bluuebunny/crossref_metadata_2025 huggingface dataset:
The Poisson Distribution as a Limit for Dependent Binomial Events with Unequal Probabilities
Authors: Walsh John E.
Published: November 2008

Many operations-research type problems are concerned with a number of events each of which has two possible outcomes (denoted by, say, “success” and “failure”). Very frequently for these problems the quantity of interest can be stated in terms of the probabilities of specified numbers of “successes” for the group of binomial events considered. The evaluation of these probabilities can be greatly simplified if it is known that they can be approximated by a Poisson distribution. For the special case where each event has the same “success” probability and the events are statistically independent, the binomial probability distribution is applicable. It is well known that the Poisson distribution approximates the binomial distribution if the number of events is large and the probability of “success” is small (see, e.g., Hoel, P. G. 1947. Introduction to Mathematical Statistics. Wiley, 50.). In Koopman [Koopman, B. O. 1950. Necessary and sufficient conditions for Poisson's distribution. Proc. Amer. Math. Soc. 1 813–823.] this result was extended to the case of independent binomial events with possibly different probabilities for “success.” This paper presents a further extension in which an event is not required to be statistically independent of all the other events. These results indicate that the Poisson distribution often is applicable to operations-research problems dealing with large numbers of binomial events that have small “success” probabilities.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
On the Numerical Solution of the Transportation Problem
Authors: Houthakker H. S.
Published: November 2008

The linear transportation problem consists in finding a pattern of shipments between m origins with given surpluses and n destinations with given deficits such that the total cost of transportation is minimized. The method of solution proposed here is iterative and will lead to the optimum in a finite number of steps. It involves finding a good first approximation by simple inspection and improving it by successive adjustments. The earlier stages of the proposed method are less laborious than the simplex method, but the latter has the advantage when the adjustments become more complicated. The proposed method may therefore be used as a starting approach to be followed by the simplex method if the optimum is not reached with simple adjustments only.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
From Plato to the Linear Program
Authors: Earl of Halsbury
Published: November 2008

Talk presented at the Third Annual Lecture in Business and Management to the Informal Seminar on Operations Research, The Johns Hopkins University, October 20, 1954.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Parametric Objective Function (Part 2)—Generalization
Authors: Gass S. I. , Saaty Thomas L.
Published: November 2008

In Part 1 (Saaty, T. L., S. I. Gass. 1954. Parametric objective function (Part 1). J. Opns. Res. Soc. Am. 2 316.), the cost function in the general linear programming problem was parametrized with one parameter and the problem of generating solutions completely studied. In Part 2, a generalization to the n-parameter case is outlined, with special emphasis on the two-parameter case. An example is supplied for this case.

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 Non-Numerical Approach to Production Scheduling Problems
Authors: Akers Sheldon B. , Friedman Joyce
Published: November 2008

In a typical production scheduling problem, n parts must be fabricated using m machines, and each part must be fabricated in a given order on the machines. It is desired to schedule the parts so that the program is optimal with respect to some given criteria. In general, (n!)m programs must be examined. To obtain the ultimate solution, it is necessary to know for each part its actual time of fabrication on each machine. However, it is shown that without consideration of numerical values, it is possible to eliminate initially a great number of the possible programs by purely non-numerical methods.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Determination of the Maximal Steady State Flow of Traffic Through a Railroad Network
Authors: Boldyreff Alexander W.
Published: November 2008

A simple and rapid method of estimating the maximal steady state flow of traffic through a railway network is described and illustrated by examples The method, as presently described, is entirely empirical in character and no generality is claimed. Essentially, it is an illustration of the application of the techniques of gaming to certain classes of mathematical problems. This study is an outcome of a suggestion by General F. S. Ross (U.S.A., Ret.), T. E. Harris, and others, and it has been prepared as a contribution to their much broader project.

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—Inequality-Constrained Stationary-Value Problems
Authors: Camp Glen D.
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.
Sensitivity Analysis of a Nonlinear Water Pollution Control Model Using an Upper Hudson River Data Base
Authors: Fiacco Anthony V. , Ghaemi Abolfazl
Published: November 2008

The sensitivity of the optimal waste treatment cost of a water pollution control model is analyzed. This analysis is conducted for the policy mandating a fixed dissolved oxygen requirement, using an upper Hudson River data base Details concerning the formulation, solution, and sensitivity analysis of the model are presented. It is shown that the maximum allowable dissolved oxygen deficit is unequivocally the parameter to which the optimal waste treatment cost is most sensitive. All of the many parameters involved in the model are analyzed and, relative to stipulated assumptions, are shown to have from significant to negligible impact on the waste treatment cost.
A Problem of Optimal Choice and Assignment
Authors: Rose John S.
Published: November 2008

