bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimal Linear Ordering of Information Items
Authors: Morse Philip M.
Published: November 2008

Efficient search of items in a store of information, such as books in a library, abstracts of articles, information in a computer data bank or the like, requires that the items most closely connected in content be close together, in order that a person looking for some particular information may concentrate his search on as small a part of the store as possible. The degree of “connectedness” between two items i and j can be expressed in terms of a correlation index nij. This paper discusses methods of estimating these indices. Once the correlation indices are known for each pair of items in the store, it is possible to assign a position xi for each item i, along a linear classification scale, such that the larger the nij between items i and j the closer the two items are on the scale. Such a scale indicates the optimal ordering of books on library shelves or of items in any other data collection. It also provides means for assigning optimal subject descriptors for a computer-based information store. A procedure is described whereby the values of the xi's may be determined in terms of the nij's. When the items in the store tend to “clump together” in classes, with much smaller correlation between items of different classes than those between items of the same class, an approximation technique may be used to locate the relative positions of the classes along the scale, as well as the distribution of the x's within each particular class. An example is given of these techniques.
Bias Considerations in Simulation Experiments
Authors: Fishman George S.
Published: November 2008

This paper uses a first-order autoregressive scheme to investigate the effects of initial conditions in a simulation on the estimation of the population mean of a process of interest. The effects are measured by bias and variance. The results show that the elimination of observations near the beginning of the simulation reduces bias, as intended, but increases the variance, sometimes significantly.
Technical Note—Fixed-Stockout-Probability Order Quantities with Lost Sales and Time Lag
Authors: Yaspan Arthur
Published: November 2008

The literature of inventory contains many examples of order quantities chosen so as to achieve some fixed probability of stockout in the period following the order's arrival. This note shows, for independent normally distributed demands, n-period delivery lag, and lost sales, how the computation of such an order quantity can be reduced to cumulative operations on a standardized (n + 1)-dimensional normal distribution.
Technical Note—On a Sequential Stopping Rule for Fixed-Sample Acceptance Tests
Authors: Schafer R. E.
Published: November 2008

Brown and Rutemiller have given a procedure for deciding whether or not to continue a fixed-sample test in the face of early failures. This paper presents a method of calculating one of the key quantities of the procedure; it eliminates the need for numerical-integration techniques in many applications and can be used if tables of the binomial distribution or tables of the incomplete beta function are available.
The (S − 1, S) Inventory Model with Arbitrary Back-Ordered Demand and Constant Delivery Times
Authors: Rose Marshall
Published: November 2008

This paper derives the important measures of supply performance for an inventory model in which the replenishment policy is to reorder a unit whenever demand occurs. The performance measures considered are: the expected number of back-orders; the expected resupply and stockout times; and the probability distribution for resupply times. All demands, described by an arbitrary distribution, are captured, but need not necessarily be satisfied immediately. The delivery times are assumed constant. Also considered is the problem of trade-offs between spares and the delivery time to achieve a given level of supply performance at least cost.
Ratios in Planning-Budgeting and Bounds on Resource Requirements
Authors: Halpern Jonathan
Published: November 2008

This paper formulates and solves a budgeting problem that originates from the use of ratios of two variables as performance criteria for an organization. There are two main features to the problem: the presence of two conflicting groups or subsystems that disagree on a desirable trend for the ratio over a planning horizon, and a lag factor, which means that if one group is in a relatively unfavorable position in a given period, then an extra weight is given to its demands, with respect to changes in the ratio, in the next period. The lag factor takes the form of constraints in the model. The two conflicting objectives in the system are translated into minimization and maximization of a real-valued function. The solution produces lower and upper bonds for the value of a decision variable; an actual budget allocation has to be within these bounds. An application of the model to the use of student-to-library-seat ratios is presented.
A Minimax Facility-Configuration Problem Involving Lattice Points
Authors: Francis Richard L.
Published: November 2008

This paper considers the problem of assigning n facilities, or departments, to locations so that the maximum of the rectilinear distances between departments is minimized. The locations are considered to be points in a lattice. It develops a simple explicit expression for the minimum value of the objective function for all values of n; this expression has as a corollary a necessary and sufficient condition for an assignment, or a configuration, to be minimax; the paper also develops a simple geometrical procedure for constructing minimax configurations. Some related problems are also examined briefly.
An Algorithm for Globally-Optimal Nonlinear-Cost Multidimensional Flows in Networks and Some Special Applications
Authors: Korsak Andrew
Published: November 2008

