bluuebunny/crossref_metadata_2025 huggingface dataset:
The Multiregion Dynamic Capacity Expansion Problem, Part I
Authors: Fong C. O. , Srinivasan V.
Published: November 2008

Consider the problem of determining a schedule of capacity expansions for m producing regions and a schedule of shipments from the regions to n markets so as to meet the market demands over a T-period planning horizon at minimum discounted capacity expansion and shipment costs. Both of these costs are assumed to be proportional to the amounts involved. The heuristic algorithm of this paper improves on feasible solutions by exchanging capacities between pairs of regions. The algorithm imbeds an optimization procedure to seek the best feasible solution in the direction specified by the heuristic. Computational results for both real and randomly generated problems show that the heuristic algorithm is computationally efficient and yields close to optimum solutions.
Suboptimal Design for Large Scale, Multimodule Systems
Authors: White Chelsea C. , Schlussel Kent
Published: November 2008

We present a general procedure for determining computationally tractable suboptimal designs, associated upper and lower bounds on the optimal expected cost function, and a procedure for determining a suboptimal design which improves these bounds for an important class of large scale, stochastic decision processes. This class, called the multimodule Markov decision process, is distinguished by the characteristic that each element of the vector state process has dynamics that operate independently of the other elements. The general suboptimal design procedure is based on the solution of a subglobal optimization problem for each module, where for each subglobal problem it is assumed that only restricted state information from the composite system is available to its associated module-decision maker. The computational implications of this suboptimal design approach are analyzed. A multi-component replacement example illustrates this suboptimal design procedure, its associated bounds, and a suboptimal procedure which improves these bounds.
Modeling Natural Gas Regulatory Proposals Using the Project Independence Evaluation System
Authors: Murphy Frederic H. , Sanders Reginald C. , Shaw Susan H. , Thrasher Richard L.
Published: November 2008

During the 1978 debates on the Natural Gas Pricing Act, Senator Henry M. Jackson of Washington, then Chairman of the Committee on Energy and Natural Resources, requested an analysis of the impact of the proposed legislation. A generic methodology was developed to represent alternative (average cost) regulatory proposals within the (marginal cost) framework of an economic equilibrium using the collection of models then known as the Project Independence Evaluation System. The results precipitated a controversy over the letter and intent of the competing legislative proposals.
Exhaustible Resource Models: The Value of Information
Authors: Chao Hung-Po
Published: November 2008

This paper investigates the effect of future uncertainties on current policy decisions relating to resource depletion. The analysis is based on an extension of the Hotelling-Nordhaus exhaustible resource model. It is assumed that existing extraction capacity will be gradually replaced as the more expensive backstop technologies become economically competitive. Under plausible conditions, it is found that short-run investment and pricing decisions are insensitive to distant future uncertainties. Hence the expected value of perfect information is low. This indicates that deterministic scenarios may provide a good approximation to a stochastic problem, and this may be used to simplify the work of policy analysis. A numerical model of the U.S. economy is employed to illustrate these ideas.
On Hedging and TRIAD Force Levels
Authors: denBroeder Jerry , Mitchell Dave
Published: November 2008

The strategic forces of the United States collectively form a TRIAD of three components consisting of ICBMs, SLBMs, and bombers. To guard against the catastrophic (total) loss of any one component, the TRIAD could be structured so that the combined capability of the two remaining components is sufficient to perform the basic TRIAD mission. With respect to this assumed hedging concept and based upon an idealized model construct, component force level requirements are derived as measured by the fraction of the mission each individual component should be able to accomplish on its own. The analysis is generalized to include combined force postures of fewer or more components. A simple cost structure for the acquisition and maintenance of individual components is introduced, permitting comparison of systems comprising two, three, four, and more components, in terms of their total costs to achieve the mission while providing the desired hedge.
Multiple Finite Production Rate Dynamic Lot Size Inventory Models
Authors: Sethi Suresh , Chand Suresh
Published: November 2008

This paper investigates the dynamic inventory model for the case when production in a period is restricted to a finite set of specified values. The model allows the production rate to be any value in the set {0, P, 2P, …, mP}, where m is a nonnegative integer. It is assumed that the setup cost is paid only once for a production block and the holding cost is monotonically or linearly increasing. Efficient planning horizon procedures have been developed for this model.
Supply-Demand Decomposition of the National Coal Model
Authors: Wagner Michael H.
Published: November 2008