Within the conventional framework of the so-called secretary problem, we introduce two decision makers, one of whom is dominant. The objectives are to select the two best objects and immediately to assign them to the decision makers so that the dominant one obtains the best object. Optimal strategies for selection and assignment, and the maximum probability of achieving the objectives, are derived. We also investigate an important suboptimal strategy: the dominant decision maker acts to maximize the probability of obtaining the very best object while, independently, the other decision maker acts to maximize the probability of selecting the second best. Although it has intuitive appeal, this suboptimal strategy is rather poor; indeed, the two decision makers may trade with one another the objects they select without affecting their chances of obtaining the desired objects. An interesting by-product of this study is that a simple solution in closed form is obtained for the problem of selecting the second best object.
Technical Note—Equity and Public Risk: Some Empirical Results
Authors: Hammerton M. , Jones-Lee M. W. , Abbott V.
Published: November 2008

Is the prospect of the certain loss of one (as yet unidentified) life in a population of N people equivalent to the exposure of the N people to independent risks of death of 1/N each? In a recent issue of this journal Keeney argued that this would, in general, not be the case and showed that a preference for a more equitable distribution of physical risk implies a preference for the independent risks rather than the certain loss of unidentified life, while “catastrophe aversion” implies the reverse. In this note we report empirical results which suggest that a majority of individuals display “catastrophe aversion” rather than “equity proneness,” at least for the kind of alternatives described above.
Optimal Integrated Control of Univoltine Pest Populations with Age Structure
Authors: Shoemaker Christine A.
Published: November 2008

A procedure is presented for calculating optima integration and timing of biological, chemical and cultural methods for control of a univoltine pest population in a random environment. The procedure describes a system of high dimension by two nested models: a stochastic dynamic programming problem with four state variables and a more detailed differential equation model describing the effect of management and weather on population demography and crop yield. A computational algorithm is presented which reduces computation requirements for the population model from about 1013 operations to 106 operations for a typical example. Results are presented from the application of the method to control the alfalfa weevil by a combination of insecticide applications, early harvesting, and biological control provided by a parasite.
An Iterative Aggregation Procedure for Markov Decision Processes
Authors: Mendelssohn Roy
Published: November 2008

An iterative aggregation procedure is described for solving large scale, finite state, finite action Markov decision processes (MDPs). At each iteration, an aggregate master problem and a sequence of smaller subproblems are solved. The weights used to form the aggregate master problem are based on the estimates from the previous iteration. Each subproblem is a finite state, finite action MDP with a reduced state space and unequal row sums. Global convergence of the algorithm is proven under very weak assumptions. The proof relates this technique to other iterative methods that have been suggested for general linear programs.
A Finite Difference Equations Approach to a Priority Queue
Authors: Brandwajn Alexandre
Published: November 2008

The main goal of this note is to demonstrate the use of a direct approach, as opposed to generating functions, for solving balance equations of a queueing system whose state is described by two independent variables. The basic idea is to consider a function of two variables as a set of functions of one independent variable. Hence the balance equations may be viewed as a set of simultaneous difference equations, and solved using the appropriate techniques. This method may allow the inclusion of queue-dependent service and arrival rates, and an easy treatment of finite queueing rooms. This is illustrated in the example of a two-level preemptive priority queue with exponentially distributed interarrival and service times.
Poisson Arrivals See Time Averages
Authors: Wolff Ronald W.
Published: November 2008

In many stochastic models, particularly in queueing theory, Poisson arrivals both observe (see) a stochastic process and interact with it. In particular cases and/or under restrictive assumptions it has been shown that the fraction of arrivals that see the process in some state is equal to the fraction of time the process is in that state. In this paper, we present a proof of this result under one basic assumption: the process being observed cannot anticipate the future jumps of the Poisson process.
Imperfect Competition in the International Energy Market: A Computerized Nash-Cournot Model
Authors: Salant Stephen W.
Published: November 2008