This paper describes an algorithm that finds globally optimum flows in networks having nonlinear costs of arc flows, the flows being finite-dimensional vectors such as multicommodity flows. The algorithm is an extension of an idea of Allsop [Trans. Sci. 2, 1–13 (1968)] for minimizing total delays in a traffic network; it is also intimately related to results in nonserial dynamic programming.
Solution Sets of Convex Programs Related to Chemical Equilibrium Problems
Authors: Kortanek K. O. , Rom W. O. , Soyster A. L.
Published: November 2008

We consider the program (I) infF(x), subject to x ∈ H and Ax = b, where H is any convex set in the positive orthant, A is any m × n matrix, b is any m-vector, and F is convex and continuous on H. A subsidiary program is used to study the nature of the constraint set and optimal solution set of program (I). The method used involves classifying duality states of the program with respect to duality states of its subsidiary program. Extensions are thereby obtained of Bigelow-DeHaven-Shapiro results [SIAM J. Appl. Math. 18, 768–775 (1970)] on the set of solutions to chemical equilibrium problems. An example of Bigelow and Shapiro is given illustrating the states by means of a simple, ideal, one-phase chemical-equilibrium problem in two dimensions.
An Algorithm for Determining Irrelevant Constraints and all Vertices in Systems of Linear Inequalities
Authors: Mattheiss T. H.
Published: November 2008

This paper describes a new method of generating all vertices of a given convex polytope. Additionally, irrelevant constraints are easily identified without the necessity of enumerating any of the vertices of the given convex polytope. The method embeds the given polytope in a one-higher-dimensional space. The projection of the additional vertices formed by the embedding process into the original space lie in the interior of the polytope and have a tree structure for one and two polytopes. For higher dimensions, the embedding process associates a number with each interior point that facilitates the construction of a spanning tree for all of the interior points. The interior points added can be efficiently generated by a variant of the simplex method. The vertices of the original polytope can be generated easily from these internal points by analyzing the appropriate simplex tableaux.
Location Theory, Dominance, and Convexity
Authors: Wendell Richard E. , Hurter Arthur P.
Published: November 2008

This paper explores the nature of optimal solutions to a plant-location problem on a plane under general distance measures. It develops conditions that guarantee an optimal location of a facility to lie in the convex hull of source and destination points. The effect of restricting the solution to some predetermined set is explored. The development is based on a generalization of Kuhn's characterization of a convex hull by dominance. When a “Manhattan” norm is employed, it is shown to be sufficient to consider, as optimal locations, the finite number of “intersection points” in the convex hull.
Technical Note—Equivalent Mixed Integer Programming Problems
Authors: Bradley Gordon H.
Published: November 2008

Every mixed integer programming problem is shown to be equivalent to an infinite number of other mixed integer programming problems. The optimal solution to any problem in a class determines the optimal solution to every other problem in the class. Canonical problems existing in every equivalence class may be solved in lieu of the original problem. For problems with rational data, the mixed Hermite canonical problem is introduced. A numerical example is included.
Technical Note—Rationalizing Discrete Programs
Authors: Gould F. J. , Rubin D. S.
Published: November 2008

In this paper we show that a bounded integer programming problem, with real data, can be replaced with another problem of the same dimension, with rational data, in such a way that the feasible solutions and optimal feasible solutions to the new problem are identical with those to the original problem.
Technical Note—Bounding Nonconvex Programs by Conjugates
Authors: Greenberg Harvey J.
Published: November 2008

We point out that the Lagrangian dual conjugation in response space provides a stronger bound and requires less computation than conjugate convexification in decision space. A homotopy is then described to lend economic interpretation in the presence of gaps.
Technical Note—The Continuity of the Perturbation Function of a Convex Program
Authors: Hogan William W.
Published: November 2008

The perturbation function of a convex program is not necessarily continuous on its domain of finiteness. However, further restrictions on the constraints will guarantee a continuous perturbation function.
Technical Note—On a Duality Theorem for a Nonlinear Programming Problem
Authors: Mond Bertram
Published: November 2008

Duality theorems were given recently for a mathematical program with a nonlinear nondifferentiable objective function. Here we point out that the converse dual theorem holds without the usually stated restrictions and assumptions.
Technical Note—A Note on Reinverting the Dantzig-Wolfe Type Decomposed LP Basis
Authors: Reich William J.
Published: November 2008

This note reports an efficient routine that has been developed and successfully applied to the reinversion of decomposed LP bases of the Dantzig-Wolfe type. In sum, if r is the total number of subproblems in the original LP problem and k is the number of subproblem vectors in the decomposed basis, then only k − r Gauss-Jordan iterations are needed to invert the decomposed basis. The larger r, the more efficient and accurate the routine. This reduction in the number of Gauss-Jordan iterations is accomplished by finding the inverse of the wrong basis rapidly, and then making the necessary corrections to get the inverse of the right basis.
Technical Note—Risk Aversion in Stochastic Programming with Recourse
Authors: Rutenberg David P.
Published: November 2008

