bluuebunny/crossref_metadata_2025 huggingface dataset:
The Supporting Hyperplane Method for Unimodal Programming
Authors: Veinott Arthur F.
Published: November 2008

This paper proposes an algorithm for maximizing a linear (unimodal) function over a compact convex set X in n-dimensional Euclidian space. The algorithm is a variant of the cutting-plane method of Cheney and Goldstein and of Kelley. In their method one maximizes the original linear (unimodal) function over successively refined approximations to X. Each approximation is the intersection of finitely many closed half spaces containing X. Any limit point of the sequence of solutions to the approximating problems solves the original problem. The principal new feature of our method is that each successive half space is defined by a hyperplane that supports X at a boundary point (Zoutendijk's MFD method also has this property). The particular boundary point is chosen as the point where the line drawn from a fixed interior point of X to the solution (exterior to X) to the most recent approximating problem pierces the boundary of X. Our method is applicable where X is described as the set on which finitely many unimodal functions are nonnegative. The cutting-plane method is applicable only under the more restrictive assumption that the above functions are concave. Our method is formulated so as to be applicable also to unimodal integer programs.
Cyclic Queuing Systems with Restricted Length Queues
Authors: Gordon William J. , Newell Gordon F.
Published: November 2008

This paper is concerned with an analysis of the stochastic behavior of a system of tandem queuing stations in which capacity restrictions are imposed on the queue lengths. The closed, cyclic systems that we consider are shown to be stochastically equivalent to open systems in which the number of customers is a random variable. A concept of duality is introduced on the basis of the simple observation that the sequential movement of customers through the stages generates a counter-sequential motion of “holes.” The implications of the duality relation are discussed at some length. The differential-difference equations for the time-dependent stochastic structure of the system are derived, and the remainder of the paper is devoted to the solution of the equilibrium equations for several special systems. First, we analyze completely systems with only two stages. The well-known results for a finite capacity queue appear as a special case. Next, systems are considered for which the number of customers is so small that there is no possibility of blocking. Then, by a duality argument, an analysis is carried out for systems with a very large number of customers in which the blocking effect dominates. Finally, we compare two extreme systems. In the one system there is no blocking and customers may queue at each stage. The other system has unit capacity at each of the M stages so that the distribution of customers is determined solely by the effect of blocking.
Laplace's Equation and Network Flows
Authors: Hu T. C.
Published: November 2008

This paper shows that the problem of Laplace's equation can be formulated as a minimum cost network flow problem with quadratic cost. Then an algorithm for solving quadratic cost network flow problems can be modified to solve the standard Laplace's equation.
On the Selection of Unmanned Probes and Launch Vehicles for Exploration of the Solar System
Authors: Morgenthaler George W.
Published: November 2008

A model is developed for aiding in the selection of unmanned probes and launch vehicles to gather basic data on solar system phenomena. The aim is to determine optimum trade-offs, under the constraint of minimum mission objectives, among such factors as incremental mission accomplishments (kinds, quality and quantity of data), instrumentation parameters (weight, reliability, resolution accuracy, cost), trajectory parameters (trip time, energy requirement), and launch vehicle and upper stage parameters (payload weight, reliability redundancy, booster costs). Using plausible, but nonauthoritative cost and performance data, the model is applied to an example, and some tentative conclusions are drawn.
Computer Aids to Clinical Treatment Evaluation
Authors: Ledley Robert S.
Published: November 2008

The growing abundance of therapeutic alternatives can present exceedingly complex sequences of medical treatment decisions and treatment plans. Extensive and systematic clinical treatment evaluation, which necessarily involves the aid of electronic computers, is indicated in the solution to these problems. The primary purpose of this paper is to discuss precise mathematical formulations of these problems and to describe computer aids to their solution. First, the use of dynamic programming is discussed as an approach to the mathematical formulation of the diagnostic-treatment cycle. Then the use of Bayes’ formula will be discussed as an aid to the collection of treatment-evaluation data. Finally, a computer system for an outpatient clinic is described. It is important to note that although we suggest basic mathematical characterizations of these problems, each particular medical specialty, and frequently each particular treatment, requires specific adaptations of the methods in order to take care of special problems that frequently arise.
Pseudo-Concave Programming and Lagrange Regularity
Authors: Kortanek K. O. , Evans J. P.
Published: November 2008

For the mathematical programming problem max f(x) subject to G(x) ≧ 0, we show that if G(x) is pseudo-concave, a property weaker than concavity but stronger than quasi-concavity, and differentiable, then the constraint set is necessarily determined by the natural gradient (tangent) inequality system of G. We then apply the duality constructs of semi-infinite programming, in a manner which admits generalizations, to this special case to show that pseudo-concave constraint functions that have an interior point are convex Lagrange regular. Analogous to a theorem of Arrow-Hurwicz-Uzawa, we characterize functions that are both pseudo-concave and pseudo-convex, and for programming problems with objective functions of this form, we obtain equivalent problems having linear objective functions.
A General Model of a Single-Channel Queue: Discrete and Continuous Time Cases
Authors: Beusch John U.
Published: November 2008

