bluuebunny/crossref_metadata_2025 huggingface dataset:
Technical Note—Monotone Optimal Issuing Policies in a Deterministic Inventory Model
Authors: Chandrasekaran R.
Published: November 2008

We consider the problem of optimal issuing policies in deterministic inventory theory. We show that monotone policies are optimal for any number of items if they are optimal for two items. We do this by extending the models in the literature to allow the possibility of replacing items before the end of their lifetime. This option simplifies proofs. Moreover, as we demonstrate under certain conditions there are optimal policies in the extended model in which no replacement occurs until the end of an item's lifetime. Connections to existing literature are provided.
Optimum Replacement of a System Subject to Shocks
Authors: Boland Philip J. , Proschan Frank
Published: November 2008

A system is subject to shocks that arrive according to a nonhomogeneous (or homogeneous) Poisson process. Since each shock weakens the system and makes it more expensive to run, it is desirable to determine a replacement policy for the system. We consider the possibility of periodic replacement of the system, and exhibit a necessary and sufficient condition for the existence of an optimal finite period. The problem is investigated for both finite and infinite time horizons. Finally, we study a particular model for a system that fails on the second shock.
Surveillance Search for a Moving Target
Authors: Tierney Luke , Kadane Joseph B.
Published: November 2008

The surveillance search problem is a generalization of the detection search problem studied by Brown and Stone, among others. In the surveillance version of the problem, the search terminates only if the time and location of a detection satisfy certain problem specific conditions; the objective is to maximize the expected value of a payoff received during and at the end of the search. For instance, we may wish to maximize the probability of finding the target in a specified subset of the state space or at a specified time. Consequently, we might detect the target several times before the search terminates. A search strategy, i.e., an allocation of the available search effort, must account for this possibility. In this paper, we formulate the surveillance search problem for applications in which the target moves according to a (not necessarily time-homogeneous) Markov process. We then derive a set of necessary conditions for the optimality of a search strategy, and develop algorithms, based on the algorithm of Brown for the detection search problem, to find strategies that satisfy these necessary conditions for problems in which the search effort is infinitely divisible.
Annihilation Prediction for Lanchester-Type Models of Modern Warfare
Authors: Taylor James G. , Brown Gerald G.
Published: November 2008

This paper introduces important new functions for analytic solution of Lanchester-type equations of modem warfare for combat between two homogeneous forces modeled by power attrition-rate coefficients with “no offset.” Tabulations of these Lanchester-Clifford-Schläfli (or LCS) functions allow one to study this particular variable-coefficient model almost as easily and thoroughly as Lanchester's classic constant-coefficient one. LCS functions allow one to obtain important information (in particular, force-annihilation prediction) without having to spend the time and effort of computing force-level trajectories. The choice of these particular functions is based on theoretical considerations that apply in general to Lanchester-type equations of modern warfare and provide guidance for developing other canonical functions. Moreover, our new LCS functions also provide valuable information about related variable-coefficient models. Also, we introduce an important transformation of the battle's time scale that not only simplifies the force-level equations, but also shows that relative fire effectiveness and intensity of combat are the only two weapon-system parameters determining the course of such variable-coefficient Lanchester-type combat.
Technical Note—On the Evaluation of Intertemporal Lotteries
Authors: Hora Stephen C. , Austin Larry M.
Published: November 2008

We consider the evaluation of intertemporal lotteries using two tools: a single univariate utility function and a set of discount coefficients. If each of the lotteries consists of a single stochastic return to be received in a future period, then these tools are sufficient only if the utility function exhibits constant proportional risk aversion. Further, if the lotteries involve returns in more than one time period, we demonstrate that the tools are sufficient if, and only if, the utility function is linear.
Solving Large-Scale Zero-One Linear Programming Problems
Authors: Crowder Harlan , Johnson Ellis L. , Padberg Manfred
Published: November 2008

In this paper we report on the solution to optimality of 10 large-scale zero-one linear programming problems. All problem data come from real-world industrial applications and are characterized by sparse constraint matrices with rational data. About half of the sample problems have no apparent special structure; the remainder show structural characteristics that our computational procedures do not exploit directly. By today's standards, our methodology produced impressive computational results, particularly on sparse problems having no apparent special structure. The computational results on problems with up to 2,750 variables strongly confirm our hypothesis that a combination of problem preprocessing, cutting planes, and clever branch-and-bound techniques permit the optimization of sparse large-scale zero-one linear programming problems, even those with no apparent special structure, in reasonable computation times. Our results indicate that cutting-planes related to the facets of the underlying polytope are an indispensable tool for the exact solution of this class of problem. To arrive at these conclusions, we designed an experimental computer system PIPX that uses the IBM linear programming system MPSX/370 and the IBM integer programming system MIP/370 as building blocks. The entire system is automatic and requires no manual intervention.
Bargaining under Incomplete Information
Authors: Chatterjee Kalyan , Samuelson William
Published: November 2008