In stochastic programming with recourse the objective is to maximize the expected net payoff. This assumes implicitly no aversion to risk. With risk aversion, the objective becomes to maximize the expected (concave) utility of the net payoffs. Because of the special structure of the problem with risk aversion, a number of computational short cuts are possible in the mathematical program that results. All the second-stage problems can be solved as linear programs. Unfortunately, whether with or without risk aversion, it is necessary to solve the first-stage problem as a nonlinear program. This note shows that the latest representation of the gradient is but a simple modification of the latest representation of the linear objective function without risk aversion.
Technical Note—Explicit Solutions of Interval Linear Programs
Authors: Zlobec S. , Ben-Israel A.
Published: November 2008

This note gives conditions for an explicit (noniterative) representation of the set of optimal solutions of interval programming problems: maximize {(c, x): a ≦ Ax ≦ b} and standard programming problems: maximize {(c, x): Ax = b, 0 ≦ x ≦ u}.
An Algorithm for Integer Linear Programming: A Combined Algebraic and Enumeration Approach
Authors: Bradley Gordon H. , Wahi Pran N.
Published: November 2008

This paper develops an algorithm for pure integer programming problems. It first transforms the integer programming problem to an algebraically equivalent Hermite canonical problem, and then employs the Fourier-Motzkin elimination. These algebraic operations transform the problem into a form that leads to an efficient implicit enumeration scheme to calculate an optimal solution. The algorithm constructs, in a finite number of operations, an optimal solution to an integer program with n variables and n or n + 1 inequality constraints. If the original problem has more than n + 1 constraints, then the integer program with only the constraints that are binding at an optimal linear programming solution is solved in place of the original problem. Computational results are presented.
Computed School Assignments in a Large District
Authors: Franklin Allen D. , Koenigsberg Ernest
Published: November 2008

The US Supreme Court decisions of 1954 on de jure segregation of schools, and recent decisions denying de facto segregation and barring “freedom-of-choice” pupil assignment, have forced school districts to devise plans for integrating public schools. Finding a feasible method of achieving racially balanced schools is difficult at best. A great number of factors must be taken into consideration. Recently, we have applied three linear programming models to a large school district (45 elementary schools, 20,000 students); they demonstrate the extent to which desegregation can be attained at moderate cost. The problems discussed in this paper include the collection and organization of data, and the problem formulation modifications necessary to conform to computer programs and storage limits. Some resulting assignment patterns are shown. Objective functions and reasonable constraints are suggested, but these can be modified. More important than the solution of a single problem is the fact that each solution represents a policy or point of view. School authorities, judges, and the public can see the logical implications of each point of view and select school assignment plans on a rational basis.
An Empirical Investigation of Optimum-Seeking in the Computer Simulation Situation
Authors: Smith Dennis E.
Published: November 2008

When computer simulation is being used to investigate a problem, any attempt at obtaining an optimum solution usually involves a search of the relevant factor space. Because a number of search techniques are available, it is desirable to have some criteria for selecting the technique to be used in a specific simulation situation. However, no mathematical basis exists for an evaluation of these techniques relative to characteristics that may vary from simulation to simulation. Thus, it is necessary to perform empirical studies in order to obtain the required information. This paper discusses the framework and results of an empirical evaluation of the performance of some search techniques. It was based on applying the techniques to various multidimensional situations that were constructed so that the true optimum was known, providing comparison of the performance of each technique with the true optimum, as well as with the performance of other techniques. Each of the search techniques was evaluated for a variety of simulation characteristics in the situation where the available number of computer runs was relatively small compared with the number of factors being examined.
Processor Utilization in Multiprogramming Systems via Diffusion Approximations
Authors: Gaver Donald P. , Shedler Gerald S.
Published: November 2008

Cyclic queuing systems have been proposed by several authors in the study of the behavior of multiprogrammed computer systems. Programs in the system wait for service at the central processor unit (CPU); then, after page fault or input-output request at a data transmission unit (DTU), the process repeats until the program completes. Semi-Markov analysis of such systems, based on the apparently plausible assumption of independently but exponentially distributed CPU burst time, and independent, but nearly constant DTU tune may be conducted. This paper presents some very simple approximations based on a continuous-state approximation—the simple diffusion with two reflecting barriers—to describe the CPU utilization. Computational experience from which the quality of the approximations can be assessed is reported.
Optimal Defensive Missile Allocation: A Discrete Min-Max Problem
Authors: Soland Richard M.
Published: November 2008