In Part I, a single-channel service system consisting of a service facility and queue, in which the possible times of arrival of units and the possible service times are discrete, is analyzed. A method of calculating the moments of the total service time of units in the system is developed. This total service time is related to the delay caused by the system. When arrivals at different times are assumed to be independent, the “values” of the resulting Markov process can be calculated. These values lead to information about the transient behavior, autocorrelation function, expected first passage time, and expected extra delay that arises if another unit is inserted into the system. An expression for the geometric transform or moment generating function of the probability distribution of the total service time of units in the system is determined. The results are derived for arbitrary arrival and service time distributions. In Part II, the continuous time analog of the system of Part I is considered and analogous results are determined.
Letter to the Editor—Some Aspects of a Minimax Location Problem
Authors: Francis Richard L.
Published: November 2008

Some aspects of a minimax version of the Steiner-Weber location problem are studied. A necessary condition is given for a minimax location, or solution; a lower bound on the value of a minimax solution is given that is attained for many problems; and an explicit minimax solution is given for the case where the lower bound is attained. Also, a geometric characterization of the minimax solution is discussed, and a closely related facility design problem is examined.
Letter to the Editor—Stronger Cuts in Integer Programming
Authors: Glover Fred
Published: November 2008

In a recent note Robert Wilson [Opns. Res. 15, 155–156 (1867)] shows how to calculate stronger cuts than those proposed by Gomory for his all-integer algorithm. We supplement Wilson's observations by providing a basis for calculating other cuts, drawing on results of Glover [Management Sci. 13, 254–268 (1966)].
Letter to the Editor—On the Nature and Form of Operations Research
Authors: King William R.
Published: November 2008

Since operations research involves the application of scientific methods and techniques to problems of organizations, and since many practitioners in the field received their education in traditional scientific disciplines, it is to be expected that the field called ‘operations research’ would have borrowed many of the trappings and appurtenances of the physical sciences. In particular, the nature and form of the Journal, Operations Research, appear to reflect traditional scientific patterns which, I believe, are inappropriate to a fledgling ‘applied’ discipline.
Letter to the Editor—On King's Note
Authors: Machol Robert E.
Published: November 2008

Response to the note King, W. R. 1967. On the nature and form of operations research. Oper. Res. 15 1177–1180.
A Tutorial on Production Smoothing and Work Force Balancing
Authors: Silver Edward A.
Published: November 2008

At the Thirtieth National Meeting of the Operations Research Society of America a special tutorial session was held, entitled “Problems in the Analysis of Production Systems.” The present article is adapted from one of the papers presented at the session. Retaining the same nature as the tutorial session the article is concerned with the basic issues of production smoothing and work force balancing and is directed at an audience generally unfamiliar with technical approaches to the analysis of production systems. A bibliography is also included.
Effectiveness of Imperfect Decoys
Authors: Hershaft A.
Published: November 2008

Mathematical relations are developed to express the effectiveness of decoys in a situation that requires the attacker to assign his weapons on the basis of imperfect classification of the targets. The analysis considers the effects of a number of pertinent parameters, such as the number of real and decoy targets and the enemy's classification ability and missile effectiveness, and calculates the probabilities of survival of real targets. A number of hypothetical examples are given to illustrate the application of the theory to practical problems.
Letter to the Editor—Some Results for the Bulk-Arrival Infinite-Server Poisson Queue
Authors: Reynolds John F.
Published: November 2008

An infinite server queue is considered in which an arrival is actually a group (of random size) of customers. A generating function for the time-dependent queue length is obtained, and used to show that the limiting distribution is compound Poisson. It is also shown that the regression of queue length at time t on the initial length is linear, and from this an expression for the autocorrelation function is deduced.
Letter to the Editor—An Optimal Strategy for a Whereabouts Search
Authors: Tognetti Keith P.
Published: November 2008

It is required to maximize the probability of knowing the whereabouts of an object as the result of a search. Before the search the object was equally likely to be located in one of n areas. The conditional probability of detection with a single search in an area is constant. If n searches are allowed it is shown that the optimal strategy is to partition the searches so as to miss one area.
Solving the Fixed Charge Problem by Ranking the Extreme Points
Authors: Murty Katta G.
Published: November 2008

