bluuebunny/crossref_metadata_2025 huggingface dataset:
Set Covering by Single-Branch Enumeration with Linear-Programming Subproblems
Authors: Lemke C. E. , Salkin H. M. , Spielberg K.
Published: November 2008

This paper presents an algorithm for the set-covering problem (that is, min c′y: Ey ≧ e, y ≧ 0, yi integer, where E is an m by n matrix of l's and 0's, and e is an m-vector of l's). The special problem structure permits a rather efficient, yet simple, solution procedure that is basically a (0, 1) search of the single-branch type coupled with linear programming and a suboptimization technique. The algorithm has been found to be highly effective for a good number of relatively large problems. Problems from 30 to 905 variables with as many as 200 rows have been solved in less than 16 minutes on an IBM 360 Model 50 computer. The algorithm's effectiveness stems from an efficient suboptimization procedure, which constructs excellent integer solutions from the solutions to linear-programming subproblems.
Hypercylindrically Deduced Cuts in Zero-One Integer Programs
Authors: Young R. D.
Published: November 2008

A zero-one mixed integer program in which the integer variables always sum to a constant k in any feasible solution has its solution set contained in the hypercylinder ∑xi2 ≦ k. Moreover, integer solutions always satisfy ∑xi2 = k, while ∑xi2 < k for fractional solutions. This situation permits the construction of valid cuts by extending the edges incident at a non-integer extreme point until they intersect the boundary of the hypercylinder; the cut hyperplane is determined by the points where the edge extensions intersect the boundary of the hypercylinder. Generalizations of this special model, due to Glover and Balas, are discussed, as is the use of these cuts in finite algorithms.
Errata
Authors: Saksena C. P. , Cole A. J.
Published: November 2008

Corrections to the authors' paper “The Bounding Hyperplane Method of Linear Programming,” Operations Research 19, 1–18 (1971).
Classification Schemes for the Strong Duality of Linear Programming Over Cones
Authors: Kortanek K. O. , Rom W. O.
Published: November 2008

Even in a finite-dimensional setting for two dual linear programming problems where the positive orthant is replaced by a closed convex cone, it is possible to have a duality gap, i.e., the infimum of one problem greater than the supremum of its dual. The absence of duality gaps is characterized in this paper by using a class of parameterized subsidiary problems of the original pair of dual problems. Characterizations are thereby obtained of “normality”—where the infimum of one problem equate the supremum of its dual. Heretofore only sufficient conditions for normality have been given. In this setting the linear programming characterizations obtained distinguish the four cases of normality where the supremum may or may not be a maximum, and the infimum may or may not be a minimum. An example is given in six dimensions of a dual pair of problems, neither of which is stable, neither of which has an optimal solution, but both of which are normal.
An Algorithm for Universal Maximal Dynamic Flows in a Network
Authors: Wilkinson W. L.
Published: November 2008

This paper presents a modification to the Ford-Fulkerson algorithm for maximal dynamic flow in a time-weighted, capacitated network. The modification is mild, as conjectured by Gale, and produces a shipping schedule representing what has been termed the universal maximal dynamic flow. The universal feature is that, in constructing a schedule for P periods, this same schedule is maximal when truncated to p less than P periods. A numerical example compares the temporally repeated and universal-type solutions.
A Generalized Approach to the Method of Steepest Ascent
Authors: Eldor H. , Koppel L. B.
Published: November 2008

This paper derives a general steepest-ascent expression to show that any “direction” in the function space can be considered to be a steepest ascent direction by selecting a proper distance metric index and/or variable scaling. Several search procedures can be thus considered to be special cases of the method of steepest ascent. An illustrative investigation shows that, in a qualitative sense, most metric indices perform comparably.
On an Allocation Problem with Multistage Constraints
Authors: Sanathanan Lalitha
Published: November 2008

This paper gives a simple algorithm for finding optimal allocations subject to a hierarchy of limits when the loss function is separable strictly convex and the resources function is linear. Its applications to capital budgeting and multistage sampling are pointed out. The allocation problem considered by Srikantan [Opns. Res. 11, 265–273 (1963)] is a special case of the problem considered in this paper.
The Near-Myopic Nature of the Lagged-Proportional-Cost Inventory Problem with Lost Sales
Authors: Morton Thomas E.
Published: November 2008

