an aircraft, a radar unit, or a satellite) is a complex combination of components which are subject to failure. For each component there are supporting inventory and/or repair facilities, and specific replacement procedures for such failures. The evaluation of system performance includes system availability and the logistic costs required to obtain that level of availability. This paper extends our earlier work which developed methods for measuring system persistence times of extended logistic systems. In particular, we propose an optimization model here for examining system design and trade-off decisions. We consider a single-echelon model for a multiple-component system where components are subject to failure. For the system to be operable, a prespecified number of each component must be available. The optimization model maximizes system availability subject to a budget constraint on system cost and a time constraint on system failure time. The latter constraint is an effort to incorporate our understanding of system dynamics into the optimization by restricting the mean time between failures for the entire system. The use of the optimization model for system design and trade-off decisions is illustrated by two examples using representative data from an Air Force program. Within the optimization context, the notion of system balance is defined.
Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations
Authors: Sherali Hanif D. , Soyster Allen L. , Murphy Frederic H.
Published: November 2008

The supply side of an oligopolistic market supplying a homogeneous product noncooperatively is modeled. In this market, there is one leader and N followers. The followers operate under the Cournot assumption of zero conjectural variation and are accordingly called Cournot firms. The leader, called a Stackelberg firm, specifically takes into account the reaction of the Cournot firms to its output. For this situation, we study the behavior and implications of the joint Cournot reaction curve as generated by plausible economic market assumptions. In particular, we study the existence and uniqueness of a Stackelberg-Nash-Cournot equilibrium. In addition, we prescribe an efficient algorithm to determine a set of equilibrating output quantities for the firms.
Optimal Locations for a Class of Nonlinear, Single-Facility Location Problems on a Network
Authors: Shier D. R. , Dearing P. M.
Published: November 2008

This paper investigates a class of single-facility location problems on an arbitrary network. Necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function. This approach produces a number of new results for locating a facility on an arbitrary network, and in addition it unifies several known results for the special case of tree networks. It also suggests algorithmic procedures for obtaining such optimal locations.
Diffusion Approximation for an M/G/m Queue
Authors: Kimura Toshikazu
Published: November 2008

This paper deals with the M/G/m queueing system in the steady-state. Applying the method of diffusion approximation, we provide approximate formulas for the distributions of the number of customers, the waiting time and the busy period. We also discuss the relation between the heavy traffic approximation and these approximations. In order to examine the accuracy of the approximate formulas, they are numerically tested on some examples.
Optimal Prediction of Times and Queue Lengths in the GI/M/1 Queue
Authors: Stanford D. A. , Pagurek B. , Woodside C. M.
Published: November 2008

This paper presents optimal predictors for variables in a GI/M/1 queue, number in the queue, time in the queue, and waiting time. The conditional-expectation predictors and optimal linear predictors are derived and compared. Close relationships are found among the predictors and their performance values, with prediction of number in queue from some previous number playing the key role. Basic properties of the predictors are illustrated with examples.
Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers
Authors: Gershwin Stanley B. , Schick Irvin C.
Published: November 2008

In an important class of systems, which arises in manufacturing, chemical process, and computer contexts, objects move sequentially from one work station to another, and rest between stations in buffers. In the manufacturing context, such systems are called transfer lines. The dynamic behavior of a buffered transfer line with unreliable work stations is modeled as a Markov chain. The system states consist of the operational conditions of the work stations and the levels of material in the buffers. The steady-state probabilities of these states are sought in order to establish relationships between system parameters and performance measures such as production rate (efficiency), forced-down times, and expected in-process inventory. The steady state probabilities are found by choosing a sum-of-products form solution for a class of states, and deriving the remaining expressions by using the transition equations. In this way, the order of the system of equations to be solved is drastically reduced. This algorithm suggests a general approach for solving large scale structured Markov chain problems.
Preemptive Scheduling of a Single Machine to Minimize Maximum Cost Subject to Release Dates and Precedence Constraints
Authors: Baker K. R. , Lawler E. L. , Lenstra J. K. , Rinnooy Kan A. H. G.
Published: November 2008

Suppose n jobs are to be processed on a single machine, subject to release dates and precedence constraints. The problem is to find a preemptive schedule which minimizes the maximum job completion cost. We present an O(n2) algorithm for this problem, generalizing previous results of E. L. Lawler.
Technical Note—A Class of Linear Programs Convertible to Network Problems
Authors: Cunningham William H.
Published: November 2008