An algorithm for ranking the basic feasible solutions corresponding to a linear programming problem in increasing order of the linear objective function is described. An application of this algorithm for obtaining the minimal cost solution to a fixed charge problem is given. This algorithm can be applied in general to solve any fixed charge problem. However, the algorithm works efficiently when the problem is nondegenerate and the range in the values of the variable costs is large compared to the fixed charges. This algorithm can also be applied when the fixed charge part of the cost function is replaced by a concave function.
A Branch-Bound Solution to the General Scheduling Problem
Authors: Greenberg Harold H.
Published: November 2008

A mixed integer formulation is presented for the general n job, m machine scheduling problem. This formulation is shown to reduce to a series of noninteger L.P. problems of moderate proportions when applying the branch-bound technique. Solutions are presented for the two problems: minimize make-span and minimize idle time. An example and some computational experience for the “minimize idle time” problem are given.
The Traveling Salesman Problem: A Survey
Authors: Bellmore M. , Nemhauser G. L.
Published: November 2008

A survey and synthesis of research on the traveling salesman problem is given. We begin by defining the problem and presenting several theorems. This is followed by a general classification of the solution techniques and a detailed description of some of the proven methods. Finally a summary of computational results is given.
A Stochastic Approach to Goal Programming
Authors: Contini Bruno
Published: November 2008

This paper deals with the problem of attaining a set of targets (goals) by means of a set of instruments (subgoals) when the relation between the two groups of variables can be expressed with a linear system of stochastic equations. The objective function consists of the maximization of the probability that a realization (in terms of target variables) will lie in a confidence region of predetermined size. Under suitable normality assumptions this problem is amenable to a quadratic programming formulation.
Two Queues Attended by a Single Server
Authors: Takács Lajos
Published: November 2008

It is supposed that customers of type 1 and type 2 arrive at a service system in accordance with a Poisson process. There are two counters in the system. Customers of type 1 receive service at counter 1 and customers of type 2, at counter 2. The customers are served by a single server who attends the two counters alternately. At each counter the service times have a general distribution. This paper is concerned with the determination of the distribution of the waiting time of a customer in a stationary process.
International Operations Research Activities
Authors: Walsh John E.
Published: November 2008

This paper reports on visits to 24 national operations-research societies (two in Germany) and to operations researchers in ten other countries. It considers each visit to a society specifically, plus some of the visits in countries not having societies. My purpose was to promote closer relations between the Operations Research Society of America and operations researchers of other countries. The first visits were made during July–August of 1967, in conjunction with the Operations Research Around-the-World Meetings. Canada was visited in November, Central and South America in December–January, and the remaining countries in Europe during March–April of 1968. These visits included all of the world's major operations-research societies, and some others.
A Simplified Primal (All-Integer) Integer Programming Algorithm
Authors: Young R. D.
Published: November 2008

This paper describes a primal, all-integer algorithm for solving a bounded and solvable pure integer programming problem. The method is a primal analogue to the Gomory All-Integer Algorithm, and is a variant of the simplex method in sense that the Gomory algorithm is a variant of the dual method. The simplified primal algorithm makes these major amendments to the simplex method: (i) a special row, indexed by L, is adjoined to the tableau and is periodically revised by a well-defined procedure; (ii) in most cycles of the algorithm the pivot column, AJ, is selected so that aLJ > 0 and (1/aLJ)AJ is lexicographically smaller than (1/aLj)Aj for all nonbasic columns Aj that have aLj > 0; (iii) in all cycles of the algorithm a Gomory cut is adjoined after selection of the pivot column, and the cut is selected so that it will have a unit coefficient in the pivot column and it will qualify (in order to be used) as the pivot row. With comparatively minor restrictions on the selection of the row used to generate the Gomory cut the simplified primal algorithm is shown to be finite.
Letter to the Editor—A Note on Divisible Activities in Critical Path Analysis
Authors: Bodin Lawrence D.
Published: November 2008

In this note, the problem of divisible activities in critical path analysis is shown to be a special case of the classical cost-time project scheduling problem.
Errata
Authors: Balas Egon
Published: November 2008

Corrections to be made in the letter to the editor “A Note on the Branch and Bound Principle” by Egon Balas Operations Research, Vol. 16, 442–445, 1968.
The Waiting Time Process for a Certain Correlated Queue
Authors: Conolly B. W.
Published: November 2008

A brief description is given of a problem that arose in a nonqueuing context but that can be interpreted in queuing terms. The result is the unusual single-server system in which the length of a customer's service is determined by the length of the interarrival interval separating himself and his predecessor. The main result is the distribution of waiting time, and its moments. It is shown numerically that this pattern of server behavior results in a drastic reduction of the mean and variance of the waiting time as compared with a conventional M/M/l system.
Minimum Variance Unbiased Estimate of a Coverage Probability
Authors: Kabe D. G.
Published: November 2008

