bluuebunny/crossref_metadata_2025 huggingface dataset:
Interactive Identification and Optimization Using a Binary Preference Relation
Authors: Wehrung Donald A.
Published: November 2008

This paper considers the problem in which a single decision maker must choose an element from a known nonempty choice set Y of multi-attributed elements when his preferences are uncertain. The preferences are uncertain in the sense that they are not explicitly available. The decision-maker's preferences are assumed to take the form of a binary relation on Y. We present an algorithm that requires the identification of preferences during the search process. The convergence of the adopted algorithm to a best element in Y relative to whatever preferences obtain is proved under the assumption that the identification of preferences is costless. We show that the sufficient conditions for convergence of this algorithm are weaker than the sufficient conditions for convergence of the interactive algorithm for the multiple criteria problem developed by Geoffrion, Dyer, and Feinberg.
A Cut Approach to the Rectilinear Distance Facility Location Problem
Authors: Picard Jean-Claude , Ratliff H. Donald
Published: November 2008

This paper is concerned with the problem of locating n new facilities in the plane when there are m facilities already located. The objective is to minimize the weighted sum of rectilinear distances. Necessary and sufficient conditions for optimality are established. We show that the optimum locations of the new facilities are dependent on the relative orderings of old facilities along the two coordinate axes but not on the distances between them. Based on these results an algorithm is presented that requires the solution of at most m − 1 minimum cut problems on networks with at most n + 2 vertices. All of these results are easily extended to the same location problem on a tree graph.
Optimum Advertising and Goodwill under Uncertainty
Authors: Tapiero Charles S.
Published: November 2008

This paper extends past studies of advertising based on goodwill to include the probabilistic effects of advertising and forgetting. A stochastic advertising model for a monopoly firm is constructed and resolved for specific forms of feedback advertising policy. Further, a diffusion-approximation model is also suggested. Using these models, we derive optimum advertising policies of the open-loop and feedback type. The essential implications of the paper are: (i) advertising is a “risky investment” in goodwill, substituting current certain expenditures for uncertain profits; (ii) risk-averse firms will advertise less and risk-taking firms more; (iii) large risk-aversion and forgetting rates both lead to the standard competitive result in advertising.
The Fixed-Charge Perishable Inventory Problem
Authors: Nahmias Steven
Published: November 2008

This paper deals with the problem of determing both optimal and approximate ordering policies for a fixed-life perishable commodity when there is a fixed charge or set-up cost for placing an order. The structure of the optimal policy can be inferred from the analysis of a one-period model under the assumption that the outdating is paid for when the order arrives rather than when the outdating actually occurs. An approximate model is constructed for which (s, S) policies are optimal by approximating the one expected single-period cost and the transfer function. Two different bounds on the expected out-dating per period are used to obtain two different (s, S) approximations. Computations are performed for a discrete version of the problem with three different demand distributions and 24 configurations of the cost structure to compare the effectiveness of both approximations with the optimal policy.
The Output of Multiserver Queuing Systems
Authors: Pack Charles D.
Published: November 2008

We derive a recurrence relation for ξn, the time until the nth departure measured from T0, any well-defined instant in time. While the recurrence, valid for the G/G/s queue, is generally not easy to work with, in certain cases we can use it to obtain the distribution and moments of ξn. We obtain limited results for the M/M/s queue but investigate the M/D/s queue in detail. For the M/D/s queue, the results are used to determine the range of system parameters, p/s (the average utilization per server) and s, for which the distribution of ξs can be approximated by one of the gamma type. The quality of the approximation for a given p and s provides insight as to when the output of the M/D/s queue is “nearly Poisson.”
Approximations for the M/G/m Queue
Authors: Hokstad Per
Published: November 2008

We study the M/G/m queue and obtain difference-differential equations for the equilibrium joint distribution of the number of customers present and of the remaining holding times for services in progress. A study of these equations leads to the proposal of a simple approximation for the queue length distribution. Approximate waiting time and busy period distributions easily follow. Simple expressions for the means of the variables in question are obtained. Some numerical results on the mean waiting time indicate that the proposed approximation is rather accurate. The technique presented in this paper can also be applied to variants of the M/G/m queue. In particular, a short treatment of the queue with finite waiting room is included.
Optimal Design of Regional Wastewater Systems: A Fixed-Charge Network Flow Model
Authors: Jarvis John J. , Rardin Ronald L. , Unger V. E. , Moore Richard W. , Schimpeler Charles C.
Published: November 2008