We consider a class of two-commodity network flow problems with additional, highly structured linear constraints in place of the usual capacity constraints. This class of linear programs arose as subproblems in a mixed integer programming formulation of a location model, and was solved by Ramakrishnan using a special purpose primal simplex algorithm. We show that, even though the constraint matrices of these problems are not transformable to constraint matrices of pure network problems, the problems themselves can be converted to pure network problems. The transformation depends on the existence of a set of variables whose non-negativity restrictions are redundant to the definition of the feasible region. We point out other situations in which such structure occurs.
Technical Note—Branch and Fathom: A Technique for Computing Functions on the Power Set of a Set
Authors: Strip David R.
Published: November 2008

Tree traversal algorithms are frequently used for ordering operations on sets. This paper describes a tree structure and traversal scheme which is applied to the computation of a reliability measure. The key to this variation is a particular labeling of the enumeration tree which locates supersets of a set S in one subtree of the node labeled with S. Exact computation by simple techniques is considerably more time-consuming than by the “branch and fathom” technique, which may also be useful in computing other functions on the power set of a set.
Accelerated Accuracy in the Simulation of Markov Chains
Authors: Fishman George S.
Published: November 2008

This paper describes a method of obtaining results from the simulation of an n + 1 finite state positive recurrent aperiodic Markov chain at a cost considerably less than that required by pure random sampling to achieve the same accuracy. The method reorganizes k independent epochs (or tours) simulated serially into k replications simulated in parallel, and therefore produces cost savings by inducing selected joint distributions across replications. The joint distributions are derived by the use of rotation sampling, a special case of the antithetic variate method. The paper first describes the method as it applies to a finite state nearest neighbor chain. In particular, it shows that even for independent parallel replications, the cost of achieving a specified accuracy with serial simulation, relative to the cost for parallel simulation, has a lower bound O(k1/2/n) as k → ∞. When rotation sampling is used, this bound is O(k2/n(ln k)3). A simulation of the M/M/1 queueing model with finite capacity n illustrates the effectiveness of the technique for selected values of k, n and activity level ρ. The paper then describes how this variance reducing technique applies to the simulation of a more general finite state chain. In particular, the lower bound on relative cost is O(k2/ϕ(ln k)3), where ϕ is the total number of transitions that can occur from all n + 1 states. A computer program that implements the method for the general finite state case is briefly described.
An Integer Programming Procedure for Assembly System Design Problems
Authors: Graves Stephen C. , Lamar Bruce W.
Published: November 2008

Recent advances in robot technology have revolutionized the concept of manufacturing and assembly systems. These advances have created the need for new mathematical models to reflect the capabilities of the new technologies. In this paper, we focus on the system design problem by defining a work station selection and task assignment problem for automated assembly systems. We formulate this problem as a zero-one integer program and describe a procedure for seeking lower and upper bounds to the optimal value of the integer program. The upper bound provides a feasible solution to the integer formulation and the lower bound is tighter than the standard linear programming relaxation of the integer formulation. Computational results indicate that the proposed bounds are extremely tight. In fact, in each of the 42 test problems evaluated, the lower and upper bound coincided, indicating that the optimal solution to the integer program had been obtained.
Two Algorithms for Constrained Two-Dimensional Cutting Stock Problems
Authors: Wang P. Y.
Published: November 2008

We propose two combinatoric methods that generate constrained cutting patterns by successive horizontal and vertical builds of ordered rectangles. Each of the algorithms uses a parameter to bound the maximum acceptable percentages of waste they create. Error bounds measure how close the pattern wastes are to the waste of the optimal solution. We also discuss computational results and applications of the methods to a general cutting stock problem.
Technical Note—The Nested Ball Principle for the Relaxation Method
Authors: Drezner Zvi
Published: November 2008

In this note, we consider finding a feasible solution to a set of linear inequalities. As is known, there is a ball that can be determined a priori from the problem data knowing the property that it contains a feasible solution if there is one. The relaxation method for solving the problem determines a sequence of shrinking balls that contain a feasible solution if there is one. We show here that if one of the smaller balls is nested inside the first ball, then there is no feasible solution to the problem. This principle is proved to be superior to the existing stopping criterion. We also show that the principle cannot be extended to the Russian method for linear programming.
An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem
Authors: Bard Jonathan F.
Published: November 2008