This paper describes the conceptual structure, properties, and solution approach of a computerized model of the international energy market. The model treats energy producers as players in a multistage, noncooperative game. The goal of each player (or cartel of players) is assumed to be maximization of discounted profit subject to technical, political, and resource constraints. The model calculates that collection of intertemporal extraction and price paths from which a player can unilaterally deviate only at a loss—the open-loop, Nash equilibrium. The model integrates the theory of exhaustible resources due to Hotelling and the theory of oligopoly due to Nash and Cournot. Although useful as a teaching device to illustrate theoretical results, its main function is to facilitate analysis of real-world resource problems. The model is flexible, allowing the user to specify not only cost, demand, and reserve information but also assumptions about who belongs to what coalition. Two shortcomings deserve note. The strategies of players are restricted to time-dated (open-loop) paths. Also, lags cannot be accommodated in the current version. The restriction of the strategy space significantly increases tractability and will permit the incorporation of lags and other complications in the future. The model was built under government contract and is in the public domain.
On Convergence of the PIES Algorithm for Computing Equilibria
Authors: Ahn Byong-Hun , Hogan William W.
Published: November 2008

Equilibria in market models with continuous market supply functions can be obtained by computing fixed points. With an activity analysis representation of production, fixed-point algorithms would converge slowly. Further, since the market model here is of a partial equilibrium nature, the market demand function may not exhibit the integratability condition, precluding the formulation of the market equilibrium problem as an economic surplus maximization problem. We examine an iterative algorithm, the PIES method, for locating equilibria in markets whose production is described by optimization over a finite set of activities and whose econometric demand function does not possess the integrability property. Convergence properties of the algorithm along with existence and uniqueness of market equilibrium are summarized.
Technical Note—On the Solution of an Inventory Model with Variable Lead Times
Authors: Sphicas Georghios P.
Published: November 2008

This paper investigates the solution to an inventory model with constant noninterchangeable demand and random lead times with a general distribution. It is shown that two distinct and complementary cases result. In each case bounds are developed for the optimal values of the decision variables. Furthermore, the solution can be reduced to a one-dimensional search for a unique root. The two cases are illustrated with the case of exponential lead times.
Technical Note—Equity in Risk Bearing
Authors: Broome John
Published: November 2008

Von Neuman-Morgenstern utility functions are found incompatible with valuing fairness and lead to an invalid conclusion about risk proneness.
An Optimizing Nuclear Exchange Model for the Analysis of Nuclear War and Deterrence
Authors: Grotte Jeffrey H.
Published: November 2008

A formulation of a two-strike nuclear exchange has enabled its global optimization by nonconvex programming. This formulation, together with a more detailed physical model involving four strategic weapon classes on both sides, is used to explore strategic war outcomes as a function of selected planning parameters.
Stochastic Allocation Rules
Authors: Agnihothri Saligrama , Karmarkar Uday S. , Kubat Peter
Published: November 2008

This paper considers the allocation of a fixed amount of resource across competing activities, where the rate of use of the allocated amounts is stochastic. The allocated amounts are said to have run out when the first of the allocations is used up and another distribution must then be considered. This problem arises in the allocation of stocks of a commodity to branch warehouses and in the allocation of production time to items that are jointly produced. It also occurs in the allocation of spares to subsystems when the total number of spares is constrained by volume or cost and when failure of one subsystem causes a failure of the whole system. Two alternative formulations are presented: the Maximization of Expected Time to Runout and the Minimization of Expected Discounted Time to Runout. Bounds are developed on the problems by using deterministic and exponential models for the time to runout. The case of two competing processes is investigated numerically, and it appears that the solutions to the bounding problems provide effective heuristics at least for such small problems.
Technical Note—Extension of the Elzinga-Hearn Algorithm to the Weighted Case
Authors: Charalambous Christakis
Published: November 2008

The problem considered in this note is that of locating a single new facility among m existing facilities with the objective of minimizing the maximum weighted Euclidean distance of the new facility from the existing facilities, without making the assumption that all the weights are equal. The new algorithm takes into consideration the structure of the problem, and it will terminate in a finite number of iterations if exact arithmetic is used.
Technical Note—Analysis of a Layered Defense Model
Authors: Nunn Walter R. , Glass David V. , Hsu Ih-Ching , Perin David A.
Published: November 2008

We consider a defense system model in which a cluster of attackers tries to penetrate several layers of defense. The layers of defense are independent and produce attrition in accordance with a binomial distribution—each layer having its own pk. The model is simplistic, but provides a useful approximation in various military settings, e.g., to an ICBM defense system. Questions of interest might pertain to distributions of surviving attackers at each stage, to the ordering of the defense layers, or to the sizing of the total defense. A complete analysis is displayed, based on a Markov chain formulation. It is shown that the distribution of survivors at each stage is binomial if the initial distribution is binomial. The class of transition matrices is shown to commute and to be closed under matrix multiplication. The eigenvectors of these transition matrices can be packaged into a triangular matrix whose nonzero rows are those of Pascal's triangle. The model illustrates a nonstationary Markov chain which admits a closed form analysis. Possible nonmilitary applications of such population modeling are also pointed out.
Optimal Control of Production Sequences: A Continuous Parameter Analysis
Authors: Vickson R. G.
Published: November 2008