A regional wastewater quality management system was modeled as a fixed-charge network flow problem. The model included alternative trunk-line connections, methods of treatment, and variation in system boundaries. The paper describes the model, development of the input data, the network flow analysis method, simplifications, and results. Particular emphasis is put on modification and simplification of the basic fixed-charge model to produce a fixed-charge network flow model of tractable size.
On Optimal Regulation Policies for Certain Multi-Reservoir Systems
Authors: Arunkumar S. , Chon K.
Published: November 2008

Optimal regulation policies for two reservoirs connected in series, with seasonal and possibly cross-correlated inflows, are analytically characterized when the immediate reward function is a piecewise linear concave function of the release and the objective is to maximize the expected discounted rewards over finite and infinite time horizons. The optimal policies are expressed in terms of certain critical numbers for which upper and lower bounds are obtained. We propose a heuristic approach for multi-reservoir systems under less restrictive assumptions and apply it to two reservoirs connected in parallel.
Optimal Repair of a Series System
Authors: Smith Donald R.
Published: November 2008

A single repairman maintains a series system whose components have exponential failure and repair distributions. It is desired to assign the repairman to maximize the expected total discounted working time or average working time for the system. Whenever the failure rates of all components are equal, the time to repair the system from any initial state is stochastically independent of the operating policy. The Laplace transform of time to repair the system and the long-run average time that the system works are explicitly available. For the two-component series system the repair time is stochastically minimized if the failed component with longest expected lifetime is always under repair. This is true even if the repairman experiences random periods of time during which repair is not allowed. For an n-component series system the policy that always repairs the failed component with longest expected lifetime stochastically minimizes the repair time over the class of policies, that repair failed components in a predetermined order. We apply the results to a queuing system.
A Bayesian Estimation of the Reliability of Coherent Structures
Authors: Mastran David V. , Singpurwalla Nozer D.
Published: November 2008

We develop a procedure for estimating the reliability of a coherent structure of independent components when a prior distribution is assigned to the reliability of the structure function and when failure data on either the structure, its components, or on both are available. We generalize our results by obtaining bounds on the moments of the posterior distribution of the reliability of the structure when its components are associated. We illustrate our procedures by simple examples.
Technical Note—A Single-Commodity Transformation for Certain Multicommodity Networks
Authors: Evans James R.
Published: November 2008

We derive a sufficient condition by which a multicommodity minimal cost network flow problem can be transformed and solved as an equivalent single-commodity problem. The condition is based on the topological structure of the network and unifies several special results that have been established. The transformation is given, and potential applications are discussed.
Technical Note—A General Inner Approximation Algorithm for Nonconvex Mathematical Programs
Authors: Marks Barry R. , Wright Gordon P.
Published: November 2008

Inner approximation algorithms have had two major roles in the mathematical programming literature. Their first role was in the construction of algorithms for the decomposition of large-scale mathematical programs, such as in the Dantzig-Wolfe decomposition principle. However, recently they have been used in the creation of algorithms that locate Kuhn-Tucker solutions to nonconvex programs. Avriel and Williams' (Avriel, M., A. C. Williams. 1970. Complementary geometric programming. SIAM J. Appl. Math. 19 125–141.) complementary geometric programming algorithm, Duffin and Peterson's (Duffin, R. J., E. L. Peterson. 1972. Reversed geometric programs treated by harmonic means. Indiana Univ. Math. J. 22 531–550.) reversed geometric programming algorithms, Reklaitis and Wilde’s (Reklaitis, G. V., D. J. Wilde. 1974. Geometric programming via a primal auxiliary problem. AIIE Trans. 6 308–317.) primal reversed geometric programming algorithm, and Bitran and Novaes' (Bitran, G. R., A. G. Novaes. 1973. Linear programming with a fractional objective function. Opns. Res. 21 22–29.) linear fractional programming algorithm are all examples of this class of inner approximation algorithms. A sequence of approximating convex programs are solved in each of these algorithms. Rosen's (Rosen, J. B. 1966. Iterative solution of nonlinear optimal control problems. SIAM J. Control 4 223–244.) inner approximation algorithm is a special case of the general inner approximation algorithm presented in this note.
Combinatorial Problems: Reductibility and Approximation
Authors: Sahni Sartaj , Horowitz Ellis
Published: November 2008