A considerable literature has been devoted to periodic-review inventory problems with proportional ordering costs and known independent demand distributions, because of the optimality under broad conditions of “base-stock” policies. An important exception is the case when order delivery is lagged and excess demand is simply lost, which is more complicated. By further restricting holding and penalty costs to be proportional, the author has extended preliminary work by Karlin and Scarf to obtain good bounds for both the optimal order policy and the associated minimum-expected-discounted-cost function for the stationary problem. These bounds possess a “newsboy” interpretation primarily in terms of costs to be incurred specifically for the review period (the period marked by the arrival of this order). In fact, the upper ordering bound is precisely the “myopic” policy in Veinott's sense. (However, the myopic policy is not base stock.) Experimental results for the one- and two-period lag problems strongly support the heuristic argument that myopic policies should, in fact, be very nearly optimal. An extension of the model to a partial backlogging situation is presented for which optimal policies may also be safely conjectured to be “myopoid.” It is hoped that interest will be stimulated toward investigating myopic policies as approximate solutions to a large class of proportional cost problems.
Technical Note—An Improved Algorithm for the Bottleneck Assignment Problem
Authors: Garfinkel Robert S.
Published: November 2008

Gross has proposed an algorithm for the bottleneck assignment problem. This note reports a test of it against a “threshold” algorithm, and finds that the latter is superior computationally.
Technical Note—A Particular Two-Priority Queue
Authors: Washburn Alan
Published: November 2008

This note describes a two-priority queue where the low-priority customers arrive in what is essentially a steady stream. It is a useful model in certain inventory problems.
Erratum
Authors: Bellmore Mandell , Malone John C.
Published: November 2008

Erratum to authors' paper “Pathology of Traveling-Salesman Subtour-Elimination Algorithms,” Opns. Res. 19, 278–307 (1971).
The Problem of Testing for the Fraction of Defectives
Authors: Breakwell J. V.
Published: November 2008

A balance is sought between (1) the cost of testing for reliability and (2) the risks, because of limiting the testing, of either accepting an insufficiently reliable product or rejecting a sufficiently reliable one. The latter risk is generally less serious than the former. With a suitably defined pay-off function, “optimum” parameters are obtained both for a fixed-size test and a sequential test of the type introduced by Wald. The mathematical treatment is valid except for very high reliabilities. Modifications are discussed for (i) an optimum sequential test when the pay-off function includes some uncertainty as to what is meant by sufficiently reliable, and (ii) an optimum sequential test between two rival products.

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

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Operations Research in Japan
Authors: Murayama Ken-Ichi
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Threats to the Growth of Operations Research in Business and Industry
Authors: Rinehart Robert F.
Published: November 2008

It is customary at annual meetings of professional societies such as ours, for the president to devote much or all of his retiring address to the many accomplishments and advances of the organization during the preceding year or years. In the case of ORSA we call point with some pride to our 40 per cent increase in membership, to the increased health and size of our Journal and to other signs of healthy growth. Our optimism regarding past achievements should not be permitted to obscure, however, those dangers or threats to our continued development which may loom in the future. I propose, therefore, to be the devil's advocate and to depart from precedent by playing the part of a viewing-with-alarm prognosticator rather than that of a pointing-with-pride historian.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Mathematical Foundations and Computational Methods for a Digital Logic Machine
Authors: Ledley Robert S.
Published: November 2008

The manipulations of the propositional calculus (and the analogous Boolean algebra) have recently become of fundamental importance in fields other than set theoretical proofs of pure mathematics. For example, in the analysis and evaluation of intelligence and military reports, preparation and analysis of tactical methods and principles, complex logical nonnumerical problems often arise more frequently than do problems of a numerical nature. Consequently there is the need for a systematic method of analyzing and solving propositional functions and equations. The purpose of this paper is to present the systematic rules of an “arithmetic” for handling propositional functions and equations, formulated in a manner amenable to easy computation and mechanization. Among the important results given are: (a) a simple method of expressing a propositional calculus in terms of the shortest digitalized words possible, (b) a systematic method for generating the simplest and absolute simplest forms for Boolean functions, (c) a method for systematically generating all true and false implications of given propositions, (d) a method for systematically generating all possible changes of variables (i.e., substitution of new variables) that can be made on a propositional calculus while preserving the logical meaning, and (e) the systematic generation of all solutions to any number of simultaneous propositional equations in any number of unknowns. The solution of this latter problem implies the ability to perform manipulations with propositional variables in a manner analogous to manipulations of ordinary algebraic equations. A number of illustrative applications to military situations are given, including an analysis of certain propositions and conclusions of Clausewitz.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Information Theory and Man-Machine Systems
Authors: Krulee Gilbert K.
Published: November 2008