In a production sequence the presence of random variations in the completion times of successive jobs causes deviations from planned schedules. The probability is high that such deviations persist over long periods, so managerial intervention will generally be required to restore schedule integrity. This paper treats two problems in the optimal control of such sequences, using a continuous work formulation in which the uncontrolled schedule deviation is a Wiener process. The first problem concerns long run production in the presence of a piecewise-linear operating cost rate during off-schedule production that can be expedited or halted at extra cost, with the latter action involving a fixed cost. An explicit average cost minimizing policy is developed and justified. The second problem concerns batch production with a piecewise-linear penalty cost for off-schedule batch completion. In this problem the controller can expedite production only. The existence of a transient single critical-number optimal policy is proved, and bounds on the critical numbers are developed. A simple but remarkably accurate formula for the critical number curve is developed using numerical methods.
Optimal Locations on a Line Are Interleaved
Authors: Denardo Eric V. , Huberman Gur , Rothblum Uriel G.
Published: November 2008

Suppose n facilities are to be located on a fine segment so as to minimize cost function. One might expect that the facilities' optimal locations have the following interleaving property: if one of the n facilities is removed and if the locations of the others are shifted by reoptimizing, each remaining facility's location shifts toward the location of the one removed, but not farther toward it than the original location of the adjacent facility. This paper presents two models whose solutions have this interleaving property and four examples of such models. An additive criterion is used in one model, a minimax criterion in the other. In the additive model, the minimum cost is a convex function of n; in the minimax model, it is nonincreasing.
Efficient Algorithms for the (Weighted) Minimum Circle Problem
Authors: Hearn Donald W. , Vijay James
Published: November 2008

The (weighted) minimum covering circle problem is a well-known single facility location problem used in emergency facility models. This paper introduces a classification scheme, based on fundamental mathematical programming concepts, for algorithms which solve both weighted and unweighted versions. One result of this classification is proof that a recently developed method is identical to one developed in the nineteenth century. Also, within the classification scheme, efficient new algorithms are given for the weighted problem. The results of some extensive computational tests identify the (empirically) fastest methods.
Technical Note—A Partitioning Problem with Additive Objective with an Application to Optimal Inventory Groupings for Joint Replenishment
Authors: Chakravarty A. K. , Orlin J. B. , Rothblum U. G.
Published: November 2008

We consider a problem of optimal grouping and provide conditions under which an optimal partition of an ordered set S = {r1, …, rn} consists of subsets of consecutive elements. We transform the problem into the problem of finding a shortest path on a directed acyclic graph with n + 1 vertices (for which efficient algorithms exist). These results may be used to solve the problem of grouping n items in stock into subgroups with a common order cycle per group so as to minimize the resulting economic order quantity costs.
Feature Article—Decision Analysis: An Overview
Authors: Keeney Ralph L.
Published: November 2008

This article, written for the nondecision analyst, describes what decision analysis is, what it can and cannot do, why one should care to do this, and how one does it. To accomplish these purposes, it is necessary first to describe the decision environment. The article also presents an overview of decision analysis and provides additional sources for its foundations, procedures, history, and applications.
Regret in Decision Making under Uncertainty
Authors: Bell David E.
Published: November 2008

Evidence exists that people do not always make decisions involving uncertain monetary rewards as if they were maximizing expected utility of final assets. Explanations for this behavior postulate that the cognitive demands of consistency to such a theory are too great. However, situations exist in which more than mental shortcuts are involved and these anomalies raise questions about expected utility theory as a guide to behavior. This paper explores the possibility that expected utility theory appears to fail because the single outcome descriptor—money—is not sufficient. After making a decision under uncertainty, a person may discover, on learning the relevant outcomes, that another alternative would have been preferable. This knowledge may impart a sense of loss, or regret. The decision maker who is prepared to tradeoff financial return in order to avoid regret will exhibit some of the behavioral paradoxes of decision theory. By explicitly incorporating regret, expected utility theory not only becomes a better descriptive predictor but also may become a more convincing guide for prescribing behavior to decision makers.
Strength of Preference and Risky Choice
Authors: Sarin Rakesh Kumar
Published: November 2008