The National Coal Model is a highly disaggregate model of domestic coal supply and demand markets. The model has been extensively and successfully applied, but its linear programming component is computationally burdensome. In this paper we report computational results from experiments to reduce solution time through decomposition. The model is decomposed into two capacitated pure networks: a supply side, whose units of flow are Btus of coal; and a demand side, whose units of flow are megawatts of electrical generation capacity. The method used for integrating these components is a market equilibration (“cobweb”) algorithm. The mechanism is not generally convergent, but it produces an excellent starting basis for completion by standard linear programming methods. Order of magnitude solution time reductions have been achieved by the combined procedure. A new decomposition algorithm for linear programs is presented. The method is motivated by the present application, but has not been implemented.
Optimal Preventive Maintenance Policies for Repairable Systems
Authors: Nguyen D. G. , Murthy D. N. P.
Published: November 2008

We study the problem of optimal preventive maintenance policies for repairable systems. After each repair the system improves but the failure rate function increases with the number of repairs carried out. Two types of preventive maintenance policies are considered. The criterion for optimal policies is to minimize the expected cost per unit time for an infinite time span. It is shown that under certain reasonable assumptions, both policies have unique solutions. An algorithm to compute the optimal solutions is described.
Single Machine Scheduling with Series-Parallel Precedence Constraints
Authors: Burns R. N. , Steiner G.
Published: November 2008

This paper considers a set of tasks to be sequenced for processing on a single machine. The possible sequences may be restricted by given precedence constraints. For each feasible sequence we have an additive cost function (e.g., tardiness or weighted tardiness) and the objective is to find a feasible sequence with minimal total cost. An efficient algorithm is presented for the case when the set of precedence constraints can be represented by a series-parallel graph. The algorithm is based on the earlier known dynamic programming approach, its main new achievement is the use of a compact labeling scheme for series-parallel graphs which is the best possible in a certain sense.
Technical Note—The Optimal Estimation of the Expected Number in a M/D/∞ Queueing System
Authors: Grassmann W. K.
Published: November 2008

This paper shows that in the M/D/∞ queueing system with service time S, the optimal way to estimate the expected number in the system is by sampling the system at time 0, S, 2S, …, kS. In this way, the best unbiased estimate from a sampling interval of length T = kS can be obtained.
Technical Note—Further Results on an Infinite Capacity Shuttle with Control at a Single Terminal
Authors: Weiss Howard J.
Published: November 2008

The infinite capacity shuttle system that is described by Ignall and Kolesar (Ignall, E., P. Kolesar. 1974. Optimal dispatching of an infinite capacity shuttle: Control at a single terminal. Opns. Res. 22 1008–1024.) is considered. Passengers arrive at each of two terminals according to independent Poisson Processes. The vehicle can be held at only one of the terminals. When the vehicle is dispatched it transports all of the passengers waiting at terminal 1 to terminal 2, immediately picks up the passengers at terminal 2 and returns to terminal 1. It is known that under general conditions the optimal vehicle dispatching policy is a control limit policy: Dispatch the shuttle if and only if the number of passengers waiting at both terminals is at least as large as some cutoff value. In this paper a method for computing the optimal cutoff value is presented. In addition we examine the savings that result when using a control limit policy rather than the more traditional policy of scheduled periodic service. Last, we prove a conjecture by Ignall and Kolesar regarding the optimal policy for instances when the dispatcher does not know the number of passengers waiting at terminal 2.
Technical Note—On Location Dominance on Spherical Surfaces
Authors: Drezner Zvi
Published: November 2008

In a recent paper Aly et al. (Aly, A. A., D. C. Kay, D. W. Litwhiler, Jr. 1979. Location dominance on spherical surfaces. Opns. Res. 27 972–981.) proved that an optimal solution to a “minisum” problem on a sphere must lie in the convex hull of the demand points if the demand points are not located entirely on a great circle arc. The case when all demand points are on a great circle arc remains an open question. In this note we prove that if demand points are located on a great circle arc, so is the optimal solution point.
Technical Note—Bounds in the Generalized Weber Problem under Locational Uncertainty
Authors: Juel Henrik
Published: November 2008

An existing analysis of the bounds on the Weber problem solution under uncertainty is incorrect. For the generalized problem with arbitrary measures of distance, we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found with little computational effort. Numerical examples illustrate the analysis.
Technical Note—An Upper Bound Useful in Optimizing Search for a Moving Target
Authors: Washburn Alan R.
Published: November 2008