Information theory has been used recently as the basis for some experimental studies of the abilities of humans as processors of information. One possible approach to the analysis of man-machine systems is to consider the implications of such experimental knowledge for the design of man-machine systems. The functions performed by human operators in these systems are primarily those of control of the energy resources of the system. Control functions involve, by their very nature, the availability of relevant information and the opportunity to transmit control decisions reached on the basis of this information. It is important not only that enough information be available to an operator in order to carry out his control responsibilities, but also that these tasks be not complicated unnecessarily by the provision of too much or irrelevant information. Moreover, in applying an informational analysis to control tasks, it is essential that consideration be given as to what sorts of categories are perceptually possible for operators since any analysis which does not take into account certain perceptual limitations of humans is likely to be invalid. Following this point of view it is suggested that intelligent design of man-machine systems involves compatibility between the control requirements of a system and the capabilities of the men in the system.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Railroad Executives Seminar—A Correction
Authors: Davidson Harold O.
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Games of Economic Survival with Discrete- and Continuous-Income Processes
Authors: Gerber Hans U.
Published: November 2008

In this model the income process of a firm is assumed to be a homogeneous Markov process (discrete or continuous). One is interested in an optimal dividend strategy, i.e., a strategy that maximizes the expected sum of the discounted dividend payments. This paper derives general results in the case where the income process is skip free to the right; in particular, it establishes the factorization formula and shows it to be closely connected with the probability of ruin. The theory is illustrated by a numerical example.
Pluralization: A Mathematical Model
Authors: Kochen Manfred , Deutsch Karl W.
Published: November 2008

This is the first of a series of simple mathematical models to explore the concept of decentralization. The primary focus is on pluralization as one of three aspects of decentralization. We derive expressions for cost and for net benefit as a function of the number of identical, uniformly dispersed facilities capable of servicing requests from sources that are uniformly distributed along a long, thin, geographical strip. The optimal, or cost-minimizing, number of such pluralized facilities is computed. We also derive conditions in terms of the basic parameters, such as the number of requests per month, transport costs per unit time, etc., which favor pluralization over centralization. The models are also analyzed for the secondary benefits of redundancy for more dependable service and to smooth fluctuations in demand. We found that, on balance of all the factors, historical trends—particularly the trend toward more requests per unit time—favor pluralization.
A Stochastic Constrained Optimal Replacement Model: The Case of Ship Replacement
Authors: Kalman Peter J.
Published: November 2008

This paper formulates a stochastically constrained equipment replacement model. Its aim is to determine a sequence of replacement dates such that the total “current account” cost of all future costs and capital expenditures over an infinite time horizon for the n initial incumbent machines is minimized subject to the constraints that, at each point in time, the expected number of machines in each of several “utility classes” has a prescribed value. The theoretical model is then solved under a set of simplifying assumptions and applied to the problem of ship replacement.
Optimal Search with Uncertain Sweep Width
Authors: Richardson Henry R. , Belkin Barry
Published: November 2008

This paper considers file problem of optimal search for a stationary target when the detection capability of the search sensor, as characterized by its sweep width, is fixed but not known in advance. Most of the results are confined to the assumption of a gamma prior sweep-width distribution and to the cases of normal and uniform prior target-location distributions. Explicit formulas are obtained for the optimal search plans, the probability of detection versus time, the expected time to detection, and the posterior marginal distributions for target location and sweep width. In the case of a normal prior target-location distribution, expected time to detection is compared for the optimal plan and search plans based on the assumption of a known value for sweep width; this includes a sensitivity analysis treating actual sweep width as a parameter. For a target of value, the search plan that maximizes expected net return is determined. This plan requires specification of a rule for terminating an unsuccessful search. Explicit results are given assuming a nonincreasing target value and a nondecreasing search-cost rate.
Technical Note—The Infinitely-Many-Server Queue with Semi-Markovian Arrivals and Customer-Dependent Exponential Service Times
Authors: Smith Woollcott
Published: November 2008

This note studies an infinitely-many-server queue with N types of customers arriving according to a semi-Markov process. The service times are independent exponential random variables with means 1/μi, where i is the type of customer being served. The stationary distribution of the embedded Markov chain and the limiting distribution of the continuous-time process are obtained.
Letter to the Editor—The Synergy of Operations Research and Computers
Authors: Mjosund Arne
Published: November 2008