This paper provides conditions under which a utility function under risk can be legitimately interpreted to measure strength of preference between consequences. These conditions require that if a decision maker regards the preference difference between acts a and b to be the same as the preference difference between acts a′ and b′ for every state of the world, then the preference difference between a and b should be regarded as equivalent to the preference difference between a′ and b′. A key assumption is that a decision maker's preference differences between acts given one state of the world should be independent of common consequences given other states of the world. Usefulness of this result is discussed.
Simulation of a Health Insurance Market with Adverse Selection
Authors: Feldman Roger D. , Dowd Bryan E.
Published: November 2008

A health insurance market is examined in which individuals with a history of high utilization of health care services tend to select fee-for-service (FFS) insurance when offered a choice between FFS and health maintenance organizations (HMOs). In addition, HMOs are assumed to practice community rating of employee groups. Based on these observations and health plan enrollment and premium data from Minneapolis-St. Paul, a deterministic simulation model is constructed to predict equilibrium market shares and premiums for HMO and FFS insurers within a firm. Despite the fact that favorable selection enhances their ability to compete with FFS insurers, the model predicts that HMOs maximize profits at less than 100% market share, and at a lower share than they could conceivably capture. That is, HMOs would not find it to their advantage to drive FFS insurers from the market even if they could. In all cases, however, the profit-maximizing HMO premium is greater than the experience-rated premium and, thus, the average health insurance premium per employee in firms offering both HMOs and FFS insurance is predicted to be greater than in firms offering one experience-rated plan. The model may be used to simulate the effects of varying the employer's method of contributing to health insurance premiums. Several contribution methods are compared. Employers who offer FFS and HMO insurance and pay the full cost of the lowest-cost plan are predicted to have lower average total premiums (employer plus employee contributions) than employers who pay any level percent of the cost of each plan.
Application of Multi-Attribute Utility Theory to Measure Social Preferences for Health States
Authors: Torrance George W. , Boyle Michael H. , Horwood Sargent P.
Published: November 2008

A four-attribute health state classification system designed to uniquely categorize the health status of all individuals two years of age and over is presented. A social preference function defined over the health state classification system is required. Standard multi-attribute utility theory is investigated for the task, problems are identified and modifications to the standard method are proposed. The modified method is field tested in a survey research project involving 112 home interviews. Results are presented and discussed in detail for both the social preference function and the performance of the modified method. A recommended social preference function is presented, complete with a range of uncertainty. The modified method is found to be applicable to the task—no insurmountable difficulties are encountered. Recommendations are presented, based on our experience, for other investigators who may be interested in reapplying the method in other studies.
An Iterative Estimation and Validation Procedure for Specification of Semi-Markov Models with Application to Hospital Patient Flow
Authors: Weiss Elliott N. , Cohen Morris A. , Hershey John C.
Published: November 2008

This article presents a methodology to identify and specify a continuous time semi-Markov model of population flow within a network of service facilities. An iterative procedure of state space definition, population disaggregation, and parameter estimation leads to the specification of a model which satisfies the underlying semi-Markov assumptions. We also present a test of the impact of occupancy upon realizations of population flows. The procedure is applied to data describing the movements of obstetric patients in a large university teaching hospital. We use the model to predict length-of-stay distributions. Finally, we compare these results with those that would have been obtained without the procedure, and show the modified model to be superior.
A Stochastic Model to Measure Patient Effects Stemming from Hospital-Acquired Infections
Authors: Kastner George T. , Shachtman Richard H.
Published: November 2008

We introduce a Markov chain model to represent a patient's path in terms of the number and type of infections s/he may have acquired during a hospitalization period. The model allows for categories of patient diagnoses, surgery, the four major types of nosocomial (hospital-acquired) infections, and discharge or death Data from a national medical records survey including 58,647 patients enable us to estimate transition probabilities and, ultimately, perform statistical tests of fit, including a validation test. Novel parameterizations (functions of the transition matrix) are introduced to answer research questions on time-dependent infection rates, time to discharge or death as a function of patient diagnostic groups and conditional infection rates reflecting intervening variables (e.g., surgery).
Planning for a Vertically Integrated Forest Industry
Authors: Barros Oscar , Weintraub Andres
Published: November 2008

A linear programming model and an information system designed for tactical planning in a vertically integrated forest industry is presented. The industry jointly manages forest lands, a pulp plant and a sawmill. The model considers technological, geographical, silvicultural and economic aspects of planning and gives guidelines for management of timber lands, the supply of timber to plant and mill, and the buying and selling of timber. An information system, with a matrix generator and a report writer, was developed to facilitate handling of input and output by users. Implementation of the model and empirical results are reported.
Periodic Replacement with Increasing Minimal Repair Costs at Failure
Authors: Boland Philip J. , Proschan Frank
Published: November 2008