A feasible solution always establishes a lower bound on the maximum value of an objective function. In the class of problems considered here, the objective function is detection probability, and it is shown how successive feasible methods of searching also establish a sequence of nondecreasing upper bounds on the maximum detection probability.
Strip Mining Phosphate Rock with Large Walking Draglines—A Problem in Operations Research
Authors: Dunlap Jack W. , Jacobs Herbert H.
Published: November 2008

The mining of phosphate rock by strip mining methods is dependent on the effectiveness of a great many managerial decisions which affect the pattern of operations. A mathematical analog was developed to simulate operation of the mining system in such a way as to make possible prediction of the consequences of any alternative decision (in value and cost terms). The results of this study were translated in such a form that they could be applied routinely to the management of mining operations. This study is reported in the three separate phases which the authors believe to characterize the operations-research method (1) formulation of the problem, (2) research and model development, and (3) translation and implementation of results.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
A Proposal for Revising New York's Subway Fare Structure
Authors: Vickrey William S.
Published: November 2008

Consideration of the effect of the fare structure on the efficiency with which transit facilities are utilized leads to the conclusion that operation of a transit system on a self-liquidating or cost-covering basis, either by a private utility company or by a public authority, will inevitably fall considerably short of arriving at an optimum adjustment. Any governmental unit whose finances are in reasonably good shape can materially improve the over-all welfare of its residents by raising the rates of some appropriate taxes and lowering transit fares to a level conducive to more efficient utilization of the transit facilities. The most efficient utilization of the New York subway system requires a fare structure rather drastically different from those now generally in use, and generally at a level which would yield revenues falling considerably short of covering total costs.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Approximate Salvo Kill Probabilities for Small and Medium Sized Targets when Cumulative Damage is Unimportant
Authors: Walsh John E.
Published: November 2008

This paper considers salvo-firing situations where the cumulative damage contribution is unimportant and presents some approximate probability expressions of an analytical nature. These results are valid if the target size and vulnerability are not too large compared to the round dispersion, and the other assumptions adopted are those ordinarily used for problems of this type. These expressions show that, for the two-dimensional situations considered, a salvo kill probability can be approximately stated as an explicit function of four parameters. These parameters are the number of ammunition rounds, the average target vulnerability times the target size, the salvo aiming error dispersion, and a function of the round dispersion and two dispersion type terms which depend on the target size, shape, and vulnerability. Thus the target properties are condensed into three numbers. Also the resulting probability expressions are of a form which permits direct examination of the effects of changes in the salvo-aiming system (fire-control system), the number and properties of the ammunition rounds, and the properties of the target.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
A Discussion of Education for Operations Research
Authors: Schultz Andrew
Published: November 2008

This paper is based upon discussion which took place during a Symposium on Education for Operations Research which was held in Ithaca in October, 1954. The participants were Dr. Russell L. Ackoff, Case Institute of Technology; Prof. J. G. Brainerd, University of Pennsylvania; Dr. Glen D. Camp, Melpar, Inc.; Dr. W. P Cunningham, U.S. Naval Post Graduate School, Dr. Harold O. Davidson, The Johns Hopkins University, Dr. Merrill M. Flood, Columbia University, Dr. Ellis A. Johnson, The Johns Hopkins University, Dr. Joseph F. McCloskey, The Johns Hopkins University, Dr. R. E. McGarrah, Cornell University; Dr. Loring G. Mitten, The Ohio State University, Prof. J. E. Morton, Cornell University, Mr. Russell R. O'Neill, University of California, Dr. Edward S. Quade, The Rand Corporation, Dean Robert H. Roy, The Johns Hopkins University, Dr. Melvin Salveson, General Electric Company, Dr. Andrew Schultz, Jr., Cornell University; and Prof. T. M. Whitin, Massachusetts Institute of Technology.

The transcript of many portions of the discussion is too sketchy to permit direct quotation or publication, and this paper represents a sincere effort to present the opinion of the group where agreement was reached, or the points of disagreement, where the latter seems appropriate. It should be emphasized that the thoughts expressed are based upon the tape and stenographic transcripts available, and cannot be taken to report the full opinion of any individual participant.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Direct Use of Extremal Principles in Solving Certain Optimizing Problems Involving Inequalities
Authors: Klein Bertram
Published: November 2008

