bluuebunny/crossref_metadata_2025 huggingface dataset:
Primal Decomposition of Mathematical Programs by Resource Allocation: II—Computational Algorithm with an Application to the Modular Design Problem
Authors: Silverman Gary J.
Published: November 2008

Part I of this paper presented a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. In this part, additional theory and development of a parametric subproblem-solution and step-size-determination technique completes the algorithm. A previously unsolved problem in the operations-research literature, the generalized modular design problem of Evans [Opns. Res. 18, 562–4 (1970)] is solved by the algorithm and numerical results provided.
The Transportation-Location Problem
Authors: Cooper Leon
Published: November 2008

This paper defines a problem type, called the transportation-location problem, that can be considered a generalization of the Hitchcock transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, it is also necessary to find, at the same time, the optimal locations of these sources with respect to a fixed and known set of destinations. This new problem is characterized mathematically, and exact and approximate methods are presented for its solution.
Sequential Search for an Unknown Number of Objects of Nonuniform Size
Authors: Cozzolino John M.
Published: November 2008

This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area. All target objects are initially present in the search area and remain at least until discovered; no new objects are generated during the search process. Targets are not moveable. The search process is characterized by the quantity of search effort. The model describes the distribution of the number and sizes of target objects present. The probability of discovery is assumed proportional to object size. The paper gives many results, including the probability distribution of the number and sizes of discovered objects, and the prior and posterior distributions of the number of objects remaining undiscovered. Then it gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process.
A Priority Queue with Low-Priority Arrivals General
Authors: Hooke John A.
Published: November 2008

This paper considers a single-server queue with two priority classes of customers. High-priority arrivals are assumed to be Poisson, but interarrival times for low-priority customers are allowed to have a general distribution. Under either the head-of-the-line or preemptive-resume discipline, a formal solution is obtained for the Laplace-Stieltjes transform of the steady-state distribution of the low-priority waiting time. A limit theorem for the low-priority waiting time is also obtained under one heavy-traffic condition for which a steady state does not exist.
Some Heavy-Traffic Limit Theorems for a Priority Queue with General Arrivals
Authors: Hooke John A.
Published: November 2008

This paper considers a single-server queue with two priority classes of customers. Interarrival times and service times for the two classes of customers are assumed to form four mutually independent renewal processes determined by general distributions. In two cases for which a steady state does not exist, limit theorems are obtained for the low-priority waiting time and for the total uncompleted service time of all customers in the system at time t.
Queues with Periodic Service and Changeover Time
Authors: Eisenberg Martin
Published: November 2008

This paper analyzes a queuing model consisting of a system of queues that are attended periodically (in a given order) by a single server. The server empties each queue before proceeding to the next queue in sequence. A changeover time is required whenever the server switches from one queue to another. For a stationary process expressions are obtained for the Laplace-Stieltjes transforms of the waiting-time and intervisit-time distributions at each queue. It is also shown how the moments of these distributions can be calculated.
On Insensitivities in Urban Redistricting and Facility Location
Authors: Larson Richard C. , Stevenson Keith A.
Published: November 2008

This paper considers one class of problems associated with urban service systems that dispatch vehicles from fixed facilities. Given the limited resources available, one important issue is the location of the facilities and the design of their response districts to minimize average response time in the face of spatially distributed demand patterns. Calculations with spatially homogeneous demands suggest that the mean travel time resulting from totally random distribution of facilities in the region served is reduced by only 25 per cent when the facilities are optimally distributed. This apparent insensitivity of mean travel time to facility location is pursued in detail by analyzing two classes of systems involving a pair of facilities. In the first case, a procedure is outlined for determining the optimal location of a second facility, given a position for the first facility, when no interfacility cooperation is allowed. In the second case, the same region is examined, but allowing a form of interfacility cooperation. These simple models suggest that, because of insensitivities, it may not be necessary to quantize geographical data finely and then to try laboriously to find the “optimal” solutions to redistricting and facility-location problems. Redistricting and facility location based on rather crude assumptions and an awareness of some of the heuristic properties illustrated by simple analytical models may yield mean travel times very near the minimum possible.
A Spatial-Allocation Model for Regional Health-Services Planning
Authors: Abernathy William J. , Hershey John C.
Published: November 2008