This paper presents and analyzes a bargaining model of bilateral monopoly under uncertainty. Under the bargaining rule proposed, the buyer and the seller each submit sealed offers that determine whether the good in question is sold and the transfer price. The Nash equilibrium solution of this bargaining game implies an offer strategy of each party that is monotonic in its own reservation price and depends on its assessment of the opponent's reservation price. Issues of relative bargaining advantage and efficiency are examined for a number of special cases. Finally, we discuss the appropriateness of the Nash solution concept.
Reconciliation of Probability Distributions
Authors: Lindley Dennis
Published: November 2008

Several people each express their opinion of an uncertain quantity by providing their mean and standard deviation of it. In this paper we discuss the problem of incorporating all these opinions into a single, reconciled, probability distribution for the quantity. The usual procedure is least squares, based on normality. The paper illustrates the advantages of using t-distributions, instead, and clarifies the role of the information provided by the standard deviations. Suitable approximations are provided for many cases.
Sensitivity Theory and Its Application to a Large Energy-Economics Model
Authors: Alsmiller R. G. , Barish J. , Drischler J. D. , Horwedel J. E. , Lucius J. L. , McAdoo J. W.
Published: November 2008

This paper discusses a nonlinear equation theory of sensitivity analysis and demonstrates its applicability to a large energy-economics model by applying it to a specific calculation carried out with the Long-Term Energy Analysis Program (LEAP). It presents numerical results for calculating derivatives of two results of interest with respect to several values of the underlying data elements for which the derivatives are appreciable. In a number of cases, the accuracy of the derivative information obtained has been verified by direct calculations and these comparisons are also presented. The theory used here is, in principle, applicable to a variety of models. It is most useful when applied to models that contain a very large number of data elements.
Technical Note—Linearization in 0-1 Variables: A Clarification
Authors: Goldman A. J.
Published: November 2008

We show that a published method for linearizing nonlinear 0-1 programs admits an invalid interpretation, but that a simple modification restores its validity and retains most of its computational advantage.
Confidence Interval Estimation Using Standardized Time Series
Authors: Schruben Lee
Published: November 2008

Observations of a stationary stochastic process can be transformed into a standardized time series. This paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions. In particular, the conditions are satisfied by stationary discrete-event simulations. Confidence intervals can be constructed using this lemma. For illustration, we develop two easily computed interval estimators for the process mean. When independent replications of the series are available, such as in computer simulation experiments, these interval estimators may be combined with the classical confidence interval estimator. These interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known. In an empirical study using three elementary simulated processes, the interval estimators presented here compare favorably with the classical interval estimator. In a recent paper, Goldsman and Schruben (Goldsman, D., L. Schruben. 1982. Asymptotic properties of some confidence interval estimators. Tech. Rep. 544, School of O.R.I.E., Cornell University, Ithaca, NY.) show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals.
Feature Article—Statistical Analysis of Simulation Output Data
Authors: Law Averill M.
Published: November 2008

We present a state-of-the-art survey of statistical analyses for simulation output data of a single simulated system. The various statistical problems associated with output data analyses such as start-up bias and determination of estimator accuracy are described in detail. We then discuss the best available techniques for addressing these problems, as well as topics for future research. The paper concludes with a discussion of how developments in simulation languages, computer graphics, and computer execution speed may affect the future of output analyses.
A Mathematical Programming Model for the Location of Access Controls in a Distributed Data Base Environment
Authors: Babad Yair M. , Hoffer Jeffrey A.
Published: November 2008

Advances in data bases and distributed processing are resulting in the development of distributed data bases that store data bases at several, distinct computer systems connected by a communication network. Although distributed data bases enable sharing of data resources by users from various nodes of the network, they present many design and control issues. Data must be efficiently stored and accessed by all users from all nodes, and yet be secured against unauthorized use. Considerable research has been devoted to physical data base design and its effects on storage and retrieval, and to security controls in data bases. On the other hand, the mutual relations of physical design and data base security and, in particular, the placement of security controls in a distributed environment has hardly been addressed. This paper fills this gap, in part, by explicitly modeling security control location and cost as part of the physical design of a distributed data base. These considerations result in the introduction of a “restricted access” design methodology, which simplifies the security control. Experimental results reported here concentrate on reducing the data transfer load of the communication network by using the restricted access method compared to more standard schemes. Suggestions are made for development of optimization algorithms for the models presented here.
Hospital Profit Planning under Medicare Reimbursement
Authors: Morey Richard C. , Dittman David A.
Published: November 2008