This paper presents an algorithm using sensitivity analysis to solve a linear two-stage optimization problem. The underlying theory rests on a set of first order optimality conditions that parallel the Kuhn-Tucker conditions associated with a one-dimensional parametric linear program. The solution to the original problem is uncovered by systematically varying the parameter over the unit interval and solving the corresponding linear program. Finite convergence is established under nondegenerate assumptions. The paper also discusses other solution techniques including branch and bound and vertex enumeration and gives an example highlighting their computational and storage requirements. By these measures, the algorithm presented here has an overall advantage. Finally, a comparison is drawn between bicriteria and bilevel programming, and underscored by way of an example.
On the M/G/1 Queue with Rest Periods and Certain Service-Independent Queueing Disciplines
Authors: Scholl Michel , Kleinrock Leonard
Published: November 2008

The M/G/1 queue with rest periods and FCFS order of service was first studied by Miller. We give further results concerning the behavior of the delay under the FCFS discipline. We then solve for the second moment of the waiting time in an M/G/1 queue with rest periods and Random Order of Service (ROS). We finally solve for the Laplace-Stieltjes transform of the distribution function of the waiting time in an M/G/1 queue with rest periods and nonpreemptive LCFS order of service. The relationship found between the second moments of the waiting time in an M/G/1 queue with rest periods under the FCFS, ROS and LCFS disciplines is precisely that found by Takács for the M/G/1 queue without rest periods.
Technical Note—The Asymptotic Extreme Value Distribution of the Sample Minimum of a Concave Function under Linear Constraints
Authors: Patel Nitin R. , Smith Robert L.
Published: November 2008

We show that the minimum value of a sample of feasible points uniformly distributed over a linear constraint set is, for concave functions, asymptotically Weibull distributed with shape parameter equal to the dimension of the feasible region.
A Selection Artifact in Delinquency Data Revisited
Authors: Tierney Luke
Published: November 2008

Studies of correctional programs have observed that delinquents exhibit a sharp rise in their arrest rates up to the time of intervention, and that they continue their activity after their release from the programs, but at a lower rate. The nature of this phenomenon has precipitated controversy; one school of thought attributes it to the effectiveness of the correctional programs, another claims that it may be due largely to a selection artifact. An analysis proposed in a recent article by Maltz and Pollock supported the artifact hypothesis. In this paper, we point out an error in Maltz and Pollock's analysis, and show analytically and by simulation that the correction of this error reduces the size of the selection artifact. However, it is still plausible to the attribute the observed phenomenon to a selection artifact.
Technical Note—An Exact Algorithm for the Time-Constrained Traveling Salesman Problem
Authors: Baker Edward K.
Published: November 2008

The time-constrained traveling salesman problem is a variation of the familiar traveling salesman problem that includes time window constraints on the time a particular city, or cities, may be visited. This note presents a concise formulation of the time-constrained traveling salesman problem. The model assumes that the distances of the problem are symmetrical and that the triangle inequality holds. Additionally, the model allows the salesman to wait at a city, if necessary, for a time window to open. The dual of the formulation is shown to be a disjunctive graph model, which is well known from scheduling theory. A longest path algorithm is used to obtain bounding information for subproblems in a branch and bound solution procedure. Computational results are presented for several small to moderate size problems.
Technical Note—A Convexity Result for a Class of GI/G/1 Queueing Systems
Authors: Tu Hung-Yuan , Kumin Hillel
Published: November 2008

This note gives a sufficient condition under which the expected number of customers in a GI/G/1/FCFS queueing system will be a convex function of the service rate. Although the result is intuitively appealing and is usually accepted without proof as a “folk theorem” of queueing theory, there are systems for which it does not hold.
Technical Note—A Note on the One Against Many Battle
Authors: Kikuta Kensaku
Published: November 2008

This paper treats a sequencing problem that appears in the one-against-many engagement, considered originally by Friedman. We define an extremal order to be an order that satisfies Friedman's necessary condition. The number of extremal orders could be greater than one. If this occurs, then it may happen that Friedman's procedure gives a nonoptimal order as we illustrate by a numerical example. We derive a necessary condition that applies to unique extremal orders and a sufficient condition for an order to be optimal.
Technical Note—Simulating the GI/G/1 Queue in Heavy Traffic
Authors: Minh Do Le , Sorli Ronald M.
Published: November 2008