Let F(x, θ) denote the distribution function of a vector variate x, whose range does not depend on the parameter θ. Then assuming that θ admits a complete and sufficient estimator θ̂, we derive minimum variance unbiased estimate of Px ≦ a= F(a, θ), where a is a known vector. The result is applied to a coverage problem in a normal set up.
A Reliability Problem with Spares and Multiple Repair Facilities
Authors: Natarajan R.
Published: November 2008

A single unit system with (N−1) spares and c repair facilities is considered. It is assumed that the failure time distribution of each unit is negative exponential with parameter λ and repair time distribution of each repair facility is again a negative exponential with parameter μ. The Time-to-System Failure Period (TSFP) process has been investigated solving the difference-differential equation through the compensating function technique. The general process probabilities are obtained through renewal arguments from TSFP process and System Down Time (SDT) process, and their ergodic properties are discussed. The long-run availability of the system and the cost implication has been illustrated by a numerical example.
The Reliability of Dependent Parallel or Standby N-Unit Redundancies
Authors: Eiss Joseph J.
Published: November 2008

This paper is concerned with evaluating the reliability of a redundant configuration, given that at any random time its surviving components are operating with failure distributions that are dependent upon the set of failed components. An expression (9) is derived for the reliability of this class of configurations and is then generalized to obtain an expression (23) for the reliability of a similar configuration whose component failure distributions are dependent also upon the time of the last such failure. These expressions are then applied to evaluating the reliability of a stand-by configuration with off-line failures, and the reliability of a parallel configuration for which at least a certain number of components must survive in order that the configuration operate satisfactorily.
On the Optimal Cutting of Defective Sheets
Authors: Hahn Susan G.
Published: November 2008

A method is developed for cutting up sheets with defective areas into given pieces while minimizing waste. The sheets, the pieces, and the defects are all rectangles, these latter to be identified by the coordinates of two opposite corners in a coordinate system attached to the sheet. The cutting is done in in three stages. If the length of the sheet is along the x-axis, the first cuts are made parallel to the y-axis, obtaining “sections.” The sections are then cut into “strips” parallel to the x-axis, and, finally, the strips into “pieces” parallel to the y-axis. The procedure uses dynamic programming, which requires a value to be attached to each size. The computer program senses the defects and fits pieces into the clear portion of the sheet in such a way that the total value is a maximum. In order to shorten machine time, some simplifying shortcuts are made.
Delays for a LIFO Queue with Constant Service Time
Authors: Peters Paul E.
Published: November 2008

Since delay distributions obtained in simulations of a LIFO queuing system have been found to disagree with those obtained from a published analytic solution, this paper determines the source of the error in the published solution and gives a corrected solution that is obtained by using a generalization of the classical ballot theorem.
Multipartite Optimization
Authors: George Robley E.
Published: November 2008

This paper considers the problem of determining the policy to be followed by each member of a team so as to optimize some over-all criterion function characterizing the objective of the team. The reasoning of dynamic programming is employed to formulate the optimization problem, and the discussion is couched in the terms of a classical network problem. The paper first formulates a simple bipartite network optimization and then presents a number of generalizations. Finally, it gives two slightly different computational solutions to an example bipartite optimization problem.
A Media Planning Calculus
Authors: Little John D. C. , Lodish Leonard M.
Published: November 2008

A convenient on-line computer system selects and schedules advertising media. The system consists of a market-response model, a heuristic search routine, and a conversational input-output program. The user supplies a list of media options, a budget, and various objective and subjective data about the media options and the desired audience. The system selects a set of options and schedules them over time, seeking to maximize total market response.

The model of market response works as follows: The population is divided into market segments. People in each segment are characterized by their sales potential and media habits. Ads placed in the media options lead people to be exposed to the advertising. The pattern of exposures in each market segment is determined by media coverage and duplication data. People tend to forget exposures and so the retained exposure level decays in the absence of new advertising. The response of an individual, in terms of the fraction of sales potential realized by the advertiser, increases with exposure level but with diminishing returns. Total market response is a sum over people, market segments, and time periods. The calculation of response is based on analytic formulas that are computationally very efficient.

A maximum-seeking, heuristic calculation starts with any schedule, adds options with a high increment of response per dollar and deletes options with a low increment per dollar until no more improvement can be found for the given budget.