It is shown how extremal principles may be used in their rigorous sense to solve certain optimizing problems involving inequalities. The method applies to both linear and non-linear type problems as illustrated by the examples included in the paper, and is particularly suited for electronic digital computation because of the trigger-type, “either-or,” nature of the solution. Certain problems concerned with the low weight design of structures, arising in the author's field of structural mechanics, can be considered to lie in the general field of operations research. Almost invariably these problems contain inequality side conditions and hence may be solved by the methods of the paper.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—The Proposed Amendment to the Constitution
Authors: Rinehart R. F.
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—The Operations-Research Professional Structure
Authors: Brennecke Charles N.
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Problem of Optimum Distribution of Effort—A Correction
Authors: Miehle William
Published: November 2008

I am indebted to Dr. John M. Danskin for pointing out the fact that my proof for additive effects in my paper on “Numerical Solution of the Problem of Optimum Distribution of Effort” in the November 1954 issue of this Journal (vol. 2, p. 433) is not entirely rigorous.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Use of Linear Programming in Capital Budgeting
Authors: Gunther Paul
Published: November 2008

Linear programming has found wide application in solving such diverse problems as determining the optimum utilization of machines, most different scheduling procedures, most economical routing of transportation, best system of salary scales, etc. An example has recently come to our attention which illustrates the value of this new technique, and the practical type of solution arrived at, in the important field of capital budgeting. In order to protect the identity of the company involved, we have modified slightly some of the figures and the nature of the product.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
An Analysis of a Railroad Classification Yard
Authors: Crane Roger R. , Brown Frank B. , Blanchard Robert O.
Published: November 2008

A freight car in the United States spends approximately two-thirds of its time stationary; a significant portion of this time in hump classification yards is spent in queues waiting to be inspected and classified into outbound trains. This paper describes the development of a model for these queues and the application of the Monte Carlo method to the analysis of these queues for a particular classification yard. An elementary form of feedback is included in the model. Using the model of yard operation, certain methods of improving yard operation are determined.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Application of Discrete Variable Servo Theory to Inventory Control
Authors: Vassian Herbert J.
Published: November 2008

Until recently the bases for designing inventory control systems have been poorly understood. This paper discusses the application of discrete variable servo theory to the analysis of inventory control systems, using the simplest periodic inventory replenishment case as an example. The objective is to design an inventory control scheme which will minimize the variance of the inventory balance subject to imposed conditions. A reorder rule is derived and shown to give minimum inventory variance. The “obvious” reorder rule derived is one of several observed in practice in situations approximating the simple case The dependence of the inventory level variance on the sales forecast error and system constants is stated explicitly. The principles and methods illustrated are applicable to more complex types of discrete control systems.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
A Challenge to Operations Research
Authors: Parkhurst George L.
Published: November 2008

Invited address at the Seventh National Meeting of the Society in Los Angeles, August 15, 1955.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Where is the New Blood?
Authors: Morse Philip M.
Published: November 2008

Speech given at the dinner of the Seventh National Meeting of the Society in Los Angeles on August 15, 1955.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Applications of Game Theory in Fighter Versus Bomber Combat
Authors: Caywood T. E. , Thomas C. J.
Published: November 2008

The theory of games offers a valuable framework in which to evaluate future or proposed weapons systems. These evaluations are generally based upon the computed performance of the various weapons systems in a typical combat situation. The computation of this performance invariably involves the specification of certain tactics which are relatively easy to change by either combatant. It is reasonable to assume that these combatants would be “rational” in the game-theoretic sense.

Although the specific type of weapons systems discussed here are those of individual aircraft, the concepts are directly applicable to other systems. However, for clarity of exposition we shall not refer to any of these generalizations.

This paper was prepared for, and portions were presented at the First Annual Meeting of the Operations Research Society in Cleveland, Ohio, May 16, 1953.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Symposium on Applications of Operations Research to Urban Services—A Determination of the Optimum Location of Fire-Fighting Units in New York City
Authors: Valinsky David
Published: November 2008

This paper discusses the multiple approaches employed in treating the problem of efficiency of fire-company locations in New York City.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Evaluating the Adequacy of Airport Parking Lots
Authors: Hurst Frederick V.
Published: November 2008

The Port Authority manages the three major airports in the New York-New Jersey Metropolitan Region.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Engineering Studies of Urban Traffic Flow
Authors: Barnes Henry A.
Published: November 2008

The one thing that a traffic engineer learns early in life is that, no matter how many statistics or how many studies he makes, he never can come up with an answer that will completely satisfy everyone. Naturally, no traffic improvement can be made without changing people's habits, without eliminating some special privileges, and, in some cases, without actually hurting people—from a business standpoint. However, if his plans are based on good, sound data, the average traffic engineer can support his program before the public or, if necessary, in our courts.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Lanchester Prize Acceptance Speech
Authors: Edie Leslie C.
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Priority Assignment—A Correction
Authors: Cobham Alan
Published: November 2008