In this paper, we suggest that instead of ignoring a certain quantity to obtain Kingman's heavy traffic approximation for the stationary expected waiting time in the GI/G/1 queue, we simulate it. This leads to a new consistent estimator for the stationary expected waiting time in queue, the variance of which is reduced substantially when the traffic intensity approaches unity.
A Unifying View of Hybrid Simulation/Analytic Models and Modeling
Authors: Shanthikumar J. G. , Sargent R. G.
Published: November 2008

In this paper we give unifying definitions for both hybrid simulation/analytic models and modeling. We present four classes of hybrid simulation/analytic models and give examples of each class, including numerical results for two of the examples Four usages of hybrid simulation/analytic modeling are also presented with examples.
The Integrated Simulation Environment (Simulation Software of the 1990s)
Authors: Henriksen James O.
Published: November 2008

The availability of good software tools is vitally important to practitioners of simulation. The purpose of this paper is to identify significant improvements that will be made in simulation software in the next 10 years. While based upon review of ongoing research efforts in programming systems, a paper such as this is necessarily speculative. Substantial research effort is already underway. Numerous papers—even entire books—describe current research and comment upon trends for the future. Since most of the current research in programming systems is being conducted in other problem contexts, we must look outside the discipline of simulation for most of our examples. In doing so, we must be careful to assess the applicability of such examples to simulation, for techniques that are successful within a narrow focus may not be readily extended to such a broad discipline as simulation. There is great cause for optimism: it appears likely that simulation practitioners of the future will work in an environment comprised of well-integrated software tools. The integrated software environment of the 1990s will make present state-of-the art simulation software tools look as primitive as the building of simulation models entirely in high-level languages like Fortran looks today.
Accelerated Convergence in the Simulation of Countably Infinite State Markov Chains
Authors: Fishman George S.
Published: November 2008

This paper describes a method of obtaining results from the simulation of a countably infinite state, positive recurrent aperiodic Markov chain at a cost considerably below that required to achieve the same accuracy with pure random sampling. Reorganizing k independent epochs or tours simulated serially into k replications simulated in parallel can induce selected joint distributions across replications that produce the cost savings. The joint distributions follow from the use of rotation sampling, a special case of the antithetic variate method. The chains considered are of the band type so that for some integer δ a transition from any state i = 0, 1, 2, … can move no further than to states i − δ and i + δ. The paper shows that an estimator of interest has variance bounded above by O(δ2(ln k)4/k2) when using rotation sampling, as compared to a variance O(1/k) for independent sampling. Moreover, the mean cost of simulation based on rotation sampling has an upper bound O((δ ln k2)) as compared to a cost of at least O(k) for independent sampling. The paper also describes how one can exploit special structure in a model together with rotation sampling to improve the bound on variance for essentially the same mean cost.
Technical Note—An Algorithm for a Class of Discrete Maximum Entropy Problems
Authors: Freund Dwight , Saxena Umesh
Published: November 2008

This note presents an exact method for solving a class of maximum entropy problems used in a decision making context. These exact solutions should prove valuable for benchmark testing of the numerical nonlinear programming methods normally applied to a large class of problems that includes those studied here. The finite algorithm developed has a complexity of order O(n) for a problem with (2n + 1) constraints. An example involving the selection of best equipment for an oil spill problem is presented.
Technical Note—Proper Efficiency and the Linear Fractional Vector Maximum Problem
Authors: Choo Eng Ung
Published: November 2008

A vector maximum problem arises when two or more criterion functions are to be simultaneously maximized over a feasible region. We prove that, in linear fractional vector maximum problems, every efficient solution satisfies the requirements of a restricted concept of efficiency, the notion of proper efficiency.
A System Point Approach to Nonuniform Advertising Insertions
Authors: Brill Percy H. , Hornik Jacob
Published: November 2008

This paper introduces a stochastic model and uses the system point theory for queues and dams to obtain the long range probability distribution function of consumer response in a single ad campaign with Poisson repetitions. The consumer response is treated analogously to the content of a dam with a general release rule and stochastically decreasing increments from higher contents. This approach to repetition effects provides an alternative technique to contemporary marketing models. The paper also discusses applications to the choice of media schedules that optimize market response and generalizations of the model.
Minimizing Costs of Resource Requirements in Project Networks Subject to a Fixed Completion Time
Authors: Möhring Rolf H.
Published: November 2008