When an expensive one unit system fails or breaks down, it is often more practical to perform “minimal repair” than to make a replacement or perform a complete overhaul. Instead replacements or complete overhauls are made periodically at fixed multiples of some predetermined time T. In this paper we treat a model for this minimal repair-periodic replacement policy, and consider the problems of determining: (1) the period T which minimizes the total expected cost of repair and replacement over a fixed time horizon [0, t), and (2) the period T which minimizes the total expected cost per unit time over an infinite time horizon.
A Holistic Methodology for Modeling Consumer Response to Innovation
Authors: Bagozzi Richard P.
Published: November 2008

A general structural equation model for representing consumer response to innovation is derived and illustrated. The approach both complements and extends an earlier model proposed by Hauser and Urban. Among other benefits, the model is able to take measurement error into account explicitly, to estimate the intercorrelation among exogenous factors if these exist, to yield a unique solution in a statistical sense, and to test complex hypotheses (e.g., systems of relations, simultaneity, feedback) associated with the measurement of consumer responses and their impact on actual choice behavior. In addition, the procedures permit one to model environmental and managerially controllable stimuli as they constrain and influence consumer choice. Limitations of the procedures are discussed and related to existing approaches. Included in the discussion is a development of four generic response models designed to provide a framework for modeling how consumers behave and how managers might better approach the design of products, persuasive appeals, and other controllable factors in the marketing mix.
Parallel Scheduling Algorithms
Authors: Dekel Eliezer , Sahni Sartaj
Published: November 2008

Parallel algorithms are given for scheduling problems such as scheduling to minimize the number of tardy jobs, job sequencing with deadlines, scheduling to minimize earliness and tardiness penalties, channel assignment, and minimizing the mean finish time. The shared memory model of parallel computers is used to obtain fast algorithms.
Feature Article—The Process of Search Planning: Current Approaches and Continuing Problems
Authors: Stone Lawrence D.
Published: November 2008

This paper discusses an approach to search planning in which the planner blends subjective and objective methods and produces plans that are a compromise between theoretical optimality and operational feasibility.
Implementation and Testing of a Primal-Dual Algorithm for the Assignment Problem
Authors: McGinnis Leon F.
Published: November 2008

State-of-the-art computational results have shown that primal simplex algorithms are more efficient than primal-dual algorithms for general minimum cost network flow problems. There is, however, some controversy concerning their relative merits for solving assignment problems. This paper presents a detailed development for a computationally efficient primal-dual algorithm and extensive computational comparisons to primal simplex algorithms.
A Class of Variance-Constrained Problems
Authors: Sniedovich Moshe
Published: November 2008

A Lagrange multiplier solution procedure is developed for a class of variance-constrained problems. The method, based on the separation of the variance and an algorithm for determining the optimal value of the mean, relies on the availability of a method of solving a modified problem in which the variance operation is replaced by the generalized variance operator. It is indicated that the procedure can be used in conjunction with dynamic programming to solve a variety of variance-constrained problems which allow the consideration of adaptive strategies. The procedure is demonstrated by a simple numerical example.
Decompositions of Multiattribute Utility Functions Based on Convex Dependence
Authors: Tamura Hiroyuki , Nakamura Yutaka
Published: November 2008

We describe a method of assessing von Neumann-Morgenstern utility functions on a two-attribute space and its extension to n-attribute spaces. First, we introduce the concept of convex dependence between two attributes, where we consider the change of shapes of conditional utility functions. Then, we establish theorems which show how to decompose a two-attribute utility function using the concept of convex dependence. This concept covers a wide range of situations involving trade-offs. The convex decomposition includes as special cases Keeney's additive/multiplicative decompositions, Fishburn's bilateral decomposition, and Bell's decomposition under the interpolation independence. Moreover, the convex decomposition is an exact grid model which was axiomatized by Fishburn and Farquhar. Finally, we extend the convex decomposition theorem from two attributes to an arbitrary number of attributes.
Order-Picking in a Rectangular Warehouse: A Solvable Case of the Traveling Salesman Problem
Authors: Ratliff H. Donald , Rosenthal Arnon S.
Published: November 2008

This paper addresses the problem of order-picking in a rectangular warehouse that contains crossovers only at the ends of aisles. An algorithm is presented for picking an order in minimum time. The computational effort required is linear in the number of aisles. The procedure has been implemented on a microcomputer A 50-aisle problem requires only about 1 minute to solve.
The Discrete-Time Sequencing Expansion Problem
Authors: Neebe A. W. , Rao M. R.
Published: November 2008