Recent research in the theory of algorithms has determined that many classical operations research problems are computationally related; i.e., an efficient algorithm for one implies the existence of efficient algorithms for everyone or a proof that one is inherently difficult implies they are all so. This paper presents a tutorial of this concept. In contrast to other surveys it does so by selecting a few problems (knapsack, traveling salesperson, multiprocessor scheduling, and flow shop) and carefully shows how they are related. References to most other problems of interest to operations researchers are given. The second part of this paper is a survey on the relatively recent progress in the study of approximation algorithms. These algorithms hold great promise for they work fast and in many cases are guaranteed to work well. Again the techniques for devising and analyzing these algorithms are explained through the continued use of these examples.
Universal Planning Horizons for Generalized Convex Production Scheduling
Authors: Morton Thomas E.
Published: November 2008

We study an infinite-horizon analog of the well-known finite-horizon convex production scheduling model with positive or negative demands, production, and inventory, and with constraints on inventory and production. We develop a forward algorithm for this problem allowing successively tighter bounds on the optimal first-period production to be given as successive demand forecasts are added to the problem. We show under very general conditions that the algorithm will always lead to an exact or asymptotic planning horizon. Planning horizon results due to others form special cases. Applications of the generalized production scheduling model include capacity expansion problems.
Decomposition and Customer Streams of Feedback Networks of Queues in Equilibrium
Authors: Beutler Frederick J. , Melamed Benjamin
Published: November 2008

Burke and Reich independently showed that the output of an M/M/1 queue in equilibrium is a Poisson process. Consequently, analysis of series (tandem) exponential servers with a Poisson input stream can be reduced to consideration of a series of M/M/1 queues. This work generalizes the above results to so-called Jackson networks, consisting of exponential servers with mutually independent Poisson exogenous inputs and random customer routings permitting customer feedback. We prove that traffic on all exit arcs of a network in equilibrium is Poisson; moreover, the customer streams leaving any exit set are mutually independent. Here an exit arc is a path from server node i such that a customer moving along the arc cannot return to i; an exit set V is a set of server nodes such that customers departing V can never re-enter V. As a special case, the traffic streams leaving a Jackson network in equilibrium are mutually independent Poisson processes. In contrast, traffic on non-exit arcs is non-Poisson, and indeed non-renewal. A canonical decomposition of the server nodes is defined as a partition of the server node set into components C*q, each consisting of communicating servers. We show that the set of all exit arcs coincides with the arcs emanating from the C*q. Finally, for a Jackson network in equilibrium, each C*q is itself a Jackson network in equilibrium.
Technical Note—A Modified Conjugate Gradient Algorithm
Authors: Perry Avinoam
Published: November 2008

We present a modification of the Fletcher-Reeves conjugate gradient algorithm. Computational experience indicates that this modification yields an improved algorithm.
Technical Note—Optimality of Monotonic Policies for Multiple-Server Exponential Queuing Systems with State-Dependent Arrival Rates
Authors: Winston Wayne
Published: November 2008

We consider an exponential queuing system consisting of several removable servers in which the arrival rate depends on the current system state. Costs are incurred at a rate that depends on both the number of customers present and the number of servers in operation. We present conditions that ensure that the number of servers in operation is a non-decreasing function of the number of customers in the system.
Optimal Jury Selection: A Game-Theoretic Model for the Exercise of Peremptory Challenges
Authors: Brams Steven J. , Davis Morton D.
Published: November 2008

Potential jurors with a priori probabilities of voting for conviction are assumed to be chosen randomly from a population and to come up one at a time for decision. Defense and prosecution must decide whether to accept or challenge a potential juror as a function of his a priori probability, the distribution of these probabilities in the population, the number of jurors remaining to be selected, and the number of peremptory challenges both sides have remaining. We find a recursive algorithm that minimizes for the defense, and maximizes for the prosecution, the expected probability of conviction in the jury-selection game. A number of conclusions are drawn from numerical calculations of optimal strategies and values in this game, and the analysis is extended to cover the case of peremptory challenges to groups of potential jurors.
A Dual-Based Procedure for Uncapacitated Facility Location
Authors: Erlenkotter Donald
Published: November 2008

We develop and test a method for the uncapacitated facility location problem that is based on a linear programming dual formation. A simple ascent and adjustment procedure frequently produces optimal dual solutions, which in turn often correspond directly to optimal integer primal solutions. If not, a branch-and-bound procedure completes the solution process. This approach has obtained and verified optimal solutions to all the Kuehn-Hamburger location problems in well under 0.1 seconds each on an IBM 360/91 computer, with no branching required. Computational tests on problems with as many as 100 potential facility locations provide evidence that this approach is superior to several other methods.
Feature Article—Energy Policy Modeling: A Survey
Authors: Manne Alan S. , Richels Richard G. , Weyant John P.
Published: November 2008