Dr. John Danskin has called to my attention the fact that formula (3) of my paper “Priority Assignment in Waiting Line Problems” (this Journal, vol. 2, p. 70, Feb. 1954), which gives the expected waiting time for units of each priority level of a single-channel waiting-line system is not, as I stated, valid when the system under consideration is in a permanently saturated state; that is, when the volume of incoming traffic is greater than can be handled by the system.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Approximating a Point Process by a Renewal Process, I: Two Basic Methods
Authors: Whitt Ward
Published: November 2008

This paper initiates an investigation of simple approximations for stochastic point processes. The goal is to develop methods for approximately describing complex models such as networks of queues and multiechelon inventory systems. The proposed approach is to decouple or decompose the model by replacing all the component flows (point processes) by independent renewal processes. Here attention is focused on ways to approximate a single point process by a renewal process. This is done in two steps: First, properties of the point process are used to specify a few moments of the interval between renewals; then a convenient distribution is fit to these moments. Two different methods are suggested for specifying the moments of the renewal interval. The stationary-interval method equates the moments of the renewal interval with the moments of the stationary interval in the point process to be approximated. The asymptotic method, in an attempt to account for the dependence among successive intervals, determines the moments of the renewal interval by matching the asymptotic behavior of the moments of the sums of successive intervals. These two procedures are applied to approximate the superposition (merging) of point processes. The purpose here is to provide a better understanding of these procedures and a general framework for making new approximations. In particular, the two basic procedures can be used as building blocks to construct refined composite procedures. Composite procedures for the ∑Gi/G/1 queue (with a superposition arrival process) are discussed by Albin in Part II. Albin has developed a hybrid procedure for approximating the mean sequence length and other characteristics in the ∑Gi/G/1 queue for which the average error when compared with simulated values was 3% over a large number of test systems.
Statistical Results on Control Variables with Application to Queueing Network Simulation
Authors: Lavenberg Stephen S. , Moeller Thomas L. , Welch Peter D.
Published: November 2008

The development and application of control variables for variance reduction in the simulation of a wide class of closed queueing networks is discussed. These networks allow multiple types of customers, priorities and blocking. Alternative methods of generating confidence intervals from independent replications of a simulation are investigated. A result is given which quantifies the loss in variance reduction caused by the estimation of the optimum control coefficients. This loss is an increasing function of the number of control variables. Good variance reduction is obtained providing that the number of control variables remains small.
Technical Note—Maintaining the All-Integer Property of an ILP when Using Cuts in Rational Data
Authors: Holm Søren
Published: November 2008

If all data for an ILP is integer and a cut is given in rational data, then there exists a transformation of the cut such that all the coefficients and the right hand side constant are integers, thus requiring the slack variable also to be an integer. By repeating this transformation inductively an all-integer problem remains all-integer. As an application of this result, it is shown how to solve an ILP by using transformed strong MILP cuts. As these cuts are superior to fractional cuts, a more efficient algorithm results.
Technical Note—Probability of Success in the Search for a Moving Target
Authors: Mangel Marc
Published: November 2008

The probability of detection in the search for a randomly moving target is calculated for the case of a target whose motion is a diffusion process and known searcher path. The probability of detection can be calculated by solving a backward diffusion equation. Corwin (Corwin, T. 1980. On multiplicative functionals on diffusion processes. SIAM J. Appl. Math. 38 112–119.) gives a solution of the backward equation for a special case. In general, exact solutions do not exist and other methods are needed. In this paper, the backward equation is solved approximately by using a formal asymptotic method, valid when the intensity of the random motion is small. The general solution is illustrated for the case of spatially homogeneous drift and diffusion coefficients. In this case, the asymptotic solution can be evaluated analytically.
Optimal Replacement for Shock Models with General Failure Rate
Authors: Gottlieb Gary
Published: November 2008

A device is subject to a series of shocks which arrive as a semi-Markov process. Shocks cause damage and eventually failure will occur at the time of arrival of one of the shocks. The device must be replaced upon failure at some cost but it also can be replaced before failure at a lower cost. We consider the general case where the failure rate need not be increasing and replacement can be made at any time. The form of the optimal replacement policy is found and conditions are determined for which a control limit policy is optimal.
Hierarchical Production Planning: A Two-Stage System
Authors: Bitran Gabriel R. , Haas Elizabeth A. , Hax Arnoldo C.
Published: November 2008