This paper considers the problem of choosing the discrete antiballistic missile (ABM) defense levels of reliable subtractive area and point defenses protecting a set of targets so as to minimize the total damage done to the targets by on optimal attack by a given number of reliable offensive missiles of one type. It assumes that the offensive side knows the ABM defense levels chosen and that the defensive side knows the number of missiles possessed by the offensive side. The cost of the defensive allocation chosen must not exceed a stated budget level; the cost function need not be continuous or separable. The 0-1 implicit enumeration scheme of Lawler and Bell is combined with a branch-and-bound procedure to effect a solution.
Distribution-Free Analysis of M/G/1 and G/M/1 Queues
Authors: Greenberg Irwin
Published: November 2008

The substantial gap between the state of the art of queuing theory and its application to real-world problems has been commented on by several authors: existing queuing models are either too specialized to be applied to a general problem or too generalized (usually in terms of Laplace transforms and/or generating functions) to be applied to a specific problem. This paper bridges this gap by constructing queuing models without making assumptions about the interarrival or service-time distributions. It obtains results for the M/G/1 and G/M/1 queues, where the “G” distributions are constructed from the observations on the queue.
Technical Note—Economic Packaging Frequency for Items Jointly Replenished
Authors: Goyal S. K.
Published: November 2008

The model described in this note is typically applicable to the batch-processing industry, where a batch of a product is packaged into more than one container types immediately after its manufacture. When a product is packaged in this way, the items (each represents a particular type or size of container) are said to be jointly replenished. A problem involving five jointly replenishable items has been solved to illustrate the recommended approach.
Technical Note—A Note on Lipstein's Model of Consumer Behavior
Authors: Dent Warren
Published: November 2008

This note gives a least-squares approach for estimating the constant causative matrix that determines a sequence of transition-probability or predisposition matrices. The method is extremely simple computationally with estimates satisfying all a priori restrictions. An extension to higher order models is discussed.
Errata
Authors: Barkan Joel D. , Bruno James E.
Published: November 2008

Correction of two errors in authors' paper “Operations Research in Planning Political Campaign Strategies,” Opns. Res. 20, 925–941.
A Three-Stage Manpower Planning and Scheduling Model—A Service-Sector Example
Authors: Abernathy William J. , Baloff Nicholas , Hershey John C. , Wandel Sten
Published: November 2008

This paper presents a staff planning and scheduling model that has specific application in the nurse-staffing process in acute hospitals, and more general application in many other service organizations in which demand and production characteristics are similar. The aggregate planning models that have been developed for goods-producing organizations are not appropriate for these types of service organizations. In this paper the process for staffing services is divided into three decision levels: (a) policy decisions, including the operating procedures for service centers and for the staff-control process itself; (b) staff planning, including hiring, discharge, training, and reallocation decisions; and (c) short-term scheduling of available staff within the constraints determined by the two previous levels. These three planning “levels” are used as decomposition stages in developing a general staffing model. The paper formulates the planning and scheduling stages as a stochastic programming problem, suggests an iterative solution procedure using random loss functions, and develops a noniterative solution procedure for a chance-constrained formulation that considers alternative operating procedures and service criteria, and permits including statistically dependent demands. The discussion includes an example application of the model and illustrations of its potential uses in the nurse-staffing process.
An Artificial-Variable Elimination Method for Solving Block-Diagonal Programming Problems
Authors: Knowles Thomas W.
Published: November 2008

The algorithms of this paper solve problems of the “decomposition” structure. It presents the basic framework for a class of algorithms, along with two possible versions. The basic algorithm generates a sequence of solutions that satisfy complementary slackness with a sequence of dual feasible solutions such that, when the linking constraints are satisfied, an optimum is obtained. Computational experience is reported for the first version in comparison with RSMFOR, a simplex program, on randomly generated problems and a three-period refinery model. Using the number of nonzero multiplications as the basis for comparison, the results show the first version substantially better than the simplex method. The computational experience is discussed at some length.
Letter to the Editor—Validating Claims for Algorithms Proposed for Publication
Authors: Ignizio James P.
Published: November 2008

This letter calls attention to the problems of validating the claims made for algorithms in published papers, and proposes a system for review that will validate such claims thoroughly before publication.
Theory of Measures of Effectiveness for General-Purpose Military Forces: Part II. Lagrange Dynamic Programming in Time-Sequential Combat Games
Authors: Pugh George E.
Published: November 2008

This paper develops a method for converting the overall objectives of a military campaign into specific time-dependent objectives, suitable for guiding strategic decisions during the evolution of the campaign. In a mathematical sense, the paper deals with time-sequential two-person zero-sum games, in which the feasible strategies in any period depend on the resources left by strategy choices in previous time periods. The technique produces time-dependent shadow values for the various types of combat forces. While these shadow values derive ultimately from the national values at stake in the war, they escalate exponentially as we move backward in time from the projected end of the war. Thus, at the start of a long war, the shadow values of military forces and equipment can completely dominate the intrinsic economic and political values, so that initial combat strategy is motivated almost exclusively by the goals of force preservation and the destruction of enemy forces. This sensitive time dependence of the values helps to explain past difficulties in assessing shadow values for general-purpose forces. However, it appears that the relative shadow values of different force types may be comparatively constant and may be quite useful.
A New Formulation of Lanchester Combat Theory
Authors: Grubbs Frank E. , Shuford John H.
Published: November 2008