The federal Medicare regulations reimburse hospitals on a pro rata share of the hospital's cost. Hence, to meet its financial requirements, a hospital is forced to shift more of the financial burdens onto its private patients. This procedure has contributed to double digit inflation in hospital prices and to proposed federal regulation to control the rate of increase in hospital revenues. In this regulatory environment, we develop nonlinear programming pricing and cost allocation models to aid hospital administrators in meeting their profit maximizing and profit satisficing goals. The model enables administrators to explore tactical issues such as: (i) studying the relationship between a voluntary or legislated cap on a hospital's total revenues and the hospital's profitability, (ii) identifying those departments within the hospital that are the most attractive candidates for cost reduction or cost containment efforts, and (iii) isolating those services that should be singled out by the hospital manager for renegotiation of the prospective or “customary and reasonable” cap. Finally, the modeling approach is helpful in explaining the departmental cross subsidies observed in practice, and can be of aid to federal administrators in assessing the impacts of proposed changes in the Medicare reimbursement formula.
Long-Range Generation Planning Using Generalized Benders' Decomposition: Implementation and Experience
Authors: Bloom Jeremy A. , Caramanis Michael , Charny Leonid
Published: November 2008

This paper describes experience in implementing and using a generalized Benders' decomposition model for planning electricity generating capacity expansion. The model divides the problem into a master linear program, which generates trial expansion plans, and a set of nonlinear subproblems, which compute production cost and system reliability for the trial plan. Modifications of the original model described in the paper include a more efficient method for the subproblem computations based on the Gram-Charlier representation of probability distributions, representation of multiple unit plants, computation of upper and lower bounds on the optimal cost, and inclusion of nonthermal generating technologies. The paper also describes computational experience with the model and comparison with a dynamic programming model of the same problem. The Appendix discusses the convexity properties of the model with the modifications introduced in the paper.
Dynamic Lot-Sizing When Demand Timing Is Uncertain
Authors: Burstein Michael C. , Nevison Christopher H. , Carlson Robert C.
Published: November 2008

We characterize optimal solutions for the dynamic lot-sizing problem when demand quantities are known, but their timing is uncertain. The characterization states that for some possible history of demands following a period of production, there is a period with zero inventory before another period with production. Using this characterization, we outline a dynamic program for the solution of these problems. Some results from sample problems illustrate the variety of optimal solutions that can occur.
A Multiple Leader Stackelberg Model and Analysis
Authors: Sherali Hanif D.
Published: November 2008

This paper presents a new multiple leader-follower model that is a consistent extension of Stackelberg's leader-follower duopoly. The development contrasts with other existing extensions by demonstrating how the leader-firms can utilize the true reaction curve of the follower-firms; it also provides sufficient conditions for some useful convexity and differentiability properties of this function. For the proposed model, we conduct a static analysis and discuss the existence, uniqueness, and computation of an equilibrium solution, as well as study certain issues regarding the relative profits of leader and follower-firms. Since the Cournot oligopoly and the Stackelberg leader-follower models are special cases of this model, the analysis in this paper hopefully provides some further insights about these types of models.
A Dichotomous Search for a Geometric Random Variable
Authors: Hassin Refael
Published: November 2008

We are given a two-state system that starts in state 0, ends in state 1, and makes a single transition from state 0 to state 1 during N periods. If the system is in state 0, it moves to state 1 in the next period with a known positive time-independent probability. Once it reaches state 1, it remains there. By observing the state of the system at some intermediate period, we can learn whether this transition occurred earlier or not. An optimal search strategy minimizes the expected number of observations needed to locate the exact transition time. In this paper we show how to compute efficiently and how to approximate the optimal strategy. Applications to the problem arise in the areas of quality control and maintenance of communication and supply lines.
Minimizing Flow Time on Parallel Identical Processors with Variable Unit Processing Time
Authors: Meilijson I. , Tamir A.
Published: November 2008

We show that minimizing total flow time on parallel identical processors with nonincreasing unit processing time is achieved with shortest processing time (SPT) scheduling: Sequence the tasks in an order of nondecreasing lengths. Following this order and starting with the shortest task, process any task by the first processor that becomes available. If the unit processing time is allowed to be increasing, e.g., quadratically, the problem becomes NP-hard.
Technical Note—On Min-Max Integer Allocation Problems
Authors: Ichimori Tetsuo
Published: November 2008

This note treats a bottleneck integer allocation problem. The results obtained supercede those in this Journal due to Zeitlin (Zeitlin, Z. 1981. Integer allocation problems of min-max type with quasiconvex separable functions. Opns. Res. 29 207–211.), who has considered a similar allocation problem with a strictly quasiconvex objective function.
Technical Note—Assessment of Risk Attitude by a Utility Dependence Condition
Authors: Harvey Charles M.
Published: November 2008