With the exception of certain simulation models, it appears that operations researchers have shown little interest in developing models for situations in which the computer is an integral part. So far, they have generally been content to develop decision models without worrying too much about processing source data. The design of the information systems that presumably provide inputs into decision models has largely been left to programmers. This letter discusses the potential benefits to be realized through research to bring these two aspects of the same problems together. Approaches to developing models that integrate variables and information-system variables are proposed.
Vicinal Sequencing Problems
Authors: Jaeschke Gerhard
Published: November 2008

This paper describes a special class of sequencing problems called vicinal problems. They are solved by a combination of the methods of graph theory and combinatorial programming. We analyze decomposition possibilities of complete, antisymmetric graphs in order to achieve the partition of the problems into several subproblems that can be solved by combinatorial programming procedures such as back-tracking and branch-and-bound. We conclude by treating a numerical example and commenting on a program written for that purpose.
System States for a Series of Finite Queues
Authors: Haydon Brian J.
Published: November 2008

This note describes a method of classifying and enumerating the feasible system states of a series of finite queues. The method utilizes matrix multiplication to combine subsystems or to add extra stations to an existing system, storing the classified states of an L-station system in an L-dimensional array.
Mathematical Models for Controlling Growing Biological Populations: A Survey
Authors: Jaquette David L.
Published: November 2008

Mathematical models of growing biological populations have existed for many years, but only recently has theoretical and practical research effort been directed to the control and also to the optimal control of these models. Both deterministic and stochastic population models serve as the basis for applying the systems-analysis and control-theory approach of operations research to find optimal, or at least efficient, control strategies for ecological management. Applications of this decision-theory methodology have been made to finding controlling strategies for epidemic and pest populations, harvesting policies for forests, catch and regulation strategies of fisheries and wildlife, treatment strategies of the spread of infection, and even to finding control policies regulating human population. This paper reviews the important contributions to and future challenges in this field and includes a complete bibliography.
An Optimal Policy for Operating a Multipurpose Reservoir
Authors: Russell C. Bradley
Published: November 2008

This paper presents an analytically determined general optimal policy for operating a multipurpose reservoir and depicts it in graphical form. Piecewise linear cost functions are used to describe downstream flow costs, reservoir level costs, and costs incurred in meeting and not meeting power demands, the cost parameters involved in these functions being left arbitrary to allow wide applicability. The paper assumes random inflows into the reservoir, known power demands, and the availability of a finite-capacity auxiliary power source. It uses dynamic programming as an analytical, as opposed to numerical, tool in determining the general form of an optimal operating policy for this model.
An Example of the Application of Nonlinear Programming to Chemical-Process Optimization
Authors: Sriram M. , Stevens William F.
Published: November 2008

This paper presents a realistic chemical-process optimization problem in detail, and notes the fact of its equivalence to the general nonlinear programming problem. The eight equality constraints that arise are handled by algebraic substitution, and the resulting four-variable problem is solved by a modified form of the Davidon-Fletcher-Powell algorithm. Details of the method are presented (including a FORTRAN computer program), and results of two typical cases are summarized.
A Convex Programming Model for Optimizing SLBM Attack of Bomber Bases
Authors: Bracken Jerome , McGill James T.
Published: November 2008

This paper formulates a convex programming model allocating submarine-launched ballistic missiles (SLBMs) to launch areas and providing simultaneously an optimal targeting pattern against a specified set of bomber bases. Flight times of missiles from launch areas to bases vary and targets decrease in value over time. A nonseparable concave objective function is given for expected destruction of bombers. An example is presented.
Technical Note—Theorems of Convergence for Improved Nonlinear Programming Algorithms
Authors: Dubois Jacques
Published: November 2008

This note presents proofs of convergence of nonlinear programming algorithms under a weaker requirement than Zangwill's convergence theorems A and C. The objective is the removal of the closedness and the weakening of the adaption properties of the map-algorithm. In this approach two map-algorithms are used: one that provides the solution points, and one that provides convergence for the former.
Technical Note—Solutions of a Special Class of Linear Programming Problems
Authors: Sposito V. A.
Published: November 2008

Explicit solutions for linear problems of the form: maximize (h, x), subject to Ax ≦ b, b ∈ R(A), are given, as well as explicit solutions for its dual problem. This note replaces the full row rank assumption on A of earlier results of Ben-Israel and Charnes by the assumption b ∈ R(A). With this assumption, explicit solutions are derived for the dual problem that are different from related results of Zlobec and Ben-Israel.
Heuristic Selection of Advanced Bases for a Class of Linear Programming Models
Authors: Dillon Martin
Published: November 2008