Lanchester's differential equations of combat are inherently deterministic in nature, although considerable effort has been devoted in recent years to introducing stochastic treatments into the theory, for example, by dealing with transition probabilities and “variable” attrition coefficients. We advance the advantageous idea here that the time to kill or time to neutralize key opposing targets is the more logical random variable to be treated on a probabilistic basis, and hence that the fraction of remaining combatants on each side should properly be estimated from the time-to-kill probability distributions sampled—in other words, from principles of the statistical theory of reliability and life testing. The advantages of such treatment include the possibility that the the future course of a battle may be predicted from data on casualties in the early stages of an engagement, and therefore that field commanders will have available information on which to base critical decisions—for example, either to withdraw or to augment fighting forces—in order to bring about more desirable future courses of combat for a given mission. Also, commanders may even use analyses suggested herein independently of information on enemy losses to decide whether the course of combat is proceeding satisfactorily or according to plan by comparing data on early casualties observed in an engagement with standards that have been determined from experience or specified in advance. Another advantage of the suggested method is that available Weibull theory leads to placing confidence bounds on the fractions of survivors for any specified mission times. The degree of confidence on final predictions depends, as would be expected, on the number of targets put out of action in an engagement or simulation, the nature of the time to kill distributions encountered or sampled, the degree of accuracy or confidence desired, and the number of runs or the size of the war game. The new formulation is illustrated with a small-scale, but informative, example on a hypothesized engagement between chief battle tanks (CBT's) that fire missiles and R10 tanks with gun armament.
Serial Correlation in a Simple Dam Processs
Authors: Blomqvist Nils
Published: November 2008

This paper deals with a dam model similar to one due to P. A. P. Moran. It assumes that both the inflow and release of water are exponentially distributed random variables and studies the dam during its steady state. It derives the serial correlation in the sequence of water levels and compares it with previous results for a corresponding queuing system. Since knowledge of the serial correlation is essential in designing simulation experiments, the paper suggests that similar investigations be performed on other systems of standard type.
State Probabilities of M/M/1 Priority Queues
Authors: Marks Barry I.
Published: November 2008

This paper considers a preemptive priority and a nonpreemptive priority queuing model in the steady state. Each model assumes two priority levels, a single-service channel, no queue-length limit, and negative exponential interarrival-time and service-time distributions. The paper develops a set of computationally efficient recursion formulas that allow exact calculation of the state probabilities. In the nonpreemptive-priority case, this is the first time that a complete solution for the equilibrium-state probabilities has been obtained.
Some Programming Problems in Population Projection
Authors: Nakamura Masao
Published: November 2008

This paper, which concerns a population model relating the birth rate to a stable age distribution and a stable rate of population growth, gives a nonlinear programming formulation based on this model that allows us to determine (1) the birth rate minimizing the sum of the costs due to changing the current birth rates and the costs of social goods and services associated with the resulting age distribution, and (2) the birth rate achieving a desired age distribution and population growth rate while minimizing the cost due to birth control.
Scheduling the 41st-ORSA-Meeting Sessions: The Visiting-Fireman Problem, II
Authors: Arnold Larry R. , Beckwith Richard E. , Jones Carl M.
Published: November 2008

The invited-paper program of the New Orleans ORSA meeting was organized so as to minimize the conflict among coscheduled sessions. A survey of a random sample of ORSA members was conducted; the respondents ranking their top session choices from a preliminary program. The results were processed into a weighted session-conflict matrix, with an optional override to reflect session chairmen's scheduling restrictions and multiple-presentation author constraints. The minimum-conflict schedule was produced heuristically by a combination of random schedule generation and discrete optimization.
Economic Models and Planning Outdoor Recreation
Authors: Cicchetti Charles J. , Fisher Anthony C. , Smith V. Kerry
Published: November 2008

The growth in outdoor recreation activity over the past decade, and the increased limitations on the supply of natural environments and facilities required as inputs to this activity, have precipitated growing concern on the part of planners and managers over the adequacy of recreational facilities. This paper reviews the major economic modeling approaches for forecasting recreation activity, and for measuring the benefits from it. These approaches are major considerations in decisions on the planning, provision, and management of recreation areas and facilities.
Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I
Authors: Fisher Marshall L.
Published: November 2008