In planning for health services, the need arises to determine the location, capacity, and number of health centers for a geographically defined region. The present paper formulates this problem in a form convenient for solution and presents results from the model to clarify some important aspects of this allocation decision. The planning region is assumed to consist of geographically defined subareas or census blocks, of known location. The population is stratified in such a way that each stratum exhibits relatively homogeneous patterns of health-care utilization. The model characterizes the effects of center locations upon aggregate utilization and utilization of individual centers, and gives optimal locations of centers with respect to several alternative criteria. An example illustrating computational feasibility and the implications of various criteria for the location decision is presented.
Optional Specification of Air-Pollution-Emission Regulations Including Reliability Requirements
Authors: Blumstein Alfred , Cassidy R. Gordon , Gorr Wilpen L. , Walters Anthony S.
Published: November 2008

A basic model for air-pollution control is a semi-infinite program that minimizes the sum of individual polluter's control costs while ensuring that ambient pollution concentrations are within air-quality standards. This paper is an extension that includes the effects of pollution-control-device breakdowns and shutdowns for planned maintenance. We use the fact that days characterized by good dispersion of pollution emissions occur periodically and can be accurately forecast for shutdown periods. A stochastic process of breakdown arrivals and servicing, and appropriate extensions of diffusion models give rise to a model for additional concentrations due to downtime. Parameters of the stochastic process are included as decision variables in a chance-constrained semi-infinite program allowing for tradeoffs between collection efficiency and various reliability characteristics. A practical implementation model and solution techniques are given for possible use in the present clean-air program.
An Estimate of Expected Critical-Path Length in PERT Networks
Authors: Lindsey J. H.
Published: November 2008

The estimate of expected critical-path length in PERT networks in this paper is usually better than the Fulkerson estimate because of greater flexibility in choosing a path whose length approximates the length of the critical path. As the calculations are based on a model approximating the actual network, the new estimate may fall on either side of the expected critical path, even though the Fulkerson estimate never exceeded the expected critical-path length. A Fortran program was written to calculate the new estimate, whose calculation is more complicated man Fulkerson's estimate. The new estimate, Fulkerson's estimate, and the expected critical-path length are compared in several examples.
Distribution of the Number of Tasks by a Repairable Machine
Authors: Scott Meckinley
Published: November 2008

This paper is concerned with determining the various probability generating functions and moments associated with the number of tasks performed by a machine subject to breakdown. The running time, waiting time before repair, and the repair time are independent random variables with general probability density functions. The generating function of the number of tasks for a given uninterrupted running time is assumed to be known. Some special cases are considered.
A Decomposition Algorithm for Arborescence Inventory Systems
Authors: Kalymon Basil A.
Published: November 2008

This paper develops an algorithm for solving an arborescence-structured production and inventory system. Arborescence structures model multi-echelon production systems in which each facility requires input from a unique immediate predecessor. Assuming known demands, and no backlogging, the objective is to schedule production over a finite planning horizon to minimize production and holding costs. The algorithm is applicable to systems in which, at all facilities with followers in the system, the production costs consist of a set-up charge plus linear costs and holding costs are linear. General costs are permitted at the lowest-echelon facilities (those without followers) with special computational efficiency resulting when these costs are concave. The algorithm exploits the known results on the structure of optimal policies in arborescence systems to decompose the problem into single-stage problems at each lowest-echelon facility. This decomposition is achieved by enumerating implicitly the feasible production set-up patterns at facilities with followers. As a result, the computational effort might increase exponentially with the number of facilities with followers, but is increasing only linearly with the number of lowest-echelon facilities in the system.
A Model for Analyzing Artillery Registration Procedures
Authors: Barr Donald R. , Piper Larry D.
Published: November 2008

This paper develops a model that extends and generalizes the methods of the bio-assay analysis by incorporating differing stopping rules, samples per level, and level magnitudes, and applies it to the problem of artillery registration in a decision-theoretic setting. It finds that significant improvements in the procedure currently used by the US Army and Marine Corps field artillery units (in terms of accuracy, timeliness, and ammunition expenditures) may well be possible. The method of analysis is applicable in a wide range of contexts involving “calibration” problems where the variance of the population being tested is known.
Optimum Locations of Centers in Networks
Authors: Hakimi S. L. , Maheshwari S. N.
Published: November 2008

This paper presents a generalization of results of Hakimi and Goldman on optimum locations of centers (warehouses) in a network. This generalization is achieved by a conceptual simplification of the previous results leading to a proof of a stronger version of Goldman's conjecture.
Problem Decomposition and Data Reorganization by a Clustering Technique
Authors: McCormick William T. , Schweitzer Paul J. , White Thomas W.
Published: November 2008