This paper describes a procedure for selecting a starting basis for a class of large linear programming models. This class, a generalization of the transportation problem, is the product of a matrix generator described elsewhere. The procedure is joined to the matrix-generator process and uses structural criteria and implicit knowledge of the model being generated to assess the attractiveness of vectors for an optimal solution. Additionally, it allows the analyst to describe, through a set of multipliers, the general features of the expected optimal solution. The multipliers are employed heuristically in conjunction with the other criteria to select a set of vectors, both logical and structural, for submission to a standard mathematical programming computational system as a starting basis. Examples of applications of the basis selector and possible extensions are presented.
The Rearrangement of Items in a Warehouse
Authors: Christofides Nicos , Colloff I.
Published: November 2008

This paper is concerned with finding the optimal way of rearranging items in a warehouse from their initial positions to their desired final locations. Such a rearrangement may become necessary because of changes in the relative demand for each item, with the result that what were once fast-moving items at the front end of the warehouse, are now only slow-moving ones that must be moved towards the “rear.” Although the problem, as treated in this paper, is addressed to the rearrangement of items in a warehouse, many other applications come immediately to mind, such as the reorganization of the layout of open-plan offices and factories. The paper gives a two-stage algorithm that produces the sequence of item movements necessary to achieve the desired rearrangement and incur the minimum cost (or time) spent in the rearranging process; the result is optimal in the restricted case where the rearrangement must be done in a number of cycles each one being of a short time duration (the case, for example, if the warehouse were to remain operative during the rearrangement).
A k-Server Queue with Phase Input and Service Distribution
Authors: Kapadia Asha Seth
Published: November 2008

This paper obtains a simple expression for the expected number of idle servers in the steady state for a queue with k servers, and a phase input and service distribution. No assumption is made regarding the order in which customers are served, except that the servers cannot sit idle as long as there are customers waiting to be served.
Probabilistic Analysis of a Two-Unit System with a Warm Standby and a Single Repair Facility
Authors: Srinivasan S. K. , Gopalan M. N.
Published: November 2008

This paper deals with the availability and the reliability of a two-unit system with a warm standby and subject to a single repair facility. It assumes the failure times of the units to be exponentially distributed with parameters λ and λ1, respectively. Initially, a unit is switched on and the other one is kept as a warm standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t) and the mean time to system failure explicitly.
Priority Queuing Systems with and without Feedback
Authors: Wignall Thomas K.
Published: November 2008

The problems discussed in this paper arose in the theory of telephone traffic, with a central processing system, such as a computer, performing numerous functions in as exchange. However, several of its more important results are applicable in many businesses offering multiple services, including ones working on a nonpriority basis. Such results as those determining the amount of storage to allocate to each service, and assessing whether the system can cope with the expected number of arriving customers are independent of the priority set, so that these results have very wide applicability.
Operations Research Education: Some Requirements and Deficiencies
Authors: Bonder Seth
Published: November 2008

In recent years some operations researchers have directed their introspection to the education of prospective OR analysts, with a resultant critical appraisal: they are ill prepared to solve problems. The purpose of this paper is to continue this introspection by presenting some conjectures on the education of the OR analyst. After examining the problem-solving process briefly and defining some requisite terminology, it gives a premise on which educational requirements for the OR analyst rest, suggests areas in which his education is deficient, discusses some reasons for these deficiencies, and notes some possible courses of remedial action.
Some Search Problems with False Contacts
Authors: Dobbie James M.
Published: November 2008

This paper describes and discusses some search problems, starting with the case of no false contacts, to provide a foundation for developing a search theory in the presence of false contacts. Important properties of the search plan are defined and illustrated by examples. After a general description of false-contact generators and alternative actions that may be used when contacts are made, the problem is formulated for the case in which false contacts are generated by real stationary objects that are investigated when contacted. It is shown that the formulation and solution of the standard optimization functionals are contingent on the number of false targets found, in general, and possibly on the locations and times of contact as well. The optimization functional is difficult to write and more difficult to solve. The formulation is made for the expected-time functional when the number of false targets is bounded. Finally, the paper outlines a procedure for finding the solution and illustrates it with an example.
The Behavior of Stock-Price Relatives—A Markovian Analysis
Authors: Fielitz Bruce D. , Bhargava T. N.
Published: November 2008