We consider the problem of minimizing the resource costs in a project network No subject to a time limit for the completion of No, when resource requirements per activity and costs for obtaining resources are independent of time. Our results show that the optimum is determined for all possible resource requirements and costs by certain sets of “feasible structures,” which are networks that extend the precedence relation of No and respect the given time limit. We characterize the least such sets, and give methods for determining them as well as for determining the optimum. Furthermore, we establish duality relations with the problem of scarce resources (minimizing project duration subject to limited resources) and characterize all “essentially different” problems.
OR Practice—A Queueing Model for Telephone Operator Staffing
Authors: Sze David Y.
Published: November 2008

This paper describes a queueing model of telephone operator staffing and the application of the model. The Bell System has used the model to reduce the cost of meeting its service criteria, for planning purposes, and to help explain to regulatory agencies changes in service measurement criteria. The model deals with large server team sizes, bimodal service time distributions, nonstationary arrivals, customer abandonments and reattempts, and certain priority queueing structures.
A Geometric Programming Model for the Optimal Design of Wastewater Treatment Plants
Authors: Smeers Yves , Tyteca Daniel
Published: November 2008

We present a complete mathematical model describing the various interactions in a wastewater treatment plant. The optimal design of the plant is studied by first reformulating the model as a signomial program; this reformulation eases function and gradient evaluations as well as data manipulation, and allows the user to test and exploit the model in an interactive and repeated way. The model departs significantly from previous work in the area by introducing no ad hoc simplification in the constituting process models, nor in the optimization procedure. Since the model includes various nonconvexities due to signomial expressions, we tested convexifying procedures, which did not produce better solutions than those obtained from the model under its original signomial form. Application of the model is illustrated not only for design purposes, but also as a useful tool for generating various types of cost information required in regional water quality management models.
OR Forum—The Origin of Operational Research
Authors: Larnder Harold
Published: November 2008

This paper presents an account of the events in the years just preceding and during the second world war that led up to the concept and practice of operational research as it is now generally understood.
A Survey of Network Reliability and Domination Theory
Authors: Agrawal Avinash , Barlow Richard E.
Published: November 2008

We present a brief survey of the current state of the art in network reliability. We survey only exact methods and do not consider Monte Carlo methods. Most network reliability problems are, in the worst case, NP-hard and are, in a sense, more difficult than many standard combinatorial optimization problems. Nevertheless, there are, in fact, linear and polynomial time algorithms for network reliability problems of special structure. We review general methods for network reliability computation and discuss the central role played by domination theory in network reliability computational complexity. We also point out the connection with the more general problem of computing the reliability of coherent structures. The class of coherent structures contains both directed and undirected networks as well as logic (or fault) trees without not gates. This topic is a rich area for further research.
Decreasing Failure Rates and Related Issues in the Social Sciences
Authors: Gerchak Yigal
Published: November 2008

Studies conducted in various social disciplines discovered that, the longer individuals remain in a state, the lower the chances of their leaving that state in subsequent periods. “Inertia” of this kind is accumulated, for example, in durations of tenure in an organization and at a residence, abstention from crime after release from prison, and durations of strikes. This concept of inertia can be formalized by utilizing measures of residual durations that are commonly used in reliability. We refine concepts of inertia to investigate the rate of inertia accumulation, as captured by the various measures. We show how desirable “second-order” negative aging properties can provide some guidance in the selection of an appropriate parametric distribution to model empirical duration data.
A General Framework for Learning Curve Reliability Growth Models
Authors: Jewell William S.
Published: November 2008

In reliability growth models, system performance improves during prototype testing, as design changes are made and operating procedures and the environment are modified. There is great interest in predicting the ultimate performance of the system, using only the epochs of the failures that occur early in the testing program. This paper constructs a general framework for learning-curve models of reliability growth, including many different model variations that have previously been analyzed. Numerical trials indicate the difficulty of estimating ultimate performance; the maximum likelihood estimator is unstable for small testing intervals with a small number of systems on test. Bayesian procedures are recommended for implementation.
On the Reliability of Repairable Systems
Authors: Brown Mark
Published: November 2008

This paper considers the time to first failure for repairable coherent systems containing independent exponential components. It derives several inequalities and relates them to previous work of the author and of Keilson to obtain approximations with error bounds for the distribution of the time to first failure.
The Interval Estimation of System Reliability from Component Test Data
Authors: Winterbottom Alan
Published: November 2008