An on-line system, called mediac, permits the use of model and heuristic at a remote console of a time-shared computer. Communication with the computer is conversational and largely self-explanatory. The system is operational. Computing costs have been a fraction of a per cent of the cost of the media scheduled. Improvements over previous schedules, as calculated by the model from the user's input data, have run from 5 per cent to over 20 per cent.
Efficient Heuristic Procedures for Integer Linear Programming with an Interior
Authors: Hillier Frederick S.
Published: November 2008

This paper presents and evaluates some new heuristic procedures for seeking an approximate solution of pure integer linear programming problems having only inequality constraints. The computation time required by these methods (after obtaining the optimal noninteger solution by the simplex method) has generally been only a small fraction of that used by the simplex method for the problems tested (which have 15 to 300 original variables). Furthermore, the solution obtained by the better procedures consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these methods also are outlined. A companion paper presents an optimal “bound-and-scan” algorithm that may be used in conjunction with these approximate procedures.
A Bound-and-Scan Algorithm for Pure Integer Linear Programming with General Variables
Authors: Hillier Frederick S.
Published: November 2008

A new algorithm for solving the pure-integer linear programming problem with general integer variables is presented and evaluated. Roughly speaking, this algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. Encouraging computational experience is reported that suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems also are outlined.
The Lanchester Attrition-Rate Coefficient: Some Comments on Seth Bonder's Paper and a Suggested Alternate Method
Authors: Barfoot C. B.
Published: November 2008

This note presents some comments on Bonder's paper on the Lanchester attrition-rate coefficient, which indicate that a valid prediction of average attrition is obtained by using the harmonic mean of the variable attrition rates rather than the arithmetic mean. This change results in a constant Lanchester attrition-rate coefficient being defined as the reciprocal of the expected time to kill a target. An alternate and more general method for obtaining the constant coefficient is presented and some comparative results are displayed. An appendix indicates the conditions for which it is appropriate to use the harmonic and arithmetic means of rates in general.
Systems Analysis for Social Decisions
Authors: Bower Joseph L.
Published: November 2008

This paper examines the nature and promise of the revolutionary approach to social problems that is represented by systems analysis. It first describes social decisions and how they are usually made. Then it examines systems analysis, considers its worth for social decisions, and describes some prerequisites required for it to be useful. Finally, the paper concludes that systems analysis of social problems can contribute substantially to the intelligent allocation of society’s resources.
A New Method for Constrained Optimization Problems
Authors: Kowalik J. , Osborne M. R. , Ryan D. M.
Published: November 2008

This paper describes an algorithm, based on a recently proposed method due to D. D. Morrison, for solving constrained optimization problems, and shows that it compares favorably with existing methods in several examples.
A Probabilistic Approach to Solving Assignment Problems
Authors: Celebiler Mehmet I.
Published: November 2008

Assignment problems arise whenever elements of a finite set have to be paired with elements of another finite set in such a way as to maximize a certain function of the pairing. In this paper three different formulations of such a problem are given. They are analyzed and a method for obtaining a low-cost solution is developed.
A Case History in Optimum Inventory Scheduling
Authors: Schussel George , Price Steve
Published: November 2008

This paper describes four computer programs that perform what were formerly management-decision functions in inventory scheduling. The first program solves the classical EOQ problem (uniform inventory usage) with quantity discounts. The second program, Economic Requirement Batching (ERB), uses dynamic programming, a heuristic search algorithm, and the relation between shipment size and material cost to locate the optimum delivery schedule for any deterministic schedule of discrete (irregular) requirements. The third program, the Alternative Delivery Schedule Evaluator (ADSE), compares any alternative delivery schedules that meet requirements, it calculates all costs associated with inventory and displays both the optimum alternative and the opportunity losses incurred by inferior alternatives. The fourth program, the Alternative Delivery Schedule Generator (ADSG), solves the difficult problem of optimally scheduling inventory in those cases requiring vendor production to special specifications and, accordingly, where the exact price of the item is unknown and depends on the manner in which it is produced. This situation is differentiated from ERB because ERB analyzes standard vendor shelf items that can be delivered according to any schedule. With little input data, ADSG generates a few highly efficient alternative delivery schedules upon which the vendor quotes. The returned bids are then evaluated by ADSE, which determines the optimum delivery schedule. Since over three years have elapsed between when this work was done and the publication of this article, it concludes with a view of the program's successes and failures and some relevant empirically observed relations.
On Some Mixing Sequences in Queuing Theory
Authors: Heyde C. C.
Published: November 2008

Mixing sequences of random variables have the remarkable property that their ordinary limit behavior is preserved under a general kind of conditioning. This note shows that the mixing property holds for some well-known limit results in queuing theory.
A Multiserver System with Preemptive Priorities
Authors: Segal M.
Published: November 2008

This paper considers a multiserver system with preemptive priorities and derives recurrence relations for the moments of the lifetime distribution.
Algorithms for Targeting Strikes in a Lines-of-Communication Network
Authors: Wollmer Richard D.
Published: November 2008