This paper introduces a utility dependence condition and shows that it implies a multiattribute utility function that has a logarithmic or power form in terms of conditional utility functions on the individual attributes.
An O(|E|) Time Algorithm for Computing the Reliability of a Class of Directed Networks
Authors: Agrawal Avinash , Satyanarayana A.
Published: November 2008

This paper studies the problem of computing the source-to-terminal reliability, the probability that a source s can communicate with a terminal t, in a probabilistic directed network. It introduces a set of reliability-preserving reductions, called 2-neighbor-node reductions. We show that for a class of directed networks, called BSP-digraphs, such reductions are always admissible and the source-to-terminal reliability can be computed in time linear in the size of the network. A directed network D = (V, E) is a BSP-digraph if its underlying undirected graph is series-parallel. The BSP-digraphs considered can be cyclic or acyclic and both vertices as well as edges can fail. Any two vertices can be chosen as s and t. Previously, no polynomial time algorithms were known for this class of digraphs. The proposed method is also applicable to mixed graphs containing directed and undirected edges.
Two Probability Models of Pyramid or Chain Letter Schemes Demonstrating that Their Promotional Claims are Unreliable
Authors: Gastwirth J. L. , Bhattacharya P. K.
Published: November 2008

A variety of chain letters and pyramid schemes continue to be offered to the public. This article reviews two probability models which were developed in response to requests by attorneys faced with prosecuting promoters of such ventures. The two models were designed to establish the fraud underlying a quota pyramid scheme (which places a limit on the maximum number of participants) and a chain letter in which a participant could sell only two letters (unless he purchases a new letter). The models emphasize how dependent a participant's potential earnings are to his time of entry in the process and show that although a small percentage of participants (some early entrants) will make money, most will lose so that pyramid scheme investors, as a class, are defrauded.
Some Reliability Models for Safety Assessment
Authors: Thompson W. A.
Published: November 2008

This paper discusses probabilistic models of safety assessment, as applied to nuclear reactors. It compares the “per demand failure rate” method for calculating the annual probability of a reactor accident with an equally reasonable event sequencing model. One aspect of safety analysis is formulated as a maximum mark problem in a marked point process. We also introduce a concept of rare events that yields special computing formulas similar to those employed by practicing engineers. Implications for quantifying the safety of nuclear reactors are discussed.
The Total Time on Test Concept and Its Use in Reliability Theory
Authors: Bergman Bo , Klefsjö Bengt
Published: November 2008

More than 30 years ago, Epstein and Sobel introduced the Total Time on Test (TTT-) concept. During the last 10 years different generalizations of this concept have been defined and studied, e.g., the TTT-transform and the TTT-plot; a basic paper was presented by Barlow and Campo in 1975. Many of these generalizations have proven to be very useful in different areas of reliability, both from a theoretical and a practical point of view. The purpose of this expository paper is to present some of these generalizations and illustrate their value.
On the Use of Replacements to Extend System Life
Authors: Derman C. , Lieberman G. J. , Ross S. M.
Published: November 2008

We consider an extreme version of the replacement problem. A vital component of a system must be replaced before it fails, otherwise the system fails with no possibility of repairing the system. We assume that n spares are available and that the distribution of a component life is known; the objective is to schedule the replacements so that the expected life of the system is maximized. Our results range from an iterative formula for constructing the optimal schedule to more general mathematical properties of optimal schedules and expected times.
Percentile Residual Life Functions
Authors: Joe Harry , Proschan Frank
Published: November 2008

The α-percentile (0 < α < 1) residual life function at time t is defined as the α-percentile of the remaining life given survival up to time t. (Note that α-percentile is used in place of 100 α-percentile.) Two classes of life distributions defined by the α-percentile residual life function are the decreasing α-percentile residual life (DPRL-α) class and the new better than used with respect to the α-percentile (NBUP-α) class. These two classes are, respectively, analogous to the well-known decreasing mean residual life (DMRL) class and the new better than used in expectation (NBUE) class that involve the mean residual life function. We obtain properties of the α-percentile residual life function and of the DPRL-α, NBUP-α and their dual classes. Some results differ notably from corresponding results for the mean residual life function.
Multivariate Phase-Type Distributions
Authors: Assaf David , Langberg Naftali A. , Savits Thomas H. , Shaked Moshe
Published: November 2008

A (univariate) random variable is said to be of phase type if it can be represented as the time until absorption in a finite state absorbing Markov chain. Univariate phase type random variables are useful because they arise from processes that are often encountered in applications, they have densities that can be written in a closed form, they possess some useful closure properties, and they can approximate any nonnegative random variable. This paper introduces and discusses several extensions to the multivariate case. It shows that the multivariate random variables possess many of the properties of univariate phase type distributions and derives explicit formulas for various probabilistic quantities of interest. Some examples are included.
Selecting an Extreme-Value Distribution and the Transforming to a Specified Distribution
Authors: Hernández Fabián , Johnson Richard A.
Published: November 2008