A new cluster-analysis method, the bond energy algorithm, has been developed recently; it operates upon a raw input object-object or object-attribute data array by permuting its rows and columns in order to find informative variable groups and their interrelations. This paper describes the algorithm and illustrates by several examples its use for both problem decomposition and data reorganization.
Operating Characteristics of a Simple Shuttle under Local Dispatching Rules
Authors: Ignall Edward , Kolesar Peter
Published: November 2008

We treat a transportation system with Poisson passenger arrivals at each of two terminals and a carrier of capacity one that shuttles back and forth between the terminals. We study the consequences of the control decision: how long should the carrier wait empty at a terminal? This dispatch decision is made without knowledge of the queue at the other terminal. Exact and approximate expressions are obtained for the number of carrier trips per unit time and average queue size at each terminal. They are used to show that it is best never to hold the carrier at the slow terminal and not to randomize in the decision process. Further, we show that holding the carrier at the fast terminal sometimes reduces both trip rate and the sum of the average queue sizes.
L = λW: A Discounted Analogue and a New Proof
Authors: Stidham Shaler
Published: November 2008

This paper presents a discounted analogue to L = λW, together with an application to a queuing optimization problem. This discounted analogue is used to construct a new proof of the classical (limiting average) version of L = λW, using as hypotheses only that the limiting averages of λ and W exist and are finite.
A Generalization of L = λW to Moments of Queue Length and Waiting Times
Authors: Brumelle Shelby L.
Published: November 2008

The well known formula L = λW relates the time-average number in queue to the expected wait in queue of a customer. This paper specializes a more general formula, denoted by H = λG, in order to obtain relations between moments of L and W other than the first. The basic queue considered is G/G/k with stationary input. The special case where the arrival times form a renewal process and the more special case where they are a Poisson process are also discussed.
Monte Carlo Simulation of Operating-Room and Recovery-Room Usage
Authors: Schmitz Homer H. , Kwak N. K.
Published: November 2008

The purpose of this paper is to provide an insight into the increased need for operating-room and recovery-room facilities and space, based on an increased bed complement. The problem is formulated into three primary questions: (1) How many more surgical procedures will be performed because of the increased bed capacity? (2) How much operating-room time and space will the surgical procedures require? (3) How much recovery-room time and space will the surgical procedures require? To answer these questions, a simulation model of the lengths of stay in the operating room and the recovery room is constructed by the Monte Carlo method, it is tested statistically and its results interpreted. This simulation model can facilitate planning, decision-making, and managerial control by providing management information.
On Symmetric Duality in Nonlinear Programming
Authors: Bazaraa M. S. , Goode J. J.
Published: November 2008

In this study we generalize the formulation of symmetric duality introduced by Dantzig, Eisenberg, and Cottle to include the case where the constraints of the inequality type are defined via closed convex cones and their polars. The new formulation retains the symmetric properties of the original programs. Under suitable convexity/concavity assumptions we generalize the known results about symmetric duality. The case where the function involved is strongly convex/strongly concave is also treated and Karamardian's result in this case is generalized. As a result, we show that every strongly convex function achieves a minimum value over any closed convex cone at a unique point. Some special cases of symmetric programs are then considered, leading to generalizations of Wolfe's duality as well as generalizations of quadratic and linear programming formulations.
Computation in Discrete Stochastic Programs with Recourse
Authors: Garstka Stanley J. , Rutenberg David P.
Published: November 2008

This paper presents a solution procedure for discrete stochastic programs with recourse (linear programs under uncertainty). It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point.
Convexity Cuts and Cut Search
Authors: Glover Fred
Published: November 2008

This note focuses on two new and related cut strategies for integer programming: the “convexity-cut” and “cut-search” strategies. The fundamental notions underlying the convexity-cut approach are due to Richard D. Young and Egon Balas, whose “hypercylindrical” and “intersection” cuts provide the conceptual starting points for the slightly more general framework developed here. We indicate the utility of our framework (and hence the importance of the original Young and Balas ideas) by specifying a variety of new cuts that can be obtained from it. The second new strategy, cut search, shares with the convexity-cut strategy the notion of generating a cut by passing a hyper-plane through the terminal endpoints of edges extended from the vertex of a cone. However, whereas the convexity-cut approach determines the extensions of these edges by reference to a convex set that contains the vertex of the cone in its interior, the cut-search approach determines these extensions by reference to associations between certain “proxy” sets of points (e.g., collections of hyperplanes) and “candidate solutions” to the integer program. The cut-search approach typically involves more work than the convexity-cut approach, but offers the chance to identify feasible solutions in the process, and can sometimes also yield somewhat stronger cuts than the convexity cuts.
Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems
Authors: Glover Fred , Woolsey Eugene
Published: November 2008