This paper presents two algorithms for targeting strikes in a lines-of-communication (LOC) network. The LOCs are represented by a network of nodes and directed arcs. It is assumed that the user of the LOCs is attempting to achieve a circulation flow at minimum cost, a very general goal that includes, as special cases, maximizing flow between two points, meeting required flows between two points at minimum cost, and combinations of these two. The algorithms presented here attempt to make such costs as large as possible over time when the effect of targeting strikes is to increase arc-cost functions and decrease arc capacities for a given period of time. The first algorithm treats the situation where arc costs are linear functions of flow; the second treats the situation where arc costs are piecewise linear functions of flow with one break point.
Parametric Priority Rules: An Approach to Optimization in Priority Queues
Authors: Balachandran K. R.
Published: November 2008

This paper analyzes priority rules that are mixtures of preemption and postponable rules. Whether a preemption occurs is made to depend on some factor in addition to priority class; dependence on the completed portion of service (age) of the lower-priority customer in service and the number of prior preemptions of the lower-priority customer in service are each considered. The stochastic model (without priorities) is that of the M/G/1 queue. The paper obtains first-moment expressions (e.g., expected number of customers in the system) in the steady-state case for each priority class as a function of the particular factor being considered. It then introduces a linear cost model that is a function of expected waiting time and expected number of preemptions, and formulates the problem of finding an optimal rule from each class by considering a parametric class of rules determined by each factor. In each case, conditions are sought for the global optimality of a rule over a class of rules, but results are obtained only after restrictions (e.g., monotone failure rates) on service distributions are imposed.
Letter to the Editor—Optimum Distribution of Armor
Authors: Rustagi J. S. , Doub T. W.
Published: November 2008

Minimizing the probability of a kill given a hit has been utilized as a criterion for armor distribution on weapons such as tanks, a procedure that reduces to the well-known technique of dynamic programming, which is specially useful in this situation, since the design data involved are available only in numerical form.
A Statistical Method for Setting Stops in Stock Trading
Authors: Barnes Robert M.
Published: November 2008

This paper applies the exponential distribution to stock price reactions to determine, at three confidence levels, the critical percentage price reaction beyond which a reaction constitutes a strong likelihood of a major reversal or halt in the stock's present general price trend. We show that these critical values can be used to determine stop losses, so that a trader's position is closed when the probability of a major reversal or halt against his position is large, and an open position is kept open when the probability that the reaction is a major one is small or moderate. The distribution fit on ten stocks on daily and weekly bases for over a year's duration each, tested using the chi-squared statistic, was found to be good. Further, three stops, corresponding to three confidence levels of the distribution were tested for each stock against a subsequent six-month period of price action. The percentage of successful tests of these stops for each of the stocks corresponded very closely to expected results ascertained by using data from the previous period.
A Black Ghetto's Research on a University
Authors: Ackoff Russell L.
Published: November 2008

This paper is based on an address to the Philadelphia Section of the Society given on June 5, 1970.
A Health-Status Index and its Application to Health-Services Outcomes
Authors: Fanshel S. , Bush J. W.
Published: November 2008

In order to develop an operational definition of health, we found it necessary first to develop the concept of function/dysfunction as a continuum, based on one's ability to carry on the usual daily activities appropriate to social roles. Then, to those operating the health system, each member of the population can be seen as belonging to one and only one state from a class of functional states that can be defined on an ordinal scale. Next, we found it necessary to assign to each state a weight defined on a cardinal scale, the set of weights for these states being called the Health Status Index (HSI). The HSI rests on value judgments, of a societal nature, expressed by the administrators responsible for policy decisions. Prognosis is then defined as the transitional probability of a change in functional state with time. Thus, the concepts “state of health” and “severity of illness” are decomposed into the parameters function/dysfunction and prognosis. Finally, together with an operational definition of time and target population, it becomes possible to give a quantitative definition of the output of a health program (or health system) as the changes in the functional history of the target population resulting from the intervention of the health program (or system). Other concepts that are given quantitative definitions are program effectiveness and population health status. This study next explores the relation between health program output and modern decision theory for program planning, and shows how these analytical tools are useful for fitting the results of the study into larger conceptual frameworks. Finally, the method developed is illustrated, first with a simplified simulated program for computer use, and then with an analysis of a small section of a tuberculosis-control program.
Letter to the Editor—A Comment on the Morse-Elston Model of Probabilistic Obsolescence
Authors: Kraft Donald H.
Published: November 2008

Morse and Elston have constructed a probabilistic model of obsolescence and fitted it to the circulation of books in a library. This note presents a modification of their model and fits it to their results to account for time dependence of their original parameter α. This revised model can be used to describe the phenomena of obsolescence as seen in such a case as the usage over time of books concerned with scientific subjects.
An Optimal Rejection Time for an M/G/1 Queuing System
Authors: Mine Hisashi , Ohno Katsuhisa
Published: November 2008