The construction of interval estimates for system reliability from component test data has presented statisticians and reliability engineers with several challenging problems. This article outlines the difficulties in making such estimates and presents a selection from the many diverse and sometimes ingenious statistical approaches that have been made. The paper summarizes some recent developments and indicates directions for some further research.
Series Systems and Reliability Demonstration Tests
Authors: Blumenthal Saul , Greenwood J. Arthur , Herbach Leon H.
Published: November 2008

For series systems at equilibrium, the exponential distribution for times between failures is reasonably well justified. In the transient state, the exponential distribution applies also, but with a time varying scale parameter. Ignoring this parameter and using a partly aged system to make inferences about the mean life of a fully aged system can lead to very misleading outcomes. In particular, we show that reliability demonstration tests may have unacceptably high consumer's risk when applied in this manner.
Models for Fiber-Matrix Composites with Local Load Sharing
Authors: Smith Richard L. , Taylor Howard M.
Published: November 2008

Because of their high strength to weight ratios, fiber composites are increasingly used to replace steel or aluminum in practice. This paper presents various models for analyzing fiber matrix composites that share load among fibers. The most important practical models are those that represent the load sharing as local around failed fibers. Two methods of analysis are discussed. The first, due to Harlow and Phoenix, is a very powerful and virtually exact method for one particular model of interest. The second method is an asymptotic technique based on extreme value theory. Although less powerful than the Harlow-Phoenix method, the second method has much greater scope for generalization to other models, and some of these generalizations are described. The paper concludes with a brief discussion of experimental evidence and plans for future experiments.
Inequalities for NBUE and NWUE Life Distributions
Authors: Launer Robert L.
Published: November 2008

This paper presents a procedure for developing reliability inequalities for several known classes of failure distributions. The inequalities are rational functions of the moments and conditional tail moments of the underlying failure distribution. The introduction of four new classes of failure distributions based on the variance behavior facilitates the development of certain inequalities for the NBUE and NWUE distributions.
Interval Estimation After Sequential Testing Based on the Total Time on Test
Authors: Padgett W. J. , Wei L. J.
Published: November 2008

Industrial life testing experiments often select m items at random to put on test. The items operate independently and are not replaced upon failure. Assume that the lifetime of each item has a probability distribution depending on an unknown parameter θ, where lifetimes with parameter θ1 tend to be smaller than lifetimes with parameter θ2 whenever θ1 is less than θ2. For example, the lifetime distribution can be exponential with mean θ. We develop a time truncated sequential procedure for testing the null hypothesis that θ is at least as large as a specified value θ0 against the alternative hypothesis that θ is less than θ0. The procedure allows quick rejection of the null hypothesis when the alternative is true and provides an accurate confidence interval for θ when the null hypothesis is accepted at the conclusion of the test. After deriving this procedure, we discuss the exponential case and illustrate our results with an example.
Inequalities between Arrival Averages and Time Averages in Stochastic Processes Arising from Queueing Theory
Authors: Niu Shun-Chen
Published: November 2008

A common scenario in stochastic models, especially in queueing theory, is that an arrival counting process both observes and interacts with another continuous time stochastic process. In the case of Poisson arrivals, Wolff (Wolff, R. W. 1982. Poisson arrivals see time averages. Opns. Res. 30 223–231.) recently proved that the proportion of arrivals finding the process in some state is equal to the proportion of time it spends there under a lack of anticipation assumption. Inspired by Wolff's approach, in this paper we study the related interesting question of when do we have inequalities between these proportions. We establish two-sided inequalities under the following three assumptions: (i) the interarrival time distributions are of type NBUE or NWUE, (ii) the process being observed have monotone sample paths between arrival epochs, and (iii) the state of the process does not depend on future jumps of the arrival process. These assumptions are typically true in all standard queueing models and hence our results have wide implications. Stochastic inequalities between limiting distributions of interest, when they exist, also follow easily from our main result.
The Output of the M/M/s Queue
Authors: Everitt D. E. , Downs T.
Published: November 2008

This paper derives an explicit expression for the transient distribution of the output process of the M/M/s queue operating in continuous time. This expression is rather complex and alternative computational techniques are presented. Some computational results are included.
Optimal Prediction of Queue Lengths and Delays in GI/M/m Multiserver Queues
Authors: Woodside C. Murray , Stanford David A. , Pagurek Bernard
Published: November 2008

We present optimal mean square predictors for queue lengths and delays in the stationary GI/M/m queue, based on a queue length measurement. The development specifies interrelationships among these predictors and numerical examples demonstrate basic properties of the predictors.
Determining the K Most Critical Paths in PERT Networks
Authors: Dodin Bajis
Published: November 2008