This paper gives rules that enable the transformation of a 0-1 polynomial programming problem into a 0-1 linear programming problem to be effected with reduced numbers of constraints. Rules are also given that provide reduced numbers of variables when the true variables of interest are not individual cross-product terms, but sums of such terms or polynomials of the form (∑xj)p.
Linear Programming with a Fractional Objective Function
Authors: Bitran G. R. , Novaes A. G.
Published: November 2008

This paper presents an algorithm, based on the simplex routine, that provides a way to solve a problem in which the objective function is not linear, but rather is represented by a ratio of two linear functions. This algorithm has a computational advantage over two previous ones because it requires neither variable transformations nor the introduction of new variables and constraints.
There Cannot be any Algorithm for Integer Programming with Quadratic Constraints
Authors: Jeroslow R. C.
Published: November 2008

This paper studies a class of integer programming problems in which squares of variables may occur in the constraints, and shows that no computing device can be programmed to compute the optimum criterion value for all problems in this class.
Optimal Design of Multiactivity Multifacility Systems by Branch and Bound
Authors: Pinkus Charles E. , Gross Donald , Soland Richard M.
Published: November 2008

This paper presents a model for designing multiactivity, multifacility systems. Given the maximum number of facilities and their possible locations, the problem is to determine which facilities to include in the system and which activities should be carried on at each facility in order to minimize the cost of the system. A branch-and-bound algorithm for solving the problem is given; the subproblems solved by the algorithm are tractable integer linear programs. The model can be used in the design of such diverse systems as neighborhood health centers, schools, and multiproduct inventory distribution systems.
An Algorithm for Assigning Uses to Sources in a Special Class of Transportation Problems
Authors: Srinivasan V. , Thompson G. L.
Published: November 2008

This paper considers a special class of transportation problems in which the needs of each user are to be supplied entirely by one of the available sources. We first show that an optimum solution to this special transportation problem is a basic feasible solution to a slightly different standard transportation problem. A branch-and-bound solution procedure for finding the desired solution to the latter is then presented and illustrated with an example. We then consider an extension of this problem by allowing the possibility of increasing (at a cost) the source capacities. The problem formulation is shown to provide a generalization to the well known assignment problem. The solution procedure appears to be relatively more efficient when the number of uses greatly exceeds the number of sources.
Technical Note—On Partitioning the Feasible Set in a Branch-and-Bound Algorithm for the Asymmetric Traveling-Salesman Problem
Authors: Garfinkel Robert S.
Published: November 2008

This note develops a branching scheme for a branch-and-bound algorithm for the traveling-salesman problem. It improves on the algorithm of Bellmore and Malone in that a partition of the feasible set is achieved at every vertex of the enumeration tree.
Technical Note—A Class of Nonlinear Chance-Constrained Programming Models with Joint Constraints
Authors: Jagannathan R. , Rao M. R.
Published: November 2008

Miller and Wagner [Opns. Res. 13, 930–945 (1965)] define joint chance-constrained programming by specifying a set of constants that are joint probability measures of the extent to which constraint violations are permitted. For the special case of a random right-hand-side vector whose elements are independent random variables, they show that an equivalent deterministic concave program exists. The purpose of this paper is to generalize this result to a class of nonlinear chance-constrained programming models with joint constraints.
Mathematical Programs with Optimization Problems in the Constraints
Authors: Bracken Jerome , McGill James T.
Published: November 2008

This paper considers a class of optimization problems characterized by constraints that themselves contain optimization problems. The problems in the constraints can be linear programs, nonlinear programs, or two-sided optimization problems, including certain types of games. The paper presents theory dealing primarily with properties of the relevant functions that result in convex programming problems, and discusses interpretations of this theory. It gives an application with linear programs in the constraints, and discusses computational methods for solving the problems.
Technical Note—Further Necessary Conditions for the Existence of a Solution to the Multi-Index Problem
Authors: Smith Graham
Published: November 2008