This paper discusses the following model: (i) Arriving customers are accepted in the system in a time interval [t0, t′] and are rejected with compensation after time t′; (ii) the server runs at the cost rate r0 in a time interval [t0, T], t0 ≦ t′ ≦ T, and runs at the increased cost rate r1(r1 > r0) after the closing time T, until the system becomes empty after time t′. The time t′ is called the rejection time. The paper finds the optimal rejection time, that is, the rejection time that minimizes the expected total cost. It can be shown that in certain cases the optimal rejection time can be determined by a nonlinear equation. Numerical examples are given for an M/M/1 queuing system, and the more generalized model is briefly discussed.
Technical Note—A Taxonomy for Operations Research
Authors: Fenske Russell W.
Published: November 2008

Early in 1968 the ORSA Publications Committee decided to develop a comprehensive index of the 829 articles published in the first fifteen years of Operations Research, covering the pioneering period from 1952 through 1967. The Committee accepted a proposal made by the author at the University of Wisconsin-Milwaukee to develop chronological, subject, and author indexes, and the result was published as Operations Research: 15 Year Index, Volumes 1–15, 1952–1967, Operations Research Society of America, Baltimore, Maryland, 1970. The major part of this task turned out to be the development of detailed subject classifications to cover every article published. The resulting taxonomy has much broader application than just as an indexing tool, and for this reason the author has felt that the readers of the Journal could benefit from a discussion of it.
Generalized Lagrange Multipliers in Integer Programming
Authors: Shapiro Jeremy F.
Published: November 2008

This paper combines the theory of generalized Lagrange multipliers with a reformulation of the integer-programming problem due to group theory. The use of multipliers enhances the algorithmic efficiency of group theory in a variety of ways. One particular application is the approximation of generalized Lagrange multipliers by generalized linear programming as suggested by Brooks and Geoffrion. This procedure is shown to be closely related to the cutting-plane method of Gomory.
Optimality Criteria in Nonlinear Programming Without Differentiability
Authors: Bazaraa M. S. , Goode J. J. , Shetty C. M.
Published: November 2008

This paper discusses stationary-point optimality conditions for inequality-constrained nonlinear programming problems where the functions involved are continuous but not necessarily differentiable. We obtain generalizations of the well known Fritz John and Kuhn-Tucker necessary conditions. We also discuss the sufficient conditions for optimality where the usual convexity assumption is replaced by a weaker assumption of “supportability.”
Robbery and Assault of Bus Drivers
Authors: Gray Paul
Published: November 2008

Robbery and assault of bus drivers in the United States increased by a factor of five between 1963 and 1968. A detailed study was, therefore, conducted to evaluate potential methods and techniques of reducing the incidence of this crime. This paper discusses the criteria used and the analysis of three of the countermeasures: exact fare, alarms, and photography.
Divisible and Movable Activities in Critical-Path Analysis
Authors: Jewell William S.
Published: November 2008

Certain jobs in large projects do not have a unique “location” in the critical-path network; they may be moved into certain slack intervals, for example, or may even be divisible into smaller subtasks, and ‘tucked in’ at several locations. A previous paper gave an analysis of a model in which a single job can be divided up in any manner among an arbitrary number of locations; the resulting algorithm was of the optimal-network-flow type, which can be simply and efficiently solved using available computer codes. The first part of the present paper extends this model to multiple jobs of divisible type. The general approach is via the decomposition method of linear programming; however, the resulting algorithm is again fairly simple. Optimal cost-time solutions, possibly infinite (or optimal network flow solutions, possibly infeasible) are generated by known algorithms. The resulting schedules or cuts are then combined in a simple, special-structure linear program whose dimensionality is equal to the number of divisible groups. Bounds on the nonintegrality of the final allocations can also be determined. When these special jobs can only be moved about the network in their entirety, or in certain indivisible modules, the probblem takes on the form of an integer program. The second part of the paper gives a branch-and-bound procedure for the problem of movable activities, together with efficient heuristics for arbitrating and bounding these locations, using only the ordinary critical-path algorithm. Examples are given for both models.
On Optimal Balking Rules and Toll Charges in the GI/M/1 Queuing Process
Authors: Yechiali Uri
Published: November 2008

This paper considers a GI/M/1 queuing process with an associated linear cost-reward structure and stationary balking process, and, based on a probabilistic analysis of the system, it derives optimal joining rules for an individual arrival, as well as for the entire community of customers. For the infinite-horizon, average-reward criterion, it shows that, among all stationary policies, the optimal strategies are control-limit rules of the form: join if and only if the queue size is not greater than some specific number. However, it finds that, in general, exercising self-optimization does not optimize public good. Accordingly, the paper explores the idea of controlling the queue size by levying tolls—thus achieving the system's over-all-optimal economic performance. Finally, it analyzes a “competition” model in which customers face a service agency that is a profit-making organization, and shows it to be similar to the monopoly model of price theory.
Two Queues with Changeover Times
Authors: Eisenberg Martin
Published: November 2008