This survey provides an exposition of seven technoeconomic models that are representative of recent work on energy policy. The paper begins with several microeconomic concepts related to energy conservation and to energy-economy interactions. We then examine three representative medium-term models which deal with pricing, import policy and investment decisions in today's conventional supply technologies. Next, we analyze four studies dealing with longer-range issues—alternative research and development strategies for a transition away from depletable energy resources. The paper concludes with a summary of unresolved issues, and with suggestions on the future role of modeling in the public policy process.
An Operational Critique of Detection Laws
Authors: Koopman B. O.
Published: November 2008

This paper applies the test of operational meaningfulness to the many detection laws that have been formulated and used in the mathematical optimization of search, and given as generalizations of those first developed in the United States Navy during and immediately following World War II. The word “operational” is used both in the sense of practical O.R. and in that of P. W. Bridgman's well-known requirement: that in applying mathematics to the material world, the physical preconditions implied in the quantities used, the operations for measuring them, and their laws of consistency must be set forth explicitly. It is submitted that this criterion will orient O.R. work toward useful developments in the search theory and may serve to identify as such those theories that are of chief interest as developments in pure mathematics. Finally, we note that the requirement that every numerical assumption of probability distributions in a study of the outside world must be based on objective evidence is perfectly consistent with the “subjective” conception of probability, viz., that its meaning is apprehended intuitively—the former measures what the latter defines.
Technical Note—Exact Solution for the Bradford Distribution and Its Use in Modeling Informational Data
Authors: Morse Philip M. , Leimkuhler Ferdinand F.
Published: November 2008

The Bradford distribution requires a logarithmic relationship between the fraction of items having “productivity” n or more and the total, cumulative “production” of these items. An exact solution is obtained for this distribution for all integer values of n ≥ 1. The result, useful in describing library and other informational data, is compared with the Zipf and the modified geometric distributions. Examples are given of the operational value of representing informational data by one of these distributions. We develop simple tests to see how well a given sample of data conforms to one or the other distribution and apply the tests to two samples; the number of operations research articles appearing in various journals in a given time interval and the rate of use of various physics periodicals in a science library. We show that the first fits the Bradford distribution quite well, while the second fits the modified geometric distribution. We discuss some of the implications of this difference.
Optimal Structures and Maintenance Policies for PABX Power Systems
Authors: Vered Goor , Yechiali Uri
Published: November 2008

A power system for a private automatic branch exchange (PABX) consists of n independent and identical rectifiers hooked up in parallel. The lifetime of each component is an exponential random variable with a known mean (MTBF). The system fails when the number of operating rectifiers is less than m(m ≤ n).

Rectifiers are distinguished by two main characteristics: the current they carry and their MTBF. The minimal number of units, m, is determined by technological considerations: for each type of rectifier, m is calculated so that the system can carry a given maximal current. This maximal current is specified for each PABX.

The system is maintained by a technician who may visit the exchange regularly every v units of time or when it fails. Several maintenance policies are considered. For each type of exchange and for each form of maintenance policy, we determine the optimal set of parameters, {m, n, MTBF, and v}, to minimize the operating cost for a required level of reliability. These results are then used as guidelines for standardizing PABX power systems.
Evaluation of Proposed Storage Sites
Authors: Keeney Ralph L.
Published: November 2008

Screening models and on-site visits by a team composed of engineers, geologists, and biologists were used to identify ten sites in the Southwest suitable for developing a pumped storage facility with a 600 MW capacity. This paper discusses the decision analysis used to rank the sites. The study included the consideration of economic, environmental, and technological concerns relating to the sites and their required transmission lines. Using sensitivity analyses, we identified factors critical to the ranking.
Feature Article—Changing the Future of Operations Research
Authors: Bonder Seth
Published: November 2008

Between 1940 and 1945, under the impetus of World War II, operations research (OR) became a recognized activity. The successes in solving many short-term and important operational problems are recorded in history. In the intervening three decades, OR has continued this short-term problem solving activity, attempted to address longer horizon, broader scope planning problems, and devoted significant effort to the development of related mathematical techniques. It is conjectured that, if it continues to pursue these directions in kind and degree, OR may lose its identity as a recognized activity and be assimilated into other fields of endeavor. This paper presents some categorical suggestions for improving practice and research to redirect the future of OR.
On Optimal Utilization of Production Processes
Authors: Pekelman Dov
Published: November 2008