This note gives three new sets of necessary conditions for the existence of a solution to the multi-index problem. One includes as subsets all of the Haley conditions, and all of the 1967 Morávek and Vlach conditions; the second includes as subsets the 1967 Morávek and Vlach conditions; while the third includes as subsets both the first and second new sets of conditions.
Technical Note—Parameterizing an Activity Vector in Linear Programming
Authors: van de Panne C.
Published: November 2008

This note demonstrates that a linear programming problem in which the coefficients of one variable depend linearly on a variable parameter can be reduced to a problem in which only one coefficient depends on the variable parameter; the latter problem is relatively easy to solve.
Enumerative Cuts: I
Authors: Burdet Claude-Alain
Published: November 2008

This paper presents new types of cutting-plane algorithms for integer-constrained optimization problems. The underlying idea of the method of enumerative cuts is to make use of an enumeration procedure in order to construct cutting planes that can be made arbitrarily deep. In recent publications, Balas and Young have established in somewhat different contexts that valid cutting planes can be generated from the intersection of (basic) rays with adequately constructed hyperspheres. This paper introduces a family of polyhedra to replace the sphere; these polyhedra are not tangential to the hypersphere and produce cutting planes with particular characteristics that are discussed. Constructive procedures are sketched for generating step-by-step cutting planes that become deeper and deeper at every step, until the deepest cut is obtained. This construction often relies on a partial enumeration scheme of the set of integer solutions.
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
Authors: Lin S. , Kernighan B. W.
Published: November 2008

This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. The procedure is based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems. The procedure produces optimum solutions for all problems tested, “classical” problems appearing in the literature, as well as randomly generated test problems, up to 110 cities. Run times grow approximately as n2; in absolute terms, a typical 100-city problem requires less than 25 seconds for one case (GE635), and about three minutes to obtain the optimum with above 95 per cent confidence.
Calculating Maximal Flows in a Network with Positive Gains
Authors: Grinold Richard C.
Published: November 2008

This paper looks at the maximal-flow-with-gains problem from a new point of view. We with to discover the maximum output possible for any input. This approach leads naturally to a two-step parametric solution procedure: The first step finds the maximum output for zero input, and resolves all difficulties with flow-generating loops; the second determines how the maximum output increases as input is increased.
Sequencing Expansion Projects
Authors: Erlenkotter Donald
Published: November 2008

This paper examines the problem of finding the sequencing of a finite set of expansion projects that meets a deterministic demand projection at minimum discounted cost. For the particular situation defined, the tuning for a next expansion may be determined directly from knowledge of projected demand and present capacity. A dynamic programming formulation for sequencing projects is developed, and solution of an example problem demonstrates that other methods proposed for this problem are not, in general, valid. Extensions of the dynamic programming formulation to include interdependence between projects and joint selection of project scale and sequencing are indicated, and conditions for decomposition or direct solution of the sequencing problem are derived.
Response-Variance Tradeoffs in Adaptive Forecasting
Authors: McClain John O. , Thomas L. Joseph
Published: November 2008

This paper centers on what happens to an exponential smoothing forecasting system when the smoothing parameters are changed. It gives sufficient conditions under which several proposed models give numerically identical results, and notes a surprising symmetry in one basic model between the smoothing constants for the smoothed average and the smoothed trend. The paper defines smoothing-constant values that cause oscillatory behavior, discusses the difficulties caused by oscillation, and finds that commonly used values of the smoothing constants lie in a region of oscillation of varying period. It uses these results in an analytical study of the tradeoff between responsiveness and variance; some dominant choices emerge. Finally, on the basis of these results, the paper examines several sample sets of data from the literature, and discusses implications for the choice of smoothing constants in complex situations.
Single-Server Queues with Service Time Dependent on Waiting Time
Authors: Posner M.
Published: November 2008

This paper discusses a class of queuing models in which the service time of a customer at a single-server facility is dependent on the amount of time that customer has spent queuing for service. A complete investigation is carried out in the particular case of exponential service times with the parameter having a step-function dependency on the waiting time. The stationary waiting-time distribution is investigated for the queue discipline by which customers are served in order of arrival. This class of model is particularly suited for applications wherein customer or item deterioration occurs during waiting or where the server wishes to provide a more appropriate level of service to counter the negative effects of customer impatience and loss of good will.
Technical Note—Comment on an Integer Maximization Problem
Authors: Weinstein Iram J. , Yu Oliver S.
Published: November 2008