If a component fails when its weakest element fails, the component failure time will be the minimum of the failure times for its elements. Because the extreme value distributions are the possible limiting distributions for minimums, they become prime candidates for the failure time distribution. We provide a statistical methodology for selecting the best fitting distribution from among the three types of extreme value distributions. Our Bayesian approach is based on a three-parameter family of transformations that transforms the extreme value distributions to the standard exponential distribution.
Estimating the Shift to Wear-Out of Systems Having Exponential-Weibull Life Distributions
Authors: Zacks S.
Published: November 2008

We develop a new family of life distributions, called the exponential-Weibull wear-out distributions, for systems whose failure rate function is a constant up to a change-point (wear-out point) and strictly increasing afterward. We derive properties of these wear-out distributions and develop a Bayes adaptive procedure for estimating the change point. Recursive formulas are given for determining the posterior probability that the change has occurred and its Bayes estimator. Results of numerical simulations are given to illustrate the properties of the adaptive procedure.
A Tandem Network of Queues with Deterministic Service and Intermediate Arrivals
Authors: Shalmon Michael , Kaplan Michael A.
Published: November 2008

We present a complete analysis of delays for a tandem network of queues with deterministic service and multiple, interfering sources. The model is of a packet-based data collection system consisting of some finite, but arbitrary, number of stations connected in tandem by a unidirectional, asynchronous transmission network. Packets, or, more generally, tasks enter the system at every station, are handed from station to station in store-and-forward fashion, and exit at the downstream end; there are no intermediate departures. The stations are provided with infinite storage, and the lines between them operate concurrently and asynchronously. Intermediate sources are Poisson; the source at the head of the network can be somewhat more general than Poisson. Tasks from each source wait at each station downstream of their point of origin. We calculate the joint steady-state moment-generating functions for these waiting times, provided that the line capacities do not increase in the direction of flow; the solution contains as a special case the steady-state moment-generating function for end-to-end delay for each source.
Conditions for Finite Ladder Height and Delay Moments
Authors: Wolff Ronald W.
Published: November 2008

We provide simple proofs for several known results: conditions for finite ladder height moments are obtained in a unified way for random walks under both the oscillating and drift cases. The random walk conditions are used to obtain conditions for finite delay moments for the GI/G/1 queue. The GI/G/1 conditions are then used to obtain the Kiefer and Wolfowitz conditions for finite moments of delay and of work in system for the GI/G/c queue.
Randomization Procedures in the Computation of Cumulative-Time Distributions over Discrete State Markov Processes
Authors: Melamed Benjamin , Yadin Micha
Published: November 2008

This paper proposes a methodology for computing numerical bounds on cumulative-time (i.e., the time spent in a specified set of states before entering another specified set of states) distributions over discrete state Markov processes. The methodology uses randomization procedures to compute results for appropriately defined transient Markov processes; the transient distribution computed is equivalent to the requisite cumulative-time distribution. A queueing application of the methodology to delay times in queueing networks is outlined and its efficacy is appraised by comparing the results with a sojourn time for a problem with a known distribution.
The Monopolistic Firm, Random Demand, and Bayesian Learning
Authors: Nguyen Dung
Published: November 2008

We extend the one-period model of a monopolistic firm with random demand into an intertemporal model under uncertainty. Compared to the myopic one-period output, the intertemporal output for the current period may be higher, equal to, or lower depending upon the effect of the current period's decisions on the discounted expected utilities derived from future periods' profits. When the demand function contains an unknown parameter whose true value the firm wishes to learn, we establish that while incurring a forgone utility in the learning process, the firm expects to realize future discounted utilities which would at least cover the expected cost of learning.
M/M/1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies
Authors: Lu F. V. , Serfozo R. F.
Published: November 2008

This paper studies an M/M/1 queueing decision process in which the arrival and service rates are chosen from a finite set whenever the queue length changes. Each choice has a switching cost depending on the chosen rates and those currently in use, and a usage cost depending on the chosen rates and the queue length; these switching and usage cost functions are submodular and satisfy additional technical conditions. The system objective is to find a policy for dynamically choosing the rates, based on the current rates and queue length, that minimizes the expected total discounted cost or average cost over an infinite horizon. We prove that there is a monotone hysteretic optimal policy in which the arrival and service rates are decreasing and increasing, respectively, in the queue length; there is a hysteresis (retardation) in the changing of the actions due to the switching costs. We establish this result by showing that such optimal policies exist for an equivalent discrete-time random walk decision process. Our results confirm a decade-old conjecture that the M/M/1 queue has a monotone hysteretic optimal control policy.
Probabilistic Analysis of Bin Packing Heuristics
Authors: Ong Hoon Liong , Magazine M. J. , Wee T. S.
Published: November 2008