We consider a sequencing expansion problem in which capacity can be added only at discrete points in time. Given is a forecast of demand in each period, and a set of expansion projects each with a given capacity and cost. The problem is to determine the sequence of expansions necessary to provide sufficient capacity to meet the demand in all periods at minimum cost. The problem is solved using Lagrangean relaxation. Computational results are given.
Feature Article—Decision-Aiding Models: Validation, Assessment, and Related Issues for Policy Analysis
Authors: Gass Saul I.
Published: November 2008

The extension of OR decision-aiding models and OR methodology from operational and technological settings to the field of policy analysis has caused analysts and users to question whether the OR process can handle the requirements of this new area. This paper reviews the evolving nature of OR methodology, the difficulties that have arisen in applying it, and the attempts to improve the use of OR methodology in policy analysis. The analyst's role in providing information to the user to determine whether and how a specific OR model can be used as a decision aid is emphasized. Relevant information for the analyst to provide covers model validation, assessment, utility, confidence and documentation.
Oil Stockpiles and Import Reductions: A Dynamic Programming Approach
Authors: Chao Hung-Po , Manne Alan S.
Published: November 2008

This paper analyzes oil stockpiling policies using models in which U.S. policy choices are restricted to just two instruments—stockpiles and disruption “tariffs.” The model considers the influence of U.S. (and, in general, OECD) import demands upon the OPEC price for oil, and the duration and severity of oil disruptions induced by disturbances among the OPEC nations. Our development is based upon a probabilistic view of disruptions analyzed by applying dynamic programming.
Mean-Variance Approximations to Expected Logarithmic Utility
Authors: Pulley Lawrence B.
Published: November 2008

In this paper, we investigate how closely functions of means and variances can approximate Von Neumann-Morgenstern expected utility modeled as a logarithmic utility-of-wealth function. Using historical security return data, we computed portfolios maximizing expected logarithmic utility and compared them to those maximizing appropriate mean-variance formulations. In all cases the approximations were very good, and in many cases the optimal portfolios were virtually identical. We conclude that the mean-variance model can serve as a useful surrogate to at least one popular alternative investment strategy.
Search for a Moving Target: The FAB Algorithm
Authors: Washburn Alan R.
Published: November 2008

We propose and study an iterative Forward And Backward (FAB) algorithm applicable to the problem of computing optimal search plans when the target's motion is modeled by a discrete space and time Markov chain. This paper generalizes the class of objective functions to which the method applies.
Technical Note—Mean Drifts and the Non-Ergodicity of Markov Chains
Authors: Sennott Linn I. , Humblet Pierre A. , Tweedie Richard L.
Published: November 2008

An important question in stochastic modeling is whether or not a denumerable state Markov chain is ergodic. We extend a result of Kaplan giving a condition for the non-ergodicity of a chain based on its drifts. We also clarify the condition under which the mean drift in the stationary chain is zero.
Technical Note—Computational Viability of a Constraint Aggregation Scheme for Integer Linear Programming Problems
Authors: Onyekwelu Denis C.
Published: November 2008

We present the results of a computational evaluation of two constraint aggregation approaches for solving integer linear programs. In some applications, particularly set partitioning problems, the schemes can aggregate significantly different number of constraints. We first discuss the implementation of these approaches using both single and multiple precision arithmetic. From these results, we empirically show that, in practical implementation and evaluation of an aggregation scheme, the degree of difficulty encountered in solving the resulting equality constrained knapsack problem is crucial. We conclude, as contrasted with the optimism expressed in some published works, that the aggregation approach has limited value for solving general integer linear programs, but may be useful in developing a heuristic algorithm for the set partitioning problem.
Time Step vs. Dynamic Optimization of Generation-Capacity-Expansion Programs of Power Systems
Authors: Levin Nissan , Tishler Asher , Zahavi Jacob
Published: November 2008

We derive conditions under which the time-step, or the myopic, approach to generation capacity planning in the power industry yields solutions identical to the solution obtained by an equivalent dynamic model that views the capacity expansion program simultaneously over time. The conditions are derived for thermal power systems for which the capacity expansion program is formulated using a convex, nonlinear mathematical programming model.
Technical Note—A Note on Waiting Times in Single Server Queues
Authors: Weber Richard R.
Published: November 2008

We show that in any single server queue having a FCFS discipline, the queueing and waiting times of every customer are nonincreasing convex functions of the service rate. An example shows that this need not be the case if the queue has more than one server.
Technical Note—Cost Formulas for Continuous Review Inventory Models with Fixed Delivery Lags
Authors: Federgruen Awi , Schechner Zvi
Published: November 2008