This note outlines three efficient solution procedures for the following problem: Maximize ∑i−1i−n Vi (mi) with respect to (m1, …, mn), subject to the conditions that the mi are nonnegative integers and ∑i−1i−n mi = M (an integer), and that each Vi is a nonnegative, concave, increasing function.
On the Optimal Size for Exploited Natural Animal Populations
Authors: Mann Stuart H.
Published: November 2008

This paper considers natural animal populations whose members are harvested for their own value, either esthetic or monetary. At the time of the harvest, population members are assumed to be indistinguishable as to sex. Revenue and cost structures are defined for these populations as they relate to the ecosystem. A stochastic description of population growth is used in which a change in the distribution of the growth parameter is described by an associated Markovian distribution process. This associated process describes the changes in environmental conditions. A harvesting policy is described in terms of an optimal population size. This policy maximizes the expected economic gain to be realized for the duration of time over which management of the system is anticipated.
An Optimization Model for Corporate Financial Planning
Authors: Hamilton William F. , Moses Michael A.
Published: November 2008

This paper describes the development and actual implementation of an optimization model for strategic planning in a large diversified organization. In contrast to previous discussions of the applicability of financial theory and mathematical programming methods in corporate planning, emphasis is placed on providing useful decision information within the practical limitations of theory, available computational capabilities, and established planning practices. The corporate model reflects the full range of financial decisions, including internal capital budgeting, acquisitions, divestments, debt creation/repayment, stock issue/repurchase, and dividend payout. Operating as an integral part of the corporate planning process, the mixed integer programming model selects optimal investment and financing programs over a multiperiod planning horizon. An on-line computational system permits extensive parametric analysis. The major features of the model, the supporting computational system, and implementation experience are presented.
Markovian Decision Processes with Uncertain Transition Probabilities
Authors: Satia Jay K. , Lave Roy E.
Published: November 2008

This paper examines Markovian decision processes in which the transition probabilities corresponding to alternative decisions are not known with certainty. The processes are assumed to be finite-state, discrete-time, and stationary. The rewards axe time discounted. Both a game-theoretic and the Bayesian formulation are considered. In the game-theoretic formulation, variants of a policy-iteration algorithm are provided for both the max-min and the max-max cases. An implicit enumeration algorithm is discussed for the Bayesian formulation where upper and lower bounds on the total expected discounted return are provided by the max-max and max-min optimal policies. Finally, the paper discusses asymptotically Bayes-optimal policies.
Bayesian Estimation of Life Parameters in the Weibull Distribution
Authors: Canavos George C. , Taokas Chris P.
Published: November 2008

This paper develops a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter θ, Bayesian estimates of θ and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results [J. Am. Stat. Assn. 62, 48–62 (1967)] for the one-parameter exponential life-testing distribution are reduced to a special case of these results. The paper develops a fully Bayesian analysis of both the scale and shape parameters θ and ξ by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of a Monte Carlo simulation and numerical-integration techniques. In both cases, the paper carries out a computer simulation and makes a comparison between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.
A Procedure for Selecting Educational Goal Areas for Emphasis
Authors: Dyer James S.
Published: November 2008

This paper presents a description of a procedure for identifying educational goal areas to be emphasized in elementary schools; it produces an index number for each goal area that approximates the incremental increase in the decision-maker's utility function arising from emphasizing it. This utility function is defined on performance measures for a group of students. The procedure has been simplified to the extent that elementary school principals can be expected to perform the required computations without assistance.
An Improved Stochastic Model for Occupancy-Related Random Variables in General-Acute Hospitals
Authors: Shonick William , Jackson James R.
Published: November 2008

This paper presents an improved stochastic model for the behavior of the daily census and associated waiting variables in general-acute hospitals. The development and form of the distributions derived follow the general approach of a previous paper by Shonick [J. Amer. Statist. Assoc. 65, 1474–1500 (1970)], but greater flexibility is provided for the health-services planner by increasing the number of decision choices available for achieving given outcomes. This increased flexibility is attained via a generalization of the queuing discipline, permitting admissions of elective patients to be suspended when the number of occupied beds reaches a predetermined level (which may be less than the total bed complement). For any emergency-elective mix of the demand for hospitalization, this model permits the computation of many measures of operating efficiency, including expected overfill rate, percentage occupancy, waiting-list length, and loss of emergency patients. A variant of the model permits computation of the expected number of patient days that will be served in “nonapproved” facilities when emergencies arriving during “full” periods are accommodated therein, rather than turned away.
Optimal Control of the Vidale-Wolfe Advertising Model
Authors: Sethi Suresh P.
Published: November 2008