A fundamental problem in PERT networks is to identify a project's critical paths and its critical activities. In this paper we define the criticality index of a path as the probability that the duration of the path is greater than or equal to the duration of every other path in the network and define the criticality index of an activity as the sum of the criticality indices of the paths containing that activity. The most critical path or K most critical paths in a PERT network could be found by enumerating all the paths and calculating the corresponding criticality indices, both of which are burdensome tasks. This paper uses stochastic dominance to develop a procedure to identify the K most critical paths without using this path enumeration. The procedure has been applied to various sized PERT networks generated at random, and the results are found to be very close to those obtained by extensive Monte Carlo sampling.
A Decomposition Algorithm for a Discrete Location-Allocation Problem
Authors: Sherali Hanif D. , Adams Warren P.
Published: November 2008

This paper considers a discrete location-allocation problem for simultaneously determining the location of a given number of capacitated facilities on certain predesignated sites, and the allocation of their products among a fixed number of customers. The objective is to determine the location and (subsequent) allocation that minimizes the total cost of construction (or location), production, and transportation. The formulation of this model is a specially structured, generally nonconvex problem. However, we specify certain sufficient conditions for the solution to two network-structured linear programs to provide an optimal solution to this problem. For other situations, we present an implicit enumeration algorithm within the framework of Benders' decomposition method, which fully exploits the structure of the problem. This method is an improvement over traditional Lagrangian approaches. Computational experience is provided to demonstrate the practicality of this algorithm for reasonable size problems, as well as its superiority over alternative implicit enumeration schemes. This paper also sheds light on the general implementation of Benders' decomposition technique.
Technical Note—A Note on Linearly Decreasing, Delay-Dependent Non-Preemptive Queue Disciplines
Authors: Bagchi Uttarayan
Published: November 2008

Previous authors have presented expressions for expected waiting time in linearly time-dependent queue disciplines. This paper points out two errors in a paper by Hsu on linearly decreasing priority systems.
A State-of-the-World Decomposition Approach to Dynamics and Uncertainty in Electric Utility Generation Expansion Planning
Authors: Borison Adam B. , Morris Peter A. , Oren Shmuel S.
Published: November 2008

Dynamics and uncertainty are central to electric utility generation expansion planning, but are difficult to handle explicitly. A state-of-the-world decomposition approach is introduced that solves the dynamic probabilistic generation expansion problem using simple static deterministic solution techniques. The main problem is decomposed into a set of static deterministic problems. Each problem represents a distinct state-of-the-world (i.e., a time and outcome scenario) and is solved individually using a new dynamic programming procedure. The problems are linked through Lagrange multipliers that are determined iteratively and that can be interpreted as “shadow” fixed costs. Consequently, one difficult problem is replaced with many easy ones. The solution obtained represents the minimum discounted expected cost generation expansion plan. It reflects the importance of future conditions in current decisions and the utility's ability to respond to the resolution of uncertainties over time.
The Linear Sharing Problem
Authors: Brown J. Randall
Published: November 2008

The linear sharing problem is defined as a linear programming problem with a maximin objective function comprised of nondecreasing, continuous tradeoff functions. This paper develops some properties, including optimality conditions, for this problem. It also develops an efficient algorithm that alternately calculates a new global upper bound on the objective function and then determines if a feasible solution exists that meets the new objective function global upper bound. The process continues until the algorithm finds a feasible and, thus, an optimal solution. The algorithm also determines if the problem contains no feasible solution or if the objective function is unbounded. A technique to handle problems with unbounded tradeoff variables is developed and computational experience is given.
Dynamic Routing in a Queueing System with a Multiple Service Facility
Authors: Filipiak Janusz
Published: November 2008

In this paper we analyze a problem of traffic assignment within a queueing system with multiple service facilities subject to a changing load. The evolution in time of the mean number in the system is approximated with a nonlinear differential equation. The dynamic flow pattern is found for which the total waiting time of all entities passing the system is minimal. A numerical example is given. For the system in a nonstationary environment an adaptive strategy developed in this paper is compared with the performance of the policy of joining the shorter queue.
Technical Note—On Waiting Times for a Queue in Which Customers Require Simultaneous Service from a Random Number of Servers
Authors: Seila Andrew F.
Published: November 2008