We investigate the optimal utilization of production processes. We focus on finding the optimal shifts from one production process to another over some finite horizon, where a cost on the rate of change is imposed. We also demonstrate the existence of planning and forecast horizons and outline a procedure that identifies them. The forecast horizon indicates the amount of information required to make an optimal decision within the planning horizon. These results are obtained by using control theory, in particular, by analyzing the effect of two state-constraints that are inherent in the problem. The results are demonstrated by numerical examples.
A Multi-Product Dynamic Lot-Size Model with Individual and Joint Set-up Costs
Authors: Kao Edward P. C.
Published: November 2008

This paper considers a multi-product dynamic lot-size problem. In addition to a separate set-up cost for each product ordered, a joint set-up cost is incurred when one or more products are ordered. We present a dynamic programming formulation for finding the optimal ordering policy that calls for a smaller state space than that proposed by Zangwill. As a convenient substitute, we also introduce a very simple heuristic procedure and two of its variants. For the two-product problem we report computational experience for evaluating the performance of these procedures.
A Production Scheduling Problem in the Glass-Container Industry
Authors: Paul R. J.
Published: November 2008

By means of a computer simulation we examine the problem of scheduling parallel production lines in the glass-container industry with a resource constraint imposed by the furnace melting rate. The results of the simulation model are combined with relevant aspects of scheduling theory to arrive at the conclusion that a shortest processing time based dispatching rule probably provides the most efficient operating policy.
The Knapsack Sharing Problem
Authors: Brown J. Randall
Published: November 2008

The knapsack sharing problem has a utility or tradeoff function for each variable and seeks to maximize the value of the smallest tradeoff function (a maximin objective function). A single constraint places an upper bound on the sum of the non-negative variables. We develop efficient algorithms for piecewise linear, nonlinear, and piecewise nonlinear tradeoff functions and for any knapsack sharing problem with integer variables. These algorithms for the knapsack sharing problem extend the sharing problem algorithm in a companion paper to any piecewise linear, nonlinear, or piecewise nonlinear tradeoff functions.
Technical Note—The EOQ Model under Stochastic Lead Time
Authors: Liberatore Matthew J.
Published: November 2008

We consider a continuous deterministic-demand, stochastic lead-time inventory model such that the individual unit demands are non-interchangeable. We derive equations that define the optimal values of the two decision variables: order size and timing. This model is shown to be a stochastic lead-time generalization of the EOQ model with backlogging of demand. An illustrative example is presented. Finally, a lower bound, which is independent of the order size, is developed for the optimal ordering time.
The Status of Nonlinear Programming Software
Authors: Waren Allan D. , Lasdon Leon S.
Published: November 2008

Desirable features of software for solving nonlinear optimization problems are discussed, and several available codes for solving NLPs are described in terms of these features. Codes are classified by algorithm type. Addresses where codes may be obtained are given. The paper concludes with a brief survey of available computational experience with several classes of algorithms and with some of the specific codes considered.
An Iterative Solution of Two-Dimensional Birth and Death Processes
Authors: Brandwajn Alexandre
Published: November 2008

This paper presents an iterative, seminumerical method for solving the balance equations of finite two-dimensional birth and death processes. The method is seminumerical in that it uses the formal knowledge of the stationary probability distribution of one variable, and the iteration is applied to the conditional probabilities of the second variable given the first one. Sufficient convergence conditions for this approach are discussed. An always convergent entirely numerical alternative solution is also presented. Empirical results indicate that both methods perform, in many cases, several times better (in terms of time required) than the commonly used Gauss-Seidel method. Possible generalizations to processes of more than two dimensions are also indicated.
Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes
Authors: Serfozo Richard F.
Published: November 2008

A continuous time Markov decision process with uniformly bounded transition rates is shown to be equivalent to a simpler discrete time Markov decision process for both the discounted and average reward criteria on an infinite horizon. This result clarifies some earlier work in this area.
Feature Article—Aggregate Advertising Models: The State of the Art
Authors: Little John D. C.
Published: November 2008

Aggregate advertising models relate product sales to advertising spending for a market as a whole. Although many models have been built, they frequently contradict each other and considerable doubt exists as to which models best represent advertising processes. An increasingly rich literature of empirical studies helps resolve these issues by revealing major advertising phenomena that models should encompass. These include sales responding upward and downward at different rates, steady state response that can be concave or S-shaped and can have positive sales at zero advertising, sales affected by competitive advertising; and advertising dollar effectiveness that can change over time. A review of aggregate models developed on a priori grounds brings out similarities and differences among those of Vidale and Wolfe, Nerlove and Arrow, Little, and others and identifies ways in which the models agree or disagree with observed phenomena. A Lanchester-motivated structure generalizes many features of these models and conforms to some but not all of the empirical observations. Although econometric studies have revealed important empirical insights, the most frequently used structural forms do not model certain key phenomena, most notably different rise and decay rates. Future work must join better models with more powerful calibration methods.
Computing Network Reliability
Authors: Ball Michael O.
Published: November 2008