This paper presents a method of Markovian analysis of changes in the natural logarithms of stock prices over time. It examines 200 stocks from the New York Stock Exchange for the period December 23, 1963, to November 29, 1968, and defines a set of three states (up, down, small change) for the process in terms of the mean absolute deviation of changes in the natural logarithms of prices. This definition of the set of states allows both the magnitude and the direction of change to be incorporated in the analysis. Standard statistical tests for stationarity and dependence in vector and individual-process Markov-chain models are employed for both fixed- and variable-time data (the latter refers to highs for a day or week interval). In addition, a method for testing the homogeneity of the vector Markov chain is given. Empirical results for the vector-process model suggest that price movements appear to be described by a first- or higher-order nonstationary Markov chain. Tests also indicate that the vector-process Markov chain is heterogeneous. Empirical results for the individual-process Markov-chain model suggest that an individual stock has a short-term memory with respect to daily price relatives, i.e., the process is first-or higher-order. However, the corresponding process lacks stationarity. No dependency appears to exist for a weekly time lag.
The Maximum-Entropy Distribution of the Future Market Price of a Stock
Authors: Cozzolino John M. , Zahner Michael J.
Published: November 2008

This paper uses the principle of maximum entropy to construct a probability distribution of future stock price for a hypothetical investor having specified expectations. The result obtained is in good agreement with observations recorded in the literature. Thus, the paper concludes that the hypothetical individual investor is representative of a large class of investors. This new derivation of the well known random-walk theory of stock-price movements leads to an improved understanding of the model parameters by relating the variance of the random-walk process to the risk aversion of the investors. A practical use of the model is proposed to help the investor form an objective opinion of his skill.
Approximate Queuing Models for Multiprogramming Computer Systems
Authors: Avi-Itzhak B. , Heyman D. P.
Published: November 2008

In a multiprogramming computer system several jobs may be handled simultaneously by utilizing the central processing unit in processing one job while other jobs are being served by the peripheral devices. Our analysis of such a computer system proceeds in the following way. First we view the system as a closed queuing network with a fixed number of jobs, and obtain exact results for customer cycle times and server utilization. Then we use these results to develop an approximate model for the open system where the computer is fed by randomly arriving jobs. For the approximate model we obtain simple closed-form expressions for the delay distribution. The approximate model is then tested by comparing its result for the expected sojourn time to the exact results that we obtain for some special cases.
Errata
Authors: Kalymon Basil A.
Published: November 2008

Corrections that should be made in the author's paper “A Decomposition Algorithm for Arborescence Inventory Systems,” Opns. Res. 20, 860–874 (1972).
Sequential Stopping Rules for Fixed-Sample Acceptance Tests
Authors: Chang R. C. , Ehrenfeld S.
Published: November 2008

This paper discusses optimal stopping rules for fixed-sample acceptance tests where the observations with time delays are obtained sequentially. It studies two cases, one with a known prior distribution and the other one without a prior distribution, discusses Bayes-optimal and minimax stopping rules, and considers a stopping rule using the maximum likelihood estimate of θ, the probability of a single success. An example is given assuming that the prior distribution is a beta distribution. It is shown that the Bayes-optimal stopping rule thus obtained approaches the stopping rule using the maximum likelihood estimate when the beta parameters, α and β, approach zero.
Multiplicative Utility Functions
Authors: Keeney Ralph L.
Published: November 2008

This paper presents sufficient conditions for a multiattribute utility function to be either multiplicative or additive. The number of requisite assumptions to imply the main result is equal to the number of attributes. Because the assumptions involve only trade-offs between two attributes at a time or lotteries over one attribute, it is reasonable to expect that decision makers can ascertain whether these assumptions are appropriate for their specific problems. Procedures are given for verifying the assumptions and assessing the resulting utility functions. The paper concludes with a sketch of a recent application of the results to a six-attribute problem relating to the development of Mexico City's airport facilities.
A Markov-Decision-Chain Approach to a Stochastic Assignment Problem
Authors: Albright S. Christian
Published: November 2008

This paper discusses a problem where jobs of random quality, or importance, arrive at random times and must be done by one of a fixed set of men on hand. The men can all complete any job in an exponential amount of time, with mean l/u, but the men are of different known qualities. Once a man finishes a job he again becomes available to do future jobs. If a man of quality p is assigned to do a job whose value is observed to be x, a reward r(p,x) is received. Also a cost of c(p) is incurred per unit time that a man of quality p is kept idle. The decision maker must observe the values of the incoming jobs and assign them to available men so as to maximize expected reward per unit time. The problem is set into the framework of a G/M/n queue with a possibly limited waiting room, and the optimization is done by techniques of Markov decision analysis.
Technical Note—A Linear-Programming Approach to Air-Cleaner Design
Authors: Advani Suresh
Published: November 2008