This paper presents an algorithm for solving resource-constrained network scheduling problems, a general class of problems that includes the classical job-shop-scheduling problem. It uses Lagrange multipliers to dualize the resource constraints, forming a Lagrangian problem in which the network constraints appear explicitly, while the resource constraints appear only in the Lagrangian function. Because the network constraints do not interact among jobs, the problem of minimizing the Lagrangian decomposes into a subproblem for each job. Algorithms are presented for solving these subproblems. Minimizing the Lagrangian with fixed multiplier values yields a lower bound on the cost of an optimal solution to the scheduling problem. The paper gives procedures for adjusting the multipliers iteratively to obtain strong bounds, and it develops a branch-and-bound algorithm that uses these bounds in the solution of the scheduling problem. Computational experience with this algorithm is discussed.
The Group-Theoretic Structure in the Fixed-Charge Transportation Problem
Authors: Kennington J. L. , Unger V. E.
Published: November 2008

The multiparametric integer programming problem for the right-hand side is to minimize c′t subject to At = b(y), t ≧ 0, t = 0 (mod 1), where b(y) can be expressed in the form b(y) = b̄ + F(y), where F is a matrix of constant coefficients, and y is an integer vector parameter. The group problem associated with any integer programming problem may be viewed as a multiparametric integer programming problem. The purpose of this paper is to show that the group problem associated with the fixed-charge transportation problem can be viewed as a multiparametric integer programming problem having a totally unimodular constraint matrix.
Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming
Authors: Soyster A. L.
Published: November 2008

This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy. Instead of specifying the feasible region by a set of convex inequalities, fi(x) ≦ bi, i = 1, 2, …, m, the feasible region is defined via set containment. Here n convex activity sets {Kj, j = 1, 2, …, n} and a convex resource set K are specified and the feasible region is given by [Formula: see text] where the binary operation + refers to addition of sets. The problem is then to find x̄ ∈ X that maximizes the linear function c · x. When the resource set has a special form, this problem is solved via an auxiliary linear-programming problem and application to inexact linear programming is possible.
Strategic Management in General Electric
Authors: Springer C. H.
Published: November 2008

This paper describes how the strategic planning functions currently operate in the General Electric Company.
Nonlinear Programming: Counterexamples to Two Global Optimization Algorithms
Authors: Zwart Philip B.
Published: November 2008

This paper gives counterexamples to: (1) Ritter's algorithm for the global maximization of a quadratic subject to linear inequality constraints, and (2) Tui's algorithm for the global minimization of a concave function subject to linear inequality constraints.
Optimal Weapon Allocation with Overlapping Area Defenses
Authors: Furman Gershon G. , Greenberg Harvey J.
Published: November 2008

We present a strategy for finding an optimal allocation of weapons to maximize the expected damage of a given collection of targets. In our scenario the area defenses can overlap, and we allow more than one weapon type. We show how the generalized Lagrange-multiplier method can be used effectively by exploiting certain graph structure when maximizing the Lagrangian.
Technical Note—Stopping Rules for Sequencing Problems
Authors: Randolph Paul H. , Swinson Gary , Ellingsen Carl
Published: November 2008

Monte Carlo methods have been proposed for finding solutions to sequencing problems. One deficiency of these methods has been the absence of appropriate roles for stopping the sampling processes. This paper presents an interesting class of stopping rules that have been found useful in computational experience.
Technical Note—On an Algorithm of Ghare and Taylor
Authors: McLeavey Dennis W.
Published: November 2008

This note points out an example in which an algorithm reported by P. M. Ghare and R. E. Taylor [Opns. Res. 17, 838–847 (1969)] for determining optimum redundancy in a series system does not produce an optimal solution. It presents the Ghare-Taylor solution along with a better feasible solution, and explains the necessary corrections to the Ghare-Taylor algorithm and the cause of the difficulty with it. The note thus questions the validity of the computer times reported by Ghare and Taylor and indicates a source yielding computer times for the corrected algorithm.
Corrections to a Paper by Hershaft on Decoy Effectiveness
Authors: Robinson Stephen L.
Published: November 2008

Corrections that should be made in a paper by A. Hershaft on “The Effectiveness of Imperfect Decoys” [Opns. Res. 16, 10–17 (1968)].
The Effects of Errors in the Estimation of the Gradient on the Frank-Wolfe Algorithm, with Implications for Interactive Programming
Authors: Dyer James S.
Published: November 2008

This paper presents an investigation of the effects of errors in the estimation of the gradient of the objective function on the Frank-Wolfe nonlinear programming algorithm. The investigation was motivated by a desire to reconcile the use of interactive programming approaches to the solution of the multiple-criteria problem with utility models that allow for intransitive statements of indifference and preference. Results are provided regarding the ultimate convergence of the algorithm, and its initial convergence rate.
von Neumann-Morgenstera Utility Functions on Two Attributes
Authors: Fishburn Peter C.
Published: November 2008