This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits in a way that maximizes the present value of net profit streams over a finite horizon. First, the special polar cases of fixed and free end points are solved with and without an upper limit on advertising rate. The complete solution to the general problem is then constructed from these polar cases. The fixed-end-point case with no upper limit on the advertising rate is solved by using Green's theorem, while the other cases require additional use of switching-point analysis based on the maximum principle. The optimal control is characterized by a combination of bang-bang, impulse, and singular control, with the singular arc forming a turnpike.
A Systems Analysis of a University-Health-Service Outpatient Clinic
Authors: Rising Edward J. , Baron Robert , Averill Barry
Published: November 2008

This paper presents a case study on the use of mathematical-computer models in developing operating policies for a university-health-service outpatient clinic. Based on results predicted by the models, actual policy changes were made in the system; the paper compares the subsequent real-world results with those predicted by the models. The comparison demonstrated the validity of the models, and significant improvements were realized in the changed system. An analysis of daily arrival patterns was used to schedule more appointment patients during periods of low walk-in demand in order to smooth the overall daily arrivals. A Monte Carlo simulation model showed the effects of alternative decision rules for scheduling appointment periods during the day to increase patient throughput and physician utilization.
The Optimal Control of Partially Observable Markov Processes over a Finite Horizon
Authors: Smallwood Richard D. , Sondik Edward J.
Published: November 2008

This paper formulates the optimal control problem for a class of mathematical models in which the system to be controlled is characterized by a finite-state discrete-time Markov process. The states of this internal process are not directly observable by the controller; rather, he has available a set of observable outputs that are only probabilistically related to the internal state of the system. The formulation is illustrated by a simple machine-maintenance example, and other specific application areas are also discussed. The paper demonstrates that, if there are only a finite number of control intervals remaining, then the optimal payoff function is a piecewise-linear, convex function of the current state probabilities of the internal Markov process. In addition, an algorithm for utilizing this property to calculate the optimal control policy and payoff function for any finite horizon is outlined. These results are illustrated by a numerical example for the machine-maintenance problem.
Optimal Operation of an M/G/1 Priority Queue with Removable Server
Authors: Bell Colin E.
Published: November 2008

An optimal operating policy is characterized for the infinite-horizon average-cost case of a queuing control problem with the following properties: N priority classes of customers each arriving according to an independent Poisson process, a holding charge of hi, per customer of class i per unit time, and a single server who provides independent identically distributed service times and who may be turned on at arrival epochs or off at departure epochs. The server costs w per unit time to operate and there are fixed charges of S1 and S2 for turning the server on and off, respectively. This paper shows that a stationary optimal policy exists that either (l) leaves the server on at all times or (2) turns the server off when the system is empty. In the latter case, if the state of the system is represented as a point in N-dimensional Euclidean space, the server is turned on at the first time that the state reaches a boundary and this boundary is a hyperplane of dimension N − 1.
Technical Note—On a Paper by Simon
Authors: Kruse W. Karl , Kaplan Alan J.
Published: November 2008

In a paper on “Stationary Properties of a Two-Echelon Inventory Model for Low-Demand Items” [Opns. Res. 19, 761–773 (1971)], R. M. Simon presents an argument for finding the stationary distribution of inventory position that is not always valid. This note gives a corrected version of Simon's method.
A Preparedness Model Dealing with N Systems Operating Simultaneously
Authors: Luss Hanan , Kander Zvi
Published: November 2008

Several components comprising a system are to be maintained, while service resources are limited. An optimal inspection and repair policy yields minimal losses. Charges are for checking, repair, and lost time elapsed from component's failure to its detection. This paper examines a model of N identical components, possessing exponential failure distributions, operating simultaneously; only one component can be served (checked or repaired) at a time. The solution is based on Howard's method for solving sequential decision processes. Numerical computations indicate that losses by the best feasible policy that disregards the future (i.e., disregards other components of the system) are almost as low as long-run minimal ones.
A Mathematical Model for Simultaneously Determining the Optimal Brand-Collection and Display-Area Allocation
Authors: Anderson Evan E. , Amato Henry N.
Published: November 2008