In continuous review models with a fixed delivery lag T, the state of the system is conveniently described by the net inventory position = (inventory on hand) plus (outstanding orders), in spite of most cost components depending on the actual inventory on hand. To relate these two inventory concepts one observes that the distribution of the inventory on hand at time t + T is determined by the inventory position at time t. This explains the standard convention of charging the expected costs incurred in [Sn + T, Sn+1 + T) to the decision made at time Sn, where Sn denotes the nth decision epoch. This paper derives simple expressions for the expected costs in [Sn + T, Sn+1 + T) as a function of the inventory position just after decision epoch Sn.
Simulation Run Length Control in the Presence of an Initial Transient
Authors: Heidelberger Philip , Welch Peter D.
Published: November 2008

This paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation. It considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present. It explores a procedure based on Schruben's Brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean. The procedure is evaluated empirically for a variety of output sequences. The performance measures considered are bias, confidence interval coverage, mean confidence interval width, mean run length, and mean amount of deleted data. If the output sequence contains a strong transient, then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias, narrower confidence intervals, and shorter run lengths than when no check for stationarity is performed. If the output sequence contains no initial transient, then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test. If the run length is short relative to the extent of the initial transient, the stationarity tests may not be powerful enough to detect the transient, resulting in a procedure with unreliable point and interval estimates.
Regenerative Simulation for Estimating Extreme Values
Authors: Iglehart Donald L. , Stone Mark L.
Published: November 2008

Let X(t) denote the regenerative process being simulated and assume that it converges in distribution to a steady state random variable. This paper considers estimating the extreme values of the regenerative process. Suppose we are interested in the largest value attained in the interval [0, t], call it X*(t). The paper develops a method for estimating the distribution of X*(t). When the regenerative process is either the GI/G/1 queue or a birth-death process, theoretical results are available for the distribution of X*(t). Our development simulated the waiting time, queue length, and virtual waiting time for an M/M/1 queue, employed the method for estimating the distribution of X*(t), and compared the simulation results with the theoretical results.
Optimal Tests for Initialization Bias in Simulation Output
Authors: Schruben L. , Singh H. , Tierney L.
Published: November 2008

We present a family of tests for detecting initialization bias in the mean of a simulation output series using a hypothesis testing framework. The null hypothesis is that the output mean does not change throughout the simulation run. The alternative hypothesis specifies a general transient mean function. The tests are asymptotically optimal based on cumulative sums of deviations about the sample mean. A particular test in this family is applied to a variety of simulation models. The test requires very modest computation and appears to be both robust and powerful.
(s, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times
Authors: Ehrhardt Richard
Published: November 2008

This study analyzes a stochastic lead time inventory model under the assumptions that (a) replenishment orders do not cross in time and (b) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. The study extends the existing literature on the finite-horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalize easily. Conditions for the optimality of myopic base-stock policies, and for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies.
Capacity Expansion/Contraction of a Facility with Demand Augmentation Dynamics
Authors: Rocklin Sol M. , Kashper Arik , Varvaloucas George C.
Published: November 2008

We analyze the cost-effective addition or removal of capacity from a facility governed by demand augmentation dynamics. That is, if the demand for goods or services exceeds the planned capacity of the facility during any period of a multiperiod planning horizon, then additional capacity must be introduced within that period to meet the deficit. The paper obtains an optimal management strategy that minimizes the sum of capital, labor, maintenance, and underpro-vision costs for N consecutive periods in the face of uncertain demands. Dynamic programming is used to demonstrate that, under certain conditions on the cost functions, an inventory-like (S′, S″) policy is optimal, appropriately interpreted to define the removal as well as the augmentation of capacity. The threshold levels S′ and S″, can be evaluated for each period without a costly search procedure. In addition, we show how to calculate various quantities of interest associated with the optimal policy.
Sequential Decision Making under Uncertain Future Preferences
Authors: White Chelsea C.
Published: November 2008

We present a model of sequential decision making under uncertain future preferences, assuming that the evolution of the trade-off weight vector is constrained by set inclusion. We consider different mechanisms for selecting the next trade-off weight vector: a mechanism working against the decision maker (DM) (M), a mechanism trying to aid the DM (B), and (briefly) a probabilistic mechanism (P). Piecewise linear, convex upper and lower bounds on the optimal value function are determined for mechanisms M and B. Conditions are given that guarantee that the optimal value function is piecewise linear and convex for all three mechanisms. Procedures for computing these bounds and determining associated strategies are presented. A hypothetical situation involving an individual seeking promotion is used to illustrate the model and the numerical techniques.