This paper presents a hierarchical approach to plan and schedule production in a manufacturing environment that can be modeled as a two-stage process. A conceptual framework for this approach is described. The specific mathematical models proposed for the various hierarchical levels are discussed. The methodology is evaluated in an actual setting. The performance of the hierarchical system is contrasted with an MRP design. Encouraging results are reported.
Action Elimination Procedures for Modified Policy Iteration Algorithms
Authors: Puterman Martin L. , Shin Moon Chirl
Published: November 2008

This paper proposes bounds and action elimination procedures for policy iteration and modified policy iteration. Procedures to eliminate nonoptimal actions for one iteration and for all subsequent iterations are presented. The implementation of these procedures is discussed and encouraging computational results are presented.
Iteration and Sensitivity for a Spatial Equilibrium Problem with Linear Supply and Demand Functions
Authors: Irwin Caulton L. , Yang Chin W.
Published: November 2008

We investigate a set of spatial equilibrium conditions which apply, for example, to a multiregional, multicommodity market or to a physical system of interconnected sources and sinks. Under additional hypotheses, the equilibrium conditions are the Kuhn-Tucker conditions for a concave, quadratic programming problem. For the case in which the equilibrium conditions do not correspond to a programming problem, an iterative process for obtaining a solution is discussed. This iteration is motivated by the Project Independence Evaluation System (PIES) energy model algorithm. An algorithmic method to determine the sensitivity of an equilibrium solution vector to data perturbations is described. Both the sensitivity analysis and the convergence of the iterative solution method are based upon a solvability lemma, which guarantees that a solution of the equilibrium conditions may be expressed in terms of the problem data. Nondegeneracy assumptions for the inter-regional flows are unnecessary for this discussion. An example of the equilibrium problem which arose in modeling the supply and demand of eastern coal is briefly described.
Solutions of M/G/1//N-type Loops with Extensions to M/G/1 and GI/M/1 Queues
Authors: Carroll J. L. , van de Liefvoort A. , Lipsky Lester
Published: November 2008

Closed form solutions of the joint equilibrium distribution of queue sizes are derived for a large class of M/G/1//N queues, i.e., any closed loop of two servers in which one is exponential (but possibly load dependent), and the other has a probability density function which has a rational Laplace transform and a queueing discipline that is FCFS. The class of G/M/k//N queues are included as special cases of load-dependent servers. The solutions are presented in terms of vectors and matrices whose size depends only on the distribution of the general server and not on the number of customers in the system. Efficient algorithms are outlined, and expressions for various system measurements are presented. Depending on the relative service rates of the two servers, solutions for both the M/G/1 and GI/M/1 open queues are derived as limiting cases of the M/G/1//N system. All results are contrasted with existing formulas.
Tandem Queues with Dependent Service Times in Light Traffic
Authors: Wolff Ronald W.
Published: November 2008

Light traffic results about delay in queue are obtained for r single-channel queues in tandem with Poisson arrivals where the r service times of the same customer at different stations have an arbitrary joint distribution. By light traffic, we mean asymptotic behavior as server utilization approaches zero. A detailed analysis of delay at the second station is presented for r = 2. An expression for expected delay is obtained for r = 3. Methods developed for these purposes may be used for arbitrary r > 3. For arbitrary r, an expression for expected delay is obtained in the special case where the r service times of the same customer are equal. For exponential service, a simple closed form expression is obtained. For r = 2, it is shown that when service times are positively quadrant dependent, expected delay is greater than when service times are independent. In some cases, the ratio between expected delays in the dependent and independent cases is very large, particularly when r is large. This agrees with and generalizes published results in several papers and conflicts with results in one paper. An explanation for this conflict is given.
The Optimality of Full Service Policies
Authors: Sobel Matthew J.
Published: November 2008

The structure of optimal service rate adjustment policies is considered here for single server, multiple server, and arborescence network models. It is shown that a full service policy, namely, always using the highest effective service rate, is optimal under general conditions. The criteria are the long-run averages of the cost per customer served and the cost per unit time. Underlying costs are assumed to include waiting time penalties and rates depending on the number of customers in the system and on the pace at which service is proceeding. The only essential restriction on probability distributions or costs is that the highest service rate minimizes the expected cost of serving a customer.
Duality and Distance Constraints for the Nonlinear p-Center Problem and Covering Problem on a Tree Network
Authors: Tansel B. C. , Francis R. L. , Lowe T. J. , Chen M. L.
Published: November 2008