This note deals with the application of linear programming to air-cleaner design, a mechanical engineering problem. It uses the simplex method to find an optimal solution under the restrictions of dust-collection efficiency, pressure loss, material shortage, minimum demand requirements, and scrap economics.
Optimal Facility Location with Concave Costs
Authors: Soland Richard M.
Published: November 2008

The following problem is considered: select plant sites from a given set of sites and choose their production and distribution levels to meet known demand at discrete points at minimum cost. The construction and operating cost of each plant is assumed to be a concave function of the total production at that plant, and the distribution cost between each plant and demand point is assumed to be a concave function of the amount shipped. There may be capacity restrictions on the plants. A branch-and-bound algorithm for identifying an optimal solution is described; it is equivalent to the solution of a finite sequence of transportation problems. The algorithm is developed as a particular case of a simplified algorithm for minimizing separable concave functions over linear polyhedra. Computational results are cited for a computer code implementing the algorithm.
Technical Note—Sharper Bounds on Nonconvex Programs
Authors: Falk James E.
Published: November 2008

Recently it was pointed out that the generalized Lagrange-multiplier method provides a sharper bound on a nonconvex program than does the solution of the program formed by taking convex envelopes of all functions involved in the original problem. This note points out that the bounds are the same if the original problem has only linear constraints, or if the problem is separable with certain properties, and give an example in which the bounds differ. The better bound is currently being used in locating global solutions of nonconvex, separable, piecewise-linear problems.
Technical Note—The Method of Successive Approximations and Markovian Decision Problems
Authors: Hordijk Arie , Tijms Henk
Published: November 2008

This note considers Howard's discrete-time Markovian decision model with the average return as criterion. Using results of Blackwell and MacQueen for the discounted return model it is shown in all generality that the Odoni bounds contain both the maximal average return and the average return of the current policy.
Technical Note—Dynamic Programming and Probabilistic Constraints
Authors: White D. J.
Published: November 2008

This note deals with the manner in which dynamic problems, involving probabilistic constraints, may be tackled using the ideas of Lagrange multipliers and efficient solutions. Both the infinite and finite time horizon are considered. Under very general conditions, Lagrange-multiplier and efficient-solution methods will readily produce, via the dynamic-programming formulations, classes of optimal solutions. However there may be gaps in the constraint levels thus generated. It is shown that, providing we admit mixed policies, these gaps can be filled in and that, furthermore, the dynamic programming calculations may, in some general circumstances, be carried out initially in terms of pure policies, and optimal mixed policies can be generated from these. The probabilistic constraints are treated in two ways, viz., by considering situations in which constraints are placed on the probabilities with which systems enter into specific states, and by considering situations in which minimum variances of performance are required subject to constraints on mean performance. Finally the mean/variance problem is viewed from the point of view of efficient solution theory. It is seen that some of the main variance-minimization theorems may be related to this more general theory, and that efficient solutions may also be obtained using dynamic-programming methods.
Resource Planning in University Management by Goal Programming
Authors: Schroeder Roger G.
Published: November 2008

Resource-planning methods for university and college management have received increasing attention by management scientists in recent years. One widely known approach yields cost-simulation models such as RRPM and CAMPUS. However, these models have two serious limitations in representing resource-management problems: (1) budget levels are outputs of the models, not inputs, and (2) faculty levels are a fixed function of enrollment. This paper proposes a goal-programming model that relieves these limitations and offers other features as well; in it the goals are faculty instruction loads, staff-to-faculty ratios, faculty distribution by rank, and teaching-assistant-to-faculty ratios. These specified goals are achieved as closely as possible, subject to constraints on the projected budget available in each year of the planning horizon and to faculty-flow constraints. The decision variables are the faculty, staff, and teaching-assistant levels in each of several academic units over the planning horizon. The model provides a vehicle for long-range budget planning and resource allocation.
Application of Programs with Maximin Objective Functions to Problems of Optimal Resource Allocation
Authors: Kaplan Seymour
Published: November 2008

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz = mini cixi, subject to AX = b, X ≧ 0. Although the ci can be in the interval (− ∞, ∞), the paper discusses the more common practical case where all ci ≧ 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the “fixed proportion” type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented.
The Operator-Scheduling Problem: A Network-Flow Approach
Authors: Segal M.
Published: November 2008

The number of telephone operators required on duty at switchboards fluctuates widely during the day. Work periods of operators are defined by start and end times of tours and by the timing of break and relief periods within tours. This paper proposes a method for determining the number of operators assigned to tours and their corresponding timing of breaks and reliefs; it relies on various network-flow formulations. An example application of the method is presented.
A Model for Evaluating Golf Handicapping
Authors: Pollock Stephen M.
Published: November 2008