In this paper we present both a probabilistic and statistical analysis of several bin packing heuristics. With mild conditions on the distribution of problem data, we show that the ratio of the expected number of bins packed for these heuristics to the number of elements converges to some constant. This constant can either be derived analytically or estimated through simulation. We analyze the variance in performance of these heuristics, and we further show that as the number of elements, n, increases, the probability that the number of bins required for these heuristics exceeds any fixed percentage of their expected performance goes to zero.
Production-Inventory with Equipment Replacement—PIER
Authors: Venkatesan M.
Published: November 2008

A two-dimensional Markov Decision Process model is used to combine the Production-Inventory problem and the Equipment Replacement problem. We provide two sets of sufficient conditions for the combined optimal policy to have a relatively simple monotonic structure.
A Separating Choice Hyperplane Algorithm for Evaluating Multiattribute Decisions
Authors: Dintersmith Ted
Published: November 2008

This paper presents an iterative algorithm for optimizing multiattribute decisions. It develops a separating choice hyperplane algorithm, which allows decision-makers to identify their most preferred point from a nonlinear convex set of feasible outcomes. In this interactive algorithm, the decision-maker reveals information about preferences by solving a series of elementary resource allocations. The resulting structure integrates a theoretically rigorous optimization procedure with intuitive assessment tasks. A practical application of the approach is presented.
Nested Renewal Processes with Special Erlangian Densities
Authors: Bendell A. , Scott N. H.
Published: November 2008

We consider the class of nested renewal processes in which all densities are Special Erlangian. We first derive explicit expressions for the transient and steady-state distributions of the accumulated number of shocks and for their mean and variance. We also consider situations with infrequent replacements. The transient and asymptotic distributions of accumulated damage are also studied. When the shape parameter of the second-order renewal distribution is large, so that replacement times are approximately normally distributed, our results show that the steady-state distribution of the accumulated number of shocks is approximately uniform. Some numerical examples are presented.
Realizable Performance Vectors of a Finite-Source Queue
Authors: Kameda Hisao
Published: November 2008

We study a scheduling problem on a finite-source queueing model which is identical to a two-stage closed Markovian cyclic queue consisting of a single-server (“processor”) and an infinite-server (“terminals”); each job has a distinct mean service time at the processor. We obtain a necessary and sufficient condition for a performance vector consisting of utilization factors (or average response times) of the processor for the jobs to be achievable by some scheduling strategy. The result is analogous to that obtained by Coffman and Mitrani on infinite-source single-server queues.
Author's Rejoinder
Authors: McCabe Bernard J.
Published: November 2008

This note responds to the critique of McCabe [McCabe, B. 1985. Accuracy and tactical implications of bearings-only ranging algorithms. Opns. Res. 33 94–103.] offered by Washburn and Daly [Washburn, A. R., Daly, P. H. 1985. Comments on “Accuracy and tactical implications of bearings-only ranging algorithms.” Opns. Res. 33 104–106].
A Queueing System with General-Use and Limited-Use Servers
Authors: Green Linda
Published: November 2008

We consider a queueing system with two types of servers and two types of customers. General-use servers can provide service to either customer type while limited-use servers can be used only for one of the two. Though the apparent Markovian state space of this system is five-dimensional, we show that an aggregation results in an exact two-dimensional representation that is also Markovian. Matrix geometric theory is used to obtain approximations for the mean delay times and other measures of interest for each customer type. We illustrate the methodology by applying it to analyze a token discount policy used by the Triborough Bridge and Tunnel Authority.
Technical Note—Alternative Model Formulations in Nonlinear Programming—Some Disastrous Results
Authors: Drud Arne
Published: November 2008

This paper describes some experiments with two alternative formulations of a nonlinear programming model. One apparently suitable formulation proves to be numerically disastrous for several algorithms. The paper discusses the reasons for this behavior and argues that solution systems need to be strengthened so that they can cope with alternative model formulations. As argued in the paper, it would be desirable to improve the numerical algorithms themselves, or to develop computerized modeling systems that can reformulate models into the form most suitable for a particular existing algorithm.
Simultaneous Bidding with a Fixed Charge if Any Bid is Successful
Authors: Smith Stephen A. , Rothkopf Michael H.
Published: November 2008