The problem of locating a fixed number, p, of facilities (centers) on a network, where there are constraints on the center locations and where the centers provide a service to customers (demand points) located at vertices of the network is addressed. The cost or “loss” of servicing a given demand point is a nonlinear function of the distance between the demand point and the closest center. We consider the case where the network has special structure (a tree network), i.e., there is a unique shortest path between any two points on the network. We also provide and interpret a dual to this problem and give polynomially bounded procedures for solving both problems. The primal location problem is solved with the aid of a related problem for which we also give a dual.
Minimizing the Number of Vehicles to Meet a Fixed Periodic Schedule: An Application of Periodic Posets
Authors: Orlin James B.
Published: November 2008

In this paper we consider countably infinite partially ordered sets (posets) in which the order relations occur periodically. We show that the problem of determining the minimum number of chains (completely ordered subsets) needed to cover all of the elements may be solved efficiently as a finite network flow problem. A special case of the chain-cover problem for periodic posets is the problem of minimizing the number of individuals to meet a fixed periodically repeating set of tasks with set-up times between tasks. For example, if we interpret tasks as flights and individuals as airplanes, the resulting problem is to minimize the number of airplanes needed to fly a fixed daily repeating schedule of flights, where deadheading between airports is allowed.
Erratum
Authors: Grassmann W. K.
Published: November 2008

My technical note “The Optimal Estimation of the Expected Number in a M/D/∞ Queueing System” (Grassmann, W. K. 1981. The optimal estimation of the expected number in a M/D/∞ queueing system. Opns. Res. 29 1208–1211) starts with the words “In stimulation.” Even though I hope that the note is stimulating, I actually meant “In simulation” because that is where the results of the paper was really be applied.
Technical Note—Reducing Space Requirements for Shortest Path Problems
Authors: Munro J. Ian , Ramirez Raul J.
Published: November 2008

The problem of determining the shortest path through a level network using as little space as possible is considered. Let k denote the number of levels and assume each level contains m nodes. A space efficient technique is presented by which the shortest route from a source to a sink may be found in a complete level graph using θ(m + k) storage locations and a factor of only θ(log k) more basic operations than space inefficient methods. If an edge from node p of level i to node q of level i + 1 exists only if p ≥ q, then the space saving technique may also be employed. In this case the run time of the algorithm is at most twice that of conventional approaches.
Assessing Risks Through the Determination of Rare Event Probabilities
Authors: Sampson Allan R. , Smith Robert L.
Published: November 2008

We consider the problem of evaluating the probability of occurrence of rare, but potentially catastrophic, events. The lack of historical data renders conventional statistical approaches inappropriate. The problem is compounded by complex multivariate dependencies that may exist across potential event sites. In order to evaluate the likelihood of one or more such catastrophic events occurring, we provide an information theoretic model for merging a decision maker's opinion with expert judgment. Also provided is a methodology for the reconciling of conflicting expert judgments. This merging approach is invariant to the decision maker's viewpoint in the limiting case of exceptionally rare events. These methods are applied to likelihood assessment of liquid natural gas tanker spills and seismic induced light water nuclear reactor meltdowns.
Conditional Rate Derivation in the Presence of Intervening Variables Using a Markov Chain
Authors: Shachtman Richard H. , Schoenfelder John R. , Hogue Carol J.
Published: November 2008

When conducting inferential and epidemiologic studies, researchers are often interested in the distribution of time until the occurrence of some specified event, a form of incidence calculation. Furthermore, this interest often extends to the effects of intervening factors on this distribution. In this paper we impose the assumption that the phenomena being investigated are governed by a stationary Markov chain and review how one may estimate the above distribution. We then introduce and relate two different methods of investigating the effects of intervening factors. In particular, we show how an investigator may evaluate the effect of potential intervention programs. Finally, we demonstrate the proposed methodology using data from a population study.
A New Dominance Concept in Scheduling n Jobs on a Single Machine with Ready Times and Due Dates
Authors: Erschler J. , Fontan G. , Merce C. , Roubellat F.
Published: November 2008

Scheduling a set of jobs on a single machine is studied where each job has a specified ready time and due date (limit times). A dominance relationship is established within the set of possible sequences and results in an important restriction of the number of sequences to be considered in solving the feasibility problem. Establishing the dominance relationship leading to this restriction requires only the ordering of ready times and due dates and is thus independent of job processing times and of any change in limit times which does not affect the given order.
A Single-Server Queue with Cyclostationary Arrivals and Arithmetic Service
Authors: Kaplan Michael
Published: November 2008