This paper develops an analytical (nonsimulation) model of the game of golf in order to investigate the “fairness” of the present handicapping scheme, as well as to compare the results of medal play with those of match play. Although many simplifying assumptions are made in order to exercise the model, the results offer general insights into the relations between handicaps and win probabilities for selected pairs of players.
Identifying Product-Safety Priorities
Authors: Locke John W.
Published: November 2008

Establishing priorities in dealing with regulatory problems requires a keen insight into the problem, a knowledge of the technical state of the art, and a calibrated eye toward the benefits that can accrue from alternative actions. In matters of health, there is an additional factor: the willingness of consumers to accept risk in using a product. This paper describes an orderly procedure for developing quantitative and qualitative factors involved in setting priorities for establishing product-safety standards. The factors specifically identified and examined in this paper include frequency of injury, severity of injury, product exposure, likelihood of regulatory “success,” cost of regulatory action, benefit due to elimination of injuries, and the citizen's willingness to incur risks. Quantification of several of these factors is already possible. Others require the systematic application of available techniques. A start has been made in quantification of risk, but applied research is needed before the techniques can be employed. Numerical examples are included for various consumer-product categories.
Random-Payoff Two-Person Zero-Sum Games
Authors: Blau Roger A.
Published: November 2008

Within the framework of chance-constrained programming, this paper formulates two related stochastic models for players competing in a random-payoff two-person zero-sum game. Under certain assumptions, it shows that a one-to-one correspondence (called stochastic pseudoduality) exists between the two formulations at their optimal values, and, furthermore, exact deterministic equivalents can be obtained for these formulations. The optimal solution for a deterministic equivalent can be found by considering an appropriate class of subproblems.
Technical Note—Approximations for a Service System with Nonindependent Interarrival Times
Authors: Granot Daniel , Granot Frieda , Lemoine Austin
Published: November 2008

This paper provides simple, readily computable approximations for the limiting behavior of the waiting-time process in a queuing system having a certain scheme of nonindependent interarrival times. Its results are obtained without recourse to stringent distribution assumptions.
Man-Machine Synthesis of Disaster-Resistant Operations
Authors: Rivas J. Roberto , Rudd Dale F.
Published: November 2008

Disaster-resistant industrial operations are created to avoid certain classes of events known to be dangerous. While a rapid and accurate synthesis of safe operations is necessary during a disaster, it is hindered by the magnitude of the logic-analysis problems encountered and by the sophistication of the operating goals. This paper develops practical methods for computer-aided synthesis of disaster-resistant operations.
Solving Constrained Transportation Problems
Authors: Klingman D. , Russell R.
Published: November 2008

This paper presents a specialized method for solving transportation problems with several additional linear constraints. The method is basically the primal simplex method, specialized to exploit fully the topological structure embedded in the problem. It couples the poly-ω technique of Charnes and Cooper with the row-column sum method to yield an “inverse compactification” that minimizes the basis information to be stored between successive iterations, and in addition minimizes the arithmetic calculations required in pivoting. In particular, the solution procedure only requires the storage of a spanning tree and a (q + 1) × q matrix (where q is the number of additional constraints) for each basis. The steps of updating costs and finding representations reduce to a sequence of simpler operations that utilize fully the triangularity of the spanning tree. Procedures for obtaining basic primal “feasible” starts are also presented.
Technical Note—Allocation of Effort Resources among Competing Activities
Authors: Luss Hanan , Gupta Shiv K.
Published: November 2008

This paper presents problems of resource allocation among many activities, such as allocating a given marketing budget among sales territories, where the return function for each territory attains different parameters. Applying the Kuhn-Tucker conditions, we derive “single pass” algorithms for different concave payoff functions, maximizing total returns under a given amount of available effort. Various extensions are also mentioned.
A Model for Predicting Average Fire Engine Travel Times
Authors: Kolesar Peter
Published: November 2008

We propose, motivate, and test a model for predicting ET, the expected fire engine travel time in a region, given the region's area, A; the number of fire engines stationed there, n; the alarm rate, λ; and the expected total service time per alarm, ES. The model is ET = α + β [A/(n − λES)]γ. Estimates of the values of parameters α, β, and γ are given for New York City, where the model has been validated, and used in analyzing fire engine deployment problems. Recent changes in the number and location of fire engines in New York City were based partially on this analysis.