We consider a queueing system, first introduced by L. Green in 1980, in which customers from a Poisson arrival stream request simultaneous service from a random number of identical servers with exponential service times. Computational formulas for the second moment of time in queue are given, along with tables of these values for selected systems. Numerical results show that the coefficient of variation for time in queue is always greater than 1 and decreases with increasing congestion.
Deterministic Approximations to Stochastic Production Problems
Authors: Bitran Gabriel R. , Yanasse Horacio H.
Published: November 2008

In this paper we consider deterministic approximations to a nonsequential stochastic production problem with setup costs. We show that, for the most commonly used probability distributions of the demands, the relative error bounds tend to be very small. We also consider a sequential stochastic problem, without setup costs, and discuss its relationship to the nonsequential case. Throughout the paper, we present limited computational results and indicate topics for further research.
Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions
Authors: Smith Robert L.
Published: November 2008

We consider the Monte Carlo problem of generating points uniformly distributed within an arbitrary bounded (measurable) region. The class of Markovian methods considered generate points asymptotically uniformly distributed within the region. Computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions.
Some Properties of Location Problems with Block and Round Norms
Authors: Thisse J.-F. , Ward J. E. , Wendell R. E.
Published: November 2008

The point-objective problem and the Weber problem are two well-known formulations for locating a new facility with respect to a set of fixed facilities. When locations are represented as points on a plane, the point-objective problem is a multiple objective formulation of minimizing the distance from a variable point to each of the fixed points. Similarly, the Weber problem is a single objective formulation of minimizing the sum of transportation costs between the variable point and the fixed points, where transportation cost is a function of distance. Generalizing solution properties for these problems from distance measures given by the Euclidean, rectilinear, Ip, and one-infinity norms; this paper develops solution properties under the broad classes of distance measures given by block and round norms. For the point-objective problem, we show that (i) the efficient set for all round norms is the convex hull of the set of fixed points and (ii) the efficient set under a block norm tends to the convex hull for a sequence of block norms approaching a round norm. For the Weber problem, we prove that (i) an optimal location for any block norm may be found in a finite set of intersection points belonging to the convex hull and (ii) this set tends to the convex hull for a sequence of block norms approaching a round norm. Finally, we use these results to propose a synthesis of some of the main properties in continuous and network location theory.
Technical Note—Determining All Optimal and Near-Optimal Solutions when Solving Shortest Path Problems by Dynamic Programming
Authors: Byers Thomas H. , Waterman Michael S.
Published: November 2008

This paper presents a new algorithm for finding all solutions with objective function values in the neighborhood of the optimum for certain dynamic programming models, including shortest path problems. The new algorithm combines the depth-first search with stacking techniques of theoretical computer science and principles from dynamic programming to modify the usual backtracking routine and list all near-optimal policies. The resulting procedure is the first practical algorithm for a variety of large problems that are of interest.
Comments on “Accuracy and Tactical Implications of Bearings-Only Ranging Algorithms”
Authors: Washburn Alan R. , Daly Peter H.
Published: November 2008

We discuss several reservations about the analysis conducted in the previous paper (McCabe [McCabe, B. J. 1985. Accuracy and tactical implications of bearings-only ranging algorithms. Opns. Res. 33 94–103.]) in this issue of the Journal.
A Stochastic Model of Personnel Mobility: Application of Reliability Theory in Manpower System Analysis
Authors: Stanford Robert E.
Published: November 2008

Given the distribution of natural losses from any rank of a graded manpower system, and the rate of promotion to higher ranks, we define the mobility of rank members as a function of the cumulative lengths of service of all rank members and those members destined for promotion. We show that when the rank contains many individuals, and promotions are made without regard to seniority, mobility decreases with time in service if the natural loss function has an increasing failure rate, and increases with time in service if the loss function has a decreasing failure rate; mobility increases with time in service if promotions are awarded by seniority. We also derive bounds for the average time in service of rank members, based on the loss function and the promotion rate. In addition, we compare the average time to promotion, average time to resignation, and average time in service for the two promotion policies mentioned above. Our results show that promotion by seniority produces the longest possible average member service times if the loss function has an increasing failure rate, and the shortest average service times if the loss function has a decreasing failure rate. Using real data, we derive and categorize the theoretical natural loss distribution for a system of university faculty, the implied promotion policy governing the transition-to-tenure process, and the individual mobility function for nontenured members. This analysis does not require a large amount of data.