This paper studies a class of nonblocking single-server queues which arise in connection with the modeling of store-and-forward message-switching multiplexors. The essential feature of these queues is that the input processes are periodic and the service times discrete. The inputs are imagined as representing the aggregate of perhaps many statistically dissimilar streams; the statistics of the interarrival and service times within one period can be complex and arbitrary. We present an exact, transform-domain analysis for steady-state virtual waiting-time. This extends existing literature on periodic queues, and illuminates the precise nature of the trade-off between computational cost and model complexity in the class of models considered. We believe that the generality permitted of the input processes is of practical interest.
Illustrative Comparison of One Utility's Coal and Nuclear Choices
Authors: Keeney Ralph L. , Sicherman Alan
Published: November 2008

The technology choices facing an individual utility are complex decision problems. The paper illustrates a method designed to assist an individual utility company in making these choices in a logically consistent manner. The resulting evaluation model, based on the principles of decision analysis, explicitly addresses the complexity to provide a basis for decision making and support for defending the decision before reviewers. The model, which incorporates economic, environmental, social, safety, and regulatory effects, is demonstrated using a coal/nuclear choice which may be faced by Utah Power and Light Company in the near future. This analysis is meant to be illustrative; more effort would be needed to gather information to support a policy decision.
Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders' Decomposition
Authors: Bloom Jeremy A.
Published: November 2008

This paper discusses application of generalized Benders' decomposition in a model for planning least-cost investments in electricity generating capacity subject to probabilistic reliability constraints. The planning problem is decomposed into a set of subproblems, each representing the operation of a set of generating plants of fixed capacity in 1 year, and a master problem, representing optimal capacity investments over the entire planning horizon. The subproblems are solved using a procedure called probabilistic simulation, which calculates the expected cost of operating the generating system, the reliability level, and dual multipliers reflecting the value of small changes in the plant capacities. The master problem is a linear program which uses these dual multipliers to approximate the nonlinear cost and reliability functions. The solution to the capacity expansion problem is found by iteratively solving the master problem and the subproblems.
Technical Note—When Does the βth Percentile Residual Life Function Determine the Distribution?
Authors: Arnold Barry C. , Brockett Patrick L.
Published: November 2008

Knowledge of the βth percentile residual life function does not uniquely determine the underlying distribution. Additional information about the tail behavior of the distribution is needed. Knowledge of both the β1 and β2 percentile residual life functions does uniquely determine the distribution provided that β1 and β2 are noncommensurate. This corrects and extends the results of Schmittlein and Morrison (Schmittlein, D. C., D. G. Morrison. 1981. The median residual lifetime; a characterization theorem and an application. Opns. Res. 29 392–399.).
Technical Note—Mathematical Pitfalls in the One Machine Multiproduct Economic Lot Scheduling Problem
Authors: Schweitzer Paul J. , Silver Edward A.
Published: November 2008

We consider a group of products sharing the same piece of production equipment, and show that two mathematical problem formulations in the literature are ill-posed. In both cases, the infimum of the cost function occurs at a boundary point that is not feasible.
An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems
Authors: Odoni Amedeo R. , Roth Emily
Published: November 2008

This paper examines the transient behavior of infinite-capacity, single-server, Markovian queueing systems. It estimates Q(t), the expected number of customers in queue at time t, by numerically solving the sets of simultaneous, first-order differential equations that describe these systems. Empirical results have been drawn from these observations. For small values of t, the behavior of Q(t) is strongly influenced by the initial state of the queueing system. For systems with deterministic initial conditions, one can roughly predict which of a small set of patterns this behavior will follow. After an initial period of time and independently of initial conditions, Q(t) approaches Q(∞) in a manner that can be approximated through a decaying exponential function. On the basis of experimental evidence, we have developed an expression that provides a good approximation to the observed values of the time constant associated with this exponential function. This expression can also be used to determine an upper bound for the amount of time required until Q(t) is close to Q(∞).
Stochastic Scheduling with Release Dates and Due Dates
Authors: Pinedo Michael
Published: November 2008

We consider stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables, the release dates are random variables with an arbitrary joint distribution, and the due dates are random variables with a joint distribution that satisfies certain conditions. Our development establishes simple policies that minimize such criteria as the expected weighted sum of completion times and the expected weighted number of late jobs. These results contrast markedly with the deterministic counterparts of these models for which no polynomial time algorithms are known.