This paper presents an algorithm to compute reliability measures on a stochastic network in which both nodes and links can fail. The measures considered are the probability that nodes s and t can communicate for all node pairs s and t, the probability that all operative node pairs can communicate, and the expected number of node pairs communicating. It also computes the latter two measures when all communication must proceed through a root node. A specialized version of the algorithm is given for networks in which only nodes can fail.
A Sequential Procedure for Determining the Length of a Steady-State Simulation
Authors: Law Averill M. , Carson John S.
Published: November 2008

A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.
A Mathematical Programming Model for Allocation of Natural Gas
Authors: O'Neill Richard P. , Williard Mark , Wilkins Bert , Pike Ralph
Published: November 2008

This paper presents a methodology for the allocation of natural gas. The model consists of several objective functions, a set of linear constraints, and a set of nonlinear constraints. The objective functions represent allocation in various categories and can be optimized sequentially. The linear constraints represent the conservation of flow equations for the pipeline network and various accounting relationships. The nonlinear constraints represent the momentum balance necessary for each pipe segment, compressor, or valve. The nonlinear constraints are linearized in a method similar to the method of approximate programming (MAP). A matrix generator is used to create the necessary files for the program execution. We have solved example problems with over 250 linear constraints, 240 nonlinear constraints, and 800 structural columns.
Algorithms and Planning Horizon Results for Production Planning Problems with Separable Costs
Authors: Kleindorfer Paul R. , Lieber Zvi
Published: November 2008

A generalization of the Modigliani-Hohn production scheduling problem including new computational algorithms and planning horizon results is first investigated. These results are then coupled with decomposition methods in providing a computational algorithm for the production scheduling and employment smoothing problems with separable convex costs.
Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models
Authors: Nahmias Steven
Published: November 2008

This paper treats three realistic versions of the classical leadtime lost-sales inventory problem: inclusion of a set-up for ordering, partial backordering, and the random leadtime lost-sales inventory problem, as well as all possible combinations of these three models. The goal of the study is to construct simple myopic approximations for these various models. We report extensive computations that compare the approximations derived with the optimal policies for leadtimes of one and two periods. In addition, we develop a simulator that determines the best S or (s, S) policies by a Fibonacci search of the appropriate response surface and compares the performance of the approximations to these policies for maximum leadtimes of five, ten, and twenty periods for a variety of configurations of the cost structure, demand distribution, and leadtime distribution.
Location Dominance on Spherical Surfaces
Authors: Aly Adel A. , Kay David C. , Litwhiler Daniel W.
Published: November 2008

This paper investigates the nature of optimal solutions for a location problem on a spherical surface with the great circle distance as measure. The results are based upon Wendell and Hurter's generalization of Kuhn's characterization of a convex hull by dominance. It is shown that the search for an optimal solution for the “minisum” single facility location problem on the sphere, where demand points are not located entirely on a great circle arc, can be restricted to the spherically convex hull of the demand points.
Variance Reduction for Population Growth Simulation Models
Authors: Fishman George S.
Published: November 2008

Most variance reduction techniques encountered in simulations are designed to operate with stationary models. However, many simulations are nonstationary in character, population growth models being an example. One way to facilitate statistical inference in a nonstationary simulation is to interchange the order of replication collection and time evolution. That is, at each time point several replications are performed to enable a user to estimate parameters at that point in time. This paper describes three variance reduction models that use this interchange between collection and evolution to induce negative correlation between replications, thereby producing estimates with smaller variances. Model 1 describes a procedure that occasionally relies on the solution of a linear program to develop an optimal sampling plan. Model 2 offers an alternative that applies when the populations in strata are large. Model 3 applies when survival probabilities are functions of an exogenous random variable such as rainfall. A female elephant population simulation illustrates the success one can expect with Model 1.
Interior Path Methods for Heuristic Integer Programming Procedures
Authors: Faaland Bruce H. , Hillier Frederick S.
Published: November 2008