A single server attends to two separate queues. Each queue has Poisson arrivals and a general service time distribution. A changeover time, with a general distribution, is required whenever the server crosses from one queue to the other. This paper investigates two queue disciplines: alternating priority and strict priority. In each case, it obtains the Laplace-Stieltjes transforms of the waiting-time distributions for a stationary process, as well as the first moments of the waiting-time distributions.
Technical Note—Optimization of the Capacity in a Storage System
Authors: Loo S. G. , Ghosal A.
Published: November 2008

This paper presents the problem of determining the optimal capacity of a storage system with respect to some specified criteria. It assumes that the storage system is subject to an input X and a release Y, at least one of which is a random variable following a known distribution function, so that the storage function Z is a stochastic process. The optimal capacity over a time horizon (0, T) is determined by maximizing the expected profit.
Technical Note—An Integer Maximization Problem
Authors: Schwartz Richard E. , Dym Clive L.
Published: November 2008

This note solves the following problem: For vi > 0 and 0 < d < 1, maximize V(m1, …, mn) = ∑i=1i=nvi(1 − dmi) with respect to (m1, …, mn), subject to the conditions that the mi are nonnegative integers and ∑i=1i=nmi = M (an integer). The solution is obtained by a simple rounding procedure applied to the (well known) solution of the corresponding continuous problem.
Expected Target Damage for Pattern Firing
Authors: Bressel Charles N.
Published: November 2008

This paper evaluates analytically the damage function for a rectangular target from a firing pattern of n rounds by extending to a pattern distribution the method of Grubbs [Opns. Res. 16, 1021–1026 (1968)] for a salvo of rounds. The delivery function for the pattern center and the dispersion of each round are taken to be noncircular normal, and the damage function law for each round is defined to be a noncircular exponential square falloff. The results are computationally somewhat more complex than for a salvo, since one must keep track of the coordinates of each round in computing the average chance that a round of the pattern (i.e., a pattern element) will damage a given target element. A series expansion for the fractional target damage by a pattern is obtained.
Accommodating Student Demand for Courses by Varying the Classroom-Size Mix
Authors: Smith R. Longworth
Published: November 2008

This paper constructs a statistical model that measures the ability of a given mix of classroom sizes to accommodate student demand for courses. Assuming known demand distributions, the model computes the probability that a course-to-classroom assignment can be made in such a way that the number of students assigned to any classroom does not exceed the number of seats in that classroom.
Optimal Whereabouts Search
Authors: Kadane Joseph B.
Published: November 2008

An optimal whereabouts search maximizes the probability of correctly stating, at the end of a search costing no more than some budget C, which box contains the object. This can be accomplished either by finding the object in the search or by guessing, at the end of an unsuccessful search, which box contains the object. Generalizing work of Tognetti, this paper shows that an optimal whereabouts search never searches the box to be guessed, and gives an algorithm for finding an optimal whereabouts-search strategy. Finally, whereabouts search is compared to a similar problem proposed by Bellman.
Optimum Network Partitioning
Authors: Jensen Paul A.
Published: November 2008

The problem of finding the optimum partition of a set of objects into disjoint collectively exhaustive subsets has been treated by several authors as a special set-covering problem. This paper considers this problem when the objects can be represented as nodes in a directed acyclical network and the subsets of the partition define subnetworks of the original network. A dynamic-programming algorithm is presented that solves the latter problem. This algorithm is, in some important cases, more efficient than the implicit-enumeration schemes that have been previously proposed for the more general set-partitioning problem.
A Sequential Stopping Rule for Fixed-Sample Acceptance Tests
Authors: Brown Gerald G. , Rutemiller Herbert C.
Published: November 2008

The occurrence of early failures in a fixed-sample acceptance test, where the sample observations are obtained sequentially, presents an interesting decision problem. It may be desirable to abandon the test at an early stage if the conditional probability of passing is small and the testing cost is high. This paper presents a stopping rule based on the maximum-likelihood estimate of total costs involved in the decision to continue beyond an early failure. A Bernoulli model, an exponential model, and a Weibull model are examined.
Letter to the Editor—Implementation of New Ideas in Bureaucracies
Authors: Deitchman S. J.
Published: November 2008

This note speculates that, in a large bureaucracy, the probability of implementing new ideas depends on the number of persons in the chain leading to the implementation. Some possible organizational consequences are mentioned.
Letter to the Editor—Application of Kuhn's Hungarian Assignment Algorithm to Posting Servicemen
Authors: Ewashko T. A. , Dudding R. C.
Published: November 2008

This communication describes the use of Kuhn's Hungarian assignment algorithm for deriving postings for servicemen. Test computer runs give favorable results.