This paper addresses a fundamental short-run resource-allocation problem confronting retail distribution: simultaneously finding the specific brands, from many, that should be displayed, and the amount of retail product-display area that should be assigned to these brands, in order to maximize the retail institution's profit. The paper decomposes total market demand according to the various levels of brand preference that could conceivably exist in final markets, and then, employs an algorithm, similar to the one used to solve the fixed-charge problem, to find the optimal brand mix and display-area allocation.
Generation of the Admissible Boundary of a Convex Polytope
Authors: Shachtman Richard
Published: November 2008

The purpose of this paper is to develop a constructive algorithm for generating the admissible boundary of a convex polytope, when the polytope is the convex hull of a given (finite) set of points, as well as to mention some related results. One application is to the sensitivity of decisions to changes in the prior distribution for problems in statistical decision theory.
Technical Note—The Effectiveness of Ordinal Dominance in Decision Analysis
Authors: Fishburn Peter C. , LaValle Irving H.
Published: November 2008

The easily applied technique of ordinal-dominance analysis in decisions under uncertainty eliminates inferior pure strategies. It is most applicable when the decision-maker’s consequence utilities are known only up to a monotonic transformation (ordinally). Each strategy eliminated by ordinal dominance will also be eliminated by cardinal dominance for every utility function that preserves the decision-maker’s preference order on the consequences. This note shows that, in finite decisions under uncertainty, if a pure strategy is not ordinally dominated, then there is some utility function that preserves the decision-maker’s preference order on the consequences such that the pure strategy is not cardinally dominated under this utility function. Hence ordinal-dominance analysis eliminates every pure strategy that can be safely eliminated when only the decision-maker's preference weak-ordering of the consequences is known.
Technical Note—Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program
Authors: Glover Fred , Woolsey Eugene
Published: November 2008

Rules are given that permit 0-1 polynomial programming problems to be converted to 0-1 linear programming problems in a manner that replaces cross-product terms by continuous rather than integer variables. Since the difficulty of mixed integer programming problems often depends more strongly on the number of integer variables than on the number of continuous variables, such rules are expected to have advantages in practical applications. In addition, the continuous variables automatically receive integer values, and hence our formulation can also be exploited by methods designed to take advantage of a pure integer structure.
Technical Note—Proper Efficiency and the Linear Vector Maximum Problem
Authors: Isermann H.
Published: November 2008

A vector maximum problem arises when more than one scalar-valued objective function is to be maximized simultaneously over a given range of definition. This note considers linear vector maximum problems and shows that each efficient solution of a linear vector maximum problem also satisfies the requirements of a restricted concept of efficiency, the notion of proper efficiency.
Technical Note—Optimal Readjustment Intervals
Authors: Wolff M. R. , Subramanian R.
Published: November 2008

This note considers systems subject to stochastic initial runtime cost immediately after a renewal and a deterministically increasing operating cost rate thereafter. The problem of establishing the cost-optimal renewal rule is generally set up as a readjustment problem. Using renewal-theoretic results, the note formulates and solves the general readjustment problem for self-contained systems. In the case of a linear cost rate, it gives the complete solution.
Technical Note—Estimation in a Truncated Circular Normal Distribution with Ballistic Applications
Authors: Dyer Danny D.
Published: November 2008

This note derives equations from which the maximum-likelihood estimates of the parameters of a circular normal distribution truncated outside a circular region may be obtained. The information matrix is included from which the asymptotic variances and covariances of the estimators may be obtained. A numerical example is given to illustrate the theory.
A Continous-Review (s, S) Inventory System with Arbitrary Interarrival Distribution between Unit Demand
Authors: Sivazlian B. D.
Published: November 2008

For a continuous-review inventory system where demand is defined by a discrete-valued process with units withdrawn from stock one at a time and where the interarrival times between successive demands are independently and identically distributed, the transient and steady-state distribution for the position inventory are derived when operating under an (s, S) policy. This paper shows that the limiting distribution of the position inventory is uniform over the set (s + 1, …, S) and is independent of the distribution of the interarrival times. When instantaneous delivery of orders is allowed, the problem is equivalent to an independent stand-by system consisting of Q = S − s operating elements subject to failure, where, following the failure of the last operating element, all Q failed elements are immediately repaired or replaced by Q new identical elements.
Estimation in Multiserver Queuing Simulations
Authors: Fishman George S.
Published: November 2008

This paper presents methods for computing point and interval estimates of descriptors of simulated queuing systems. The methods, which rely on the renewal process representation of certain processes, extend the results of Crane and Iglehart, and the author. In particular, the paper shows that computation of three sample quantities suffices to generate point and interval estimates for twelve system descriptors.