This paper considers heuristic procedures for general mixed integer linear programming with inequality constraints. It focuses on the question of how to most effectively initialize such procedures by constructing an “interior path” from which to search for good feasible solutions. These paths lead from an optimal solution for the corresponding linear programming problem (i.e., deleting integrality restrictions) into the interior of the feasible region for this problem. Previous methods for constructing linear paths of this kind are analyzed from a statistical viewpoint, which motivates a promising new method. These methods are then extended to piecewise linear paths in order to improve the direction of search in certain cases where constraints that are not binding on the optimal linear programming solution become particularly relevant. Computational experience is reported.
New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem
Authors: Loulou Richard , Michaelides Eleftherios
Published: November 2008

In this paper, we develop four heuristic methods to obtain approximate solutions to the multidimensional 0-1 knapsack problem. The four methods are tested on a number of problems of various sizes. The solutions are compared to the rigorous optimum as well as to a heuristic method of Toyoda. They are statistically better than the latter, with average relative errors of the order of less than 1%.
Approximations of the Mean Waiting Time in an M/G/s Queueing System
Authors: Boxma O. J. , Cohen J. W. , Huffels N.
Published: November 2008

This paper considers the problem of obtaining approximate expressions for the first moment WGs of the stationary waiting time distribution in an M/G/s queueing system. Special attention is paid to the case G ≡ D, i.e., constant service times. Most known approximations are in fact heavy traffic approximations which have rather large relative errors in the light traffic case. In the present study both the light traffic and heavy traffic behavior of WGs (WDs) are taken into account. In order to obtain mean waiting time approximations it appears to be useful to introduce a quantity (the “normed cooperation coefficient”) which is inversely proportional to WGs and which is in some sense a measure for the “cooperation” between the servers of the service facility. A part of the paper is devoted to the analysis of this normed cooperation coefficient.
The Age Replacement Problem with Minimal Repair and Random Repair Costs
Authors: Cléroux R. , Dubuc S. , Tilquin C.
Published: November 2008

Age replacement policies are investigated. When a unit reaches age T, a preventive replacement is made. If a failure occurs prior to age T and if the random repair cost is less than a fixed constant, a minimal repair is made. Otherwise the unit is replaced at failure.
Technical Note—Approximations for Overflows from Queues with a Finite Waiting Room
Authors: Rath John H. , Sheng Diane
Published: November 2008

We report in this note a study of the use of the interrupted Poisson process (IPP) as an approximation to the overflow process from a M/M/C/K queue (a queue with a Poisson arrival process, C servers each with exponentially distributed service times, and a maximum of K customers in the system). The IPP has been used successfully by Kuczura to approximate the overflow from a M/M/C/C queue. Numerical comparisons are made for a number of examples and both the maximum absolute errors and percent errors are plotted.
On Value and Strategic Role of Information in Semi-Normalized Decisions
Authors: LaValle Irving H.
Published: November 2008

EVPI and its extensions to nonlinear utility were developed under formulations and probability assumptions not ordinarily encountered in general decision-analytic contexts other than classical sampling. This note extends the framework for evaluating a prospective acquisition of information in two ways: first, by showing how information value may depend upon judgments not needed in the natural (but nonclassical) formulation of some decision problems; and second, by examining the impact that a “public” acquisition of information might have upon the decision-maker's prior judgments—and thus upon the value of such information, even to the possible extent of making its value negative.
The Use and Value of Models in Decision Analysis
Authors: Nickerson Robert C. , Boyd Dean W.
Published: November 2008

A normative approach to the use of models is presented in which modeling is viewed as a source of information. The value of modeling can then be interpreted from the value of information perspective. The expected value of modeling is defined as the increase in the expected value of the outcome that results from the use of the model-supplied information. With this definition the value of modeling is characterized under a variety of conditions. From a practical point of view the most useful result is that, under certain conditions, the expected value of modeling is maximum when the prior expectations of the value of the outcome for each alternative are equal.
Analysis of Risks to Life and Limb
Authors: Bodily Samuel E.
Published: November 2008

Industrial safety, environmental and health planning, energy policy, and many other areas of public and private management require the comparison of risks to life and limb and the allocation of resources to competing risk-reducing activities. Several issues that must be taken into consideration in evaluating alternatives affecting life and limb are described. A methodology employing multiattribute decision analysis is developed to account for these issues in a consistent way. The methodology combines analysis of an individuals willingness to pay to reduce risks to himself with collective analysis of the value of reducing risks to others. Illustrative applications of the methodology are provided.
The Problem of “Utility Weights” in Group Preference Aggregation
Authors: Brock Horace W.
Published: November 2008