We consider the situation in which a bidder faces a group of simultaneous auctions that carry a single fixed charge, which is incurred if and only if one or more of the auctions are won. In a decision theoretic framework, we analyze the bidder's optimal strategy for three alternative formulations of the problem. If the bidder's only decision is selecting the auctions in which to bid, a simple decision rule is derived that holds regardless of the probabilities of winning. We also obtain necessary conditions for selecting the optimal bid levels. Finally, we present a single state variable dynamic programming formulation for obtaining the optimal amounts to bid in statistically independent auctions.
Geometric Programming: Estimation of Lagrange Multipliers
Authors: Rijckaert M. J. , Walraven E. J. C.
Published: November 2008

This paper presents a method for estimating Lagrange multipliers for generalized Geometric Programming. The Lagrange multipliers of a linearized problem serve as estimates of the generalized Geometric Programming multipliers.
Accuracy and Tactical Implications of Bearings-Only Ranging Algorithms
Authors: McCabe Bernard J.
Published: November 2008

Passive (bearings-only) ranging uses only directional information to deduce the distance to a moving target. This paper derives an estimate for the accuracy of a least squares passive ranging algorithm. The formula can be used to compare the effectiveness of various tactics.
Optimal Unemployment Insurance Policy
Authors: Zuckerman Dror
Published: November 2008

In this paper, we construct a theoretical model of unemployment insurance. Using techniques and concepts of game theory, we investigate, on one hand, the objectives and strategies of government, and on the other, those of an unemployed job seeker. Most of our results describing the job seeker's optimal strategies agree with the results found in the empirical literature in the area of unemployment insurance.
Equilibrium Analysis of Disaggregate Facility Choice Systems Subject to Congestion-Elastic Demand
Authors: Lee Hau Leung , Cohen Morris A.
Published: November 2008

This paper considers the impact of congestion on the spatial distribution of customer utilization of service facilities in a stochastic-dynamic environment. Previous research has assumed that the rate of demand for service is independent of the attributes of the facilities. We consider the more general case in which facility utilization is determined both by individual facility choice (based on the stochastic disaggregate choice mechanism) and by the rate of demand for service. We develop generalized results for proving that equilibria exist and describe sufficient conditions for the uniqueness and global stability of these equilibria. These conditions depend upon the elasticity of demand with respect to the level of congestion at the facilities, and on whether customers are congestion-averse or are congestion-loving. Finally, we examine special cases when these conditions are satisfied.
Optimal Ordering Strategies for Announced Price Increases
Authors: Taylor Sam G. , Bradley Charles E.
Published: November 2008

The familiar model for determining the optimal ordering strategy, given an announced price increase, assumes that the buyer has an opportunity to place an order at the end of the next economic order quantity cycle before the price increase takes effect. This paper extends the price increase model by relaxing the requirement on the timing of the price increase. Specifically, we develop optimal ordering strategies for situations where the price increase becomes effective at any future specified time. We also calculate savings for alternate ordering strategies.
The Transient Behavior of the M/M/s Queue, with Implications for Steady-State Simulation
Authors: Kelton W. David , Law Averill M.
Published: November 2008

Although the transient behavior of a queueing system is often of interest, available analytical results are usually quite restricted or are very complicated. We consider the M/M/s queue with an arbitrary number of customers present at time zero. We obtain probabilities in a relatively simple closed form that can be used to evaluate exactly several measures of system performance, including the expected delay in queue of each arriving customer. A numerical examination is carried out to see how the choice of initial condition affects the nature of convergence of the expected delays to their steady-state values. We also discuss the implications of these results for the initialization of steady-state simulations.
The Push-Out-Priority Queue Discipline
Authors: Heyman Daniel P.
Published: November 2008

We introduce a priority queue-discipline that is designed for loss systems (i.e., those with no waiting positions) in which the priority class of a customer can be determined only when the customer starts service. When the arrival processes are Poisson and the service times are exponentially distributed, we obtain a simple formula for the steady-state probability that an arrival of a given class will be served.
The Sequential Design of Bernoulli Experiments Including Switching Costs
Authors: Kolonko Michael , Benzing Harald
Published: November 2008

We consider a sequence of N trials, each of which must be performed on one of two given Bernoulli experiments. We assume the success probability of one experiment is known and the other is unknown. Performing two successive trials on different experiments incurs a switching cost. The problem is to choose an experiment for each trial in order to maximize the expected number of successes minus the expected switching costs. We show that an optimal design shares some well-known monotonicity properties, such as the “stopping-rule” and the “stay-on-a-winner” rule. We also show how to use these results to derive a simple algorithm for calculating the optimal design. Since the model contains the one-armed bandit problem as a special case, we also obtain new proofs for known results.
Technical Note—Forest Outturn Optimization by Dantzig-Wolfe Decomposition and Dynamic Programming Column Generation
Authors: Eng G. , Daellenbach H. G.
Published: November 2008