Five special forms for a von Neumann-Morgenstern utility function u on a product set A×X are examined. Each expresses u as a combination of functions defined on the separate factors A and X. The five forms include the additive and multiplicative forms, u=u1+u2 and u=f1 f2, respectively, and the additive form with independent product expressed by u=u1+u2+f1f2. Necessary and sufficient preference conditions are identified for each form, along with admissible transformations on the single-argument functions.
Coordinating Aggregate and Detailed Scheduling Decisions in the One-Machine Job Shop: Part I. Theory
Authors: Gelders L. , Kleindorfer P. R.
Published: November 2008

This paper presents a formal model of the one-machine job-shop scheduling problem with variable capacity. Its primary interest focuses on the trade-off between overtime and detailed scheduling costs. The scheduling problem considered is minimizing the sum of weighted tardiness and weighted flow-time costs for a given capacity plan (i.e., a given overtime plan). The paper generalizes sequence-theory results to this case where possible, analyzes various lower-bounding structures for the problem, outlines a preliminary branch-and-bound algorithm, and illustrates several interesting features of the algorithm and bounding structures by an example. Extensions of the results to more complex environments are discussed.
Using the Set-Covering Problem to Assign Fire Companies to Fire Houses
Authors: Walker Warren
Published: November 2008

This paper gives a set-covering-problem formulation for determining locations for two types of ladder trucks used by the New York City Fire Department. It shows that the formulation can accommodate several different realistic restrictions on the solutions.
The Design of Production and Inventory Systems for Multifacility and Multiwarehouse Companies
Authors: Wagner Harvey M.
Published: November 2008

This paper presents an overall structure for the design of combined production and inventory systems. The suggested approach is a synthesis of several recent applications in large-scale manufacturing companies. The paper lists a comprehensive set of questions whose answers serve to characterize the complete systems design. A three-phase program is outlined for conducting an inventory and production systems analysis, design, and implementation project. The paper treats in some detail the component steps to be followed at each phase, the management functions that must be included in a workable design, and the usefulness of operations-research techniques in such computer-based systems.
A Discrete-Time Population-Control Model with Setup Cost
Authors: Jaquette David L.
Published: November 2008

A discrete-time stochastic model is often used to describe a natural animal, pest, or epidemic population. Control action, representing harvesting, exterminating, etc., can be taken periodically to reduce the current population level, and so modify its future growth. Dynamic programming can be used to determine optimal control policies for models where growth and control produce economically measurable benefits and/or costs. When controlling action incurs a setup charge plus a cost component linear in the amount of state reduction produced, the optimal policy is found to be characterized by a pair (sn, Sn), where reduction is made in period n to state sn if the native population is found to be above state Sn. Analogy with inventory theory is exploited in proving the result.
Fractional Programming with Homogeneous Functions
Authors: Bradley Stephen P. , Frey Sherwood C.
Published: November 2008

This paper extends the well known results for linear fractional programming to the class of programming problems involving the ratio of nonlinear functionals subject to nonlinear constraints, where the constraints are homogeneous of degree one and the functionals are homogeneous of degree one to within a constant. Two rather general auxiliary problems are developed, and the relations between the solutions of the auxiliary problems and the solutions of the original problem are codified. Applications of the results for specific problems are also presented.
Technical Note—Location Theory: A Selective Bibliography
Authors: Francis R. L. , Goldstein J. M.
Published: November 2008

This note lists 226 papers published largely during the last ten years dealing with normative approaches to solving location problems.
Technical Note—A Last Word on L = λW
Authors: Stidham Shaler
Published: November 2008

This note gives a rigorous proof of the queuing formula L = λW, using as hypotheses only that the limiting averages, λ and W, exist and are finite. The proof is related to one given in a previous paper by the author that used a discounted analogue and Tauberian theorems. The proof in the present paper, however, is direct and avoids the use of transforms. Some comments are offered on the relation between the proof and the heuristic arguments for L = λW commonly encountered in the literature.
Technical Note—The Monte Carlo Simulation of Operating-Room and Recovery-Room Usage
Authors: Kuzdrall Paul J. , Kwak N. K. , Schmitz Homer H.
Published: November 2008

This note describes a simulation with GPSS of hospital operating-room and recovery-room usage, given a variation in patient load.
Technical Note—A Two-State Markovian Correlated Combat
Authors: Jain G. C. , Nagabhushanam A.
Published: November 2008