The problem of interpersonal comparisons of utility is discussed, and a new distinction between hypothetical and operational interpersonal comparisons is introduced. A theory of preference aggregation is then developed that sheds light on the question of how much relative weight should be given to the interests of the various parties affected by a group decision. The results of this theory are related to the NASH-HARSANYI theory of bargaining.
Utility Functions for Life Years and Health Status
Authors: Pliskin Joseph S. , Shepard Donald S. , Weinstein Milton C.
Published: November 2008

Multiattribute utility theory is used to suggest a form for a utility function over life years and health status. The analysis is motivated by consideration of two diseases—coronary artery disease and chronic kidney disease—in which the choice of treatment may depend on the patient's tradeoff between these attributes. Certain plausible independence properties lead to a quasi-additive utility function for life years and health status. Particular attention is given to utility functions for life years exhibiting constant proportional risk posture. An empirical assessment shows that stated preferences appear consistent with this functional form. The derived utility functions have been applied to the treatment decision of whether to prescribe coronary artery bypass graft surgery in patients with coronary artery disease.
Multiattribute Decision Making by Sequential Resource Allocation
Authors: Morris Peter A. , Oren Shmuel S.
Published: November 2008

A new approach is proposed for addressing decision problems in which the outcomes are multidimensional and possibly interdependent. The method is based on decomposing the problem into a sequence of simpler decision problems. The solution to each subproblem is elicited from the decision-maker by converting it to a simple resource allocation task that may be solved by inspection. Our experience indicates that these resource allocation tasks are considerably simpler and more intuitive than the local tradeoff assessments required by existing iterative methods. The information provided by the decision-maker at each stage is used to generate a sequence of successively improving attribute bundles converging to the solution to the original complex decision problem. The approach is illustrated in the context of a financial planning problem.
Negotiation of International Oil Tanker Standards: An Application of Multiattribute Value Theory
Authors: Ulvila Jacob W. , Snider Warren D.
Published: November 2008

Quantitative decision analysis techniques are applied to a particular problem of bargaining and negotiation: How should a negotiating team representing the United States prepare for an international conference on tanker safety and pollution prevention? The negotiating team had a short time to prepare for the Conference, which was to consider a number of complex and difficult measures on which there were considerable differences of opinion. The analytic approach used focused on a multiattribute value model that incorporated the views of many of the negotiating countries. This model was refined over the preparation period by both analysts and negotiators. The U.S. negotiators found that the model was useful for evaluating alternative proposals, anticipating and understanding the negotiating positions of other countries, generating promising compromise proposals, and communicating with other U.S. interest groups. The modeling effort helped the negotiators to identify a compromise proposal very similar to the one finally adopted by the Conference. As a result of the Conference important new international measures to improve the safety of oil tankers and help prevent pollution of the seas from ships were adopted.
An Annotated Bibliography of Decision Analytic Applications to Health Care
Authors: Krischer Jeffrey P.
Published: November 2008

This paper describes 110 applications of decision analysis to health care. Each paper is characterized according to the particular problem it addresses and the methods employed in the application. These applications span 15 years of study and are reported in a widely dispersed literature. Nearly half of the published articles appear in journals with a medical audience and more than 25% of the studies remain unpublished. The major areas of application identified in this review have been the evaluation of alternatives in treatment and health policy planning. Studies discussing conceptual issues in the application of decision analysis represent a substantial portion of those identified. Almost equal numbers of applications involve the use of single and multiattribute utilities in scaling decision outcomes and relatively few apply to group utilities. General discussions of decision analysis methods and applications focused on probability assessments/analyses represent the other major categories of studies cited.
A Multibrand Stochastic Model Compounding Heterogeneous Erlang Timing and Multinomial Choice Processes
Authors: Jeuland Abel P. , Bass Frank M. , Wright Gordon P.
Published: November 2008

The model developed in this paper incorporates two submodels a purchase timing model which describes the occurrence over time of purchases of the product class and a multibrand stochastic choice model which specifies how any brand may be chosen on a given purchase occasion. The mathematical derivations obtained by combining both submodels lead to the identification of the formal connection between the aggregates of the market—in particular, market share, penetration, duplication and brand switching. The combining is done under the assumption of independence between the zero-order choice process and the Erlang purchase timing process. The model is fully determined when the following four types of parameters are known the market shares, mn, a measure of heterogeneity of the population in terms of choice, p, the order of the Erlang timing process, r, and two parameters which describe the distribution over the population of the purchase rate of the product class—a shape parameter k and a scale parameter c. An empirical test of the model is reported.