In this paper, we show how Dantzig-Wolfe decomposition, with delayed column generation by means of dynamic programming, can be used to determine the optimal set of bucking policies for entire stands of trees. Determined in this way, the bucking policies are consistent with wood resource qualities and quantities and end use product requirements, and represent the activities of a linear programming model that covers supply and demand constraints. We determine optimal bucking policies using dynamic programming techniques.
Signature Methods for the Assignment Problem
Authors: Balinski M. L.
Published: November 2008

The “signature” of a dual feasible basis of the assignment problem is an n-vector whose ith component is the number of nonbasic activities of type (i, j). This paper uses signatures to describe a method for finding optimal assignments that terminates in at most (n − 1)(n − 2)/2 pivot steps and takes at most O(n3) work.
Optimal Server Location on a Network Operating as an M/G/1 Queue
Authors: Berman Oded , Larson Richard C. , Chiu Samuel S.
Published: November 2008

This paper extends Hakimi's one-median problem by embedding it in a general queueing context. Demands for service arise solely on the nodes of a network G and occur in time as a Poisson process. A single mobile server resides at a facility located on G. The server, when available, is dispatched immediately to any demand that occurs. When a demand finds the server busy with a previous demand, it is either rejected (Model 1) or entered into a queue that is depleted in a first-come, first-served manner (Model 2). Service time for each demand comprises travel time to the scene, on-scene time, travel time back to the facility and possibly additional off-scene time. One desires to locate the facility on G so as to minimize average cost of response, which is either a weighted sum of mean travel time and cost of rejection (Model 1), or the sum of mean queueing delay and mean travel time. For Model 1, one finds that the optimal location reduces to Hakimi's familiar nodal result. For Model 2, nonlinearities in the objective function can yield an optimal solution that is either at a node or on a link. Properties of the objective function for Model 2 are utilized to develop efficient finite-step procedures for finding the optimal location. Certain interesting properties of the optimal location as a function of demand rate are also developed.
The Solution of Distance Constrained Mini-Sum Location Problems
Authors: Watson-Gandy C. D. T.
Published: November 2008

The problem considered in this paper requires determining the location of a given number of centers or facilities to minimize the sum of weighted distances to customers being served, subject to the constraint that no customer receives inadequate service. The method proposed is a partial enumerative procedure that employs both a graph-coloring algorithm (to generate feasible partitions) and an iterative location procedure with feasibility tests (to determine optimal locations). The procedure ensures the global optimum to this otherwise non-convex location-allocation problem. The procedure has been programmed and computational results are presented.
A Parametric Method for Solving the Linear Fractional Programming Problem
Authors: Wolf Hartmut
Published: November 2008

This paper describes an approach for determining the optimal solution of the linear fractional programming problem. This approach is based mainly on a parametric analysis of a related linear substitution problem. Whereas existing algorithms for linear fractional programs concentrate solely on determining the optimal solution, the approach described in this paper provides the decision maker with additional insights and valuable information on the underlying decision problem. When the usual algorithms are applied, this additional information, which is gained by the parametric analysis of the substitution problem, can be obtained only by further computational effort.
Explicit Solutions of M/G/C/ /N-type Queueing Loops with Generalizations
Authors: Lipsky Lester
Published: November 2008

Using recently developed Matrix-Algebraic techniques, we find explicit steady-state solutions of M/G/C/ /N-type loops that depend on a set of recursively defined matrices. We show that such systems are special cases of arbitrary service centers that contain (load dependent) exponential servers in which no more than C customers can be active simultaneously. We also outline a recursive algorithm that can be used to evaluate the properties of small- to moderate-sized systems. The solution to the M/G/C open system is then found by letting the overall customer population N go to infinity. The solutions for closed systems in general are not of the matrix geometric type, and only in the limit does the solution become geometric in form.
Using Confidence Limits for the Global Optimum in Combinatorial Optimization
Authors: Derigs Ulrich
Published: November 2008

Let z* be the (unknown) optimal value of a combinatorial optimization problem (in minimization form) and let z be a constant satisfying Prob(z* ≥ z) ≥ 1 − α for a fixed α ∈ (0, 1). Then z is called a statistical or probabilistic lower bound at significance level 1 − α. We discuss how statistical lower bounds can be used to measure the effectiveness of an approximate solution and to fathom subproblems in a branch and bound approach. After reviewing some methods for obtaining statistical lower bounds, we report on extensive computational experience for two notoriously difficult combinatorial optimization problems—the traveling salesman problem and the quadratic assignment problem. From our experience we conclude that statistical bounds are highly useful for quadratic assignment problems. In this problem context, the quality of simple analytic formulas is comparable to the quality of the maximum likelihood formula. In general, using statistics to aid in the solution of combinatorial optimization problems should be most useful when such problems are “large.”