This note considers a combat between two opposing forces where there is a correlation between two consecutive casualties. It derives the probability distributions of the numbers of survivors and the winning probabilities irrespective of the numbers of survivors.
A Generalized System of Prognosis Curves to Facilitate Utilizing the Survival-Rate Criterion
Authors: Payne E. E. , Lutz R. P.
Published: November 2008

This paper develops a method for representing prognosis data and determining victim survival rate as a function of victim category, time, and treatment. Such a determination allows the evaluation of a community's emergency care system using the criterion of patient survival rather than some secondary evaluation criterion used in the absence of prognosis data. Typical prognosis curves are developed that express the probability of death from a specific illness or injury as a function of time and care received. Finally, examples are provided that show the probabilistic relation of mortality to time under varying assumptions of treatment and victim category.
Transitive Majority Rule and the Theorem of the Alternative
Authors: Bowman V. J. , Colantoni C. S.
Published: November 2008

In this paper the theorem of the alternative is used to show the equivalence between transitive majority rule and the problem of finding positive solutions to a certain set of linear inequalities. A system of linear inequalities is derived whose possession of a strictly positive solution for every triple of alternatives is both necessary and sufficient for the transitivity of majority rule. The consequence of this is that we can consider not only restrictions on admissible individual preference patterns but also restrictions on the distribution of votes over these patterns to ensure transitivity.
Technical Note—Conditional Delays Measured in Events for the M/M/c Queue
Authors: Heyman D. P. , Segal M.
Published: November 2008

In many queuing systems the state of the system is known at each arrival epoch. Given an arrival and given the state of the system, the question of what the probability is that the new arrival will be delayed less than t units of time is often posed. For queuing systems with Poisson arrivals, negative exponential service times and various queue disciplines, this may involve considerable computation. In this paper we develop, for the M/M/c queue, recursive relations for calculating the conditional delays where t is measured in events rather than in units of time. These calculations are often simple to perform, even for some queuing models where the delay in units of time has not yet been obtained in closed form.
The Disjunctive-Facet Problem: Formulation and Solution Techniques
Authors: Glover F. , Klingman D. , Stutz J.
Published: November 2008

Many practical operations-research problems have the form in which the objective is to select an optimal production schedule, rental policy, distribution pattern, etc., from among a variety of alternatives, each of which has an associated set of constraints that must all be satisfied if a particular alternative is chosen. The disjunctive-facet problem provides a “direct” formulation for such problems, circumventing the need to resort to artifices involving the creation of discrete variables and supporting constraints to model these problems as mixed integer programs. We provide special cutting planes that are designed to take particular advantage of the disjunctive-facet problem structure. Thus, our results not only give a more compact representation of certain classes of discrete optimization problems, but provide more powerful methods for solving these problems as well.
The Elementary Redundancy-Optimization Problem: A Case Study in Probabilistic Multiple-Goal Programming
Authors: Hendrix G. G. , Stedry A. C.
Published: November 2008

This paper deals with systems (such as electronic devices and corporations) that are designed to accomplish multiple goals and whose internal structures are characterized by networks of interacting component parts. Each component of such a system is typically associated with a probability of failure, while each system goal is associated with a reward value. Failure of any network component may ultimately result in the inability to achieve one or more goals and force the forfeiture of the associated rewards. A basic problem in component-system design is to determine how the expectation of total reward may be maximized through the cost-limited acquisition of redundant (backup) components. This paper provides a formal statement of this redundancy-optimization problem and argues that the problem may not be solved easily by standard linear or integer programming techniques. It introduces an algorithm to solve this problem, proves its convergence, and presents computational results taken from a battery of test problems and an algorithm-efficiency study based on these tests.
Technical Note—Generalized Upper Bounds and Triangular Decomposition in the Simplex Method
Authors: Tomlin J. A.
Published: November 2008

This note shows how the new updating techniques for triangular factors of the basis can be modified for the generalized upper-bounding algorithm.
Modeling the Movement of Coronary Patients within a Hospital by Semi-Markov Processes
Authors: Kao Edward P. C.
Published: November 2008

This paper studies the use of a collection of semi-Markov processes (referred to as paths) to describe the movement of coronary patients within a hospital. Two earlier papers by the same author [Health Serv. Res. 7, 191–208 (1972) and IEEE Trans, on Systems, Man, and Cybernetics SMC-3, 327–336 (1973)] define the state of a patient by a specific set of care requirements dictated by his “state of health;” this paper considers a state definition based solely on the care unit in which the patient resides. This new state definition is simpler to administer, especially when patients of different diagnoses are included in the model. The paper uses field data to estimate the parameters of the underlying processes and evaluate the adequacy of using such a model. Procedures involving simple matrix operations are introduced to obtain length-of-stay and patient-day statistics in each care unit as well as in the hospital. An approach for reconstructing the original arrival distribution based on admission data is also presented with application.