bluuebunny/crossref_metadata_2025 huggingface dataset:
Trends in Operations Research
Authors: Morse Philip M.
Published: November 2008

The field of operations research has been rapidly growing this past year. The Operations Research Society of America has been founded and now has about 500 members. More and more large companies—aircraft and electrical manufacturers, railroads and oil companies, insurance companies and department stores—are forming their own operations-research groups or are buying consulting services in operations research. It will not be long before more positions will be open in industrial than in military operations research. We should no longer have trouble explaining the scope and methods of operations research to the layman. We already can say: Operations research is the activity carried on by members of the Operations Research Society; its methods are those reported in our Journal. Very soon this definition will be more instructive and convincing than any number of special explanatory articles and talks.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Operational Research as a Science
Authors: Goodeve Charles
Published: November 2008

We hear a lot these days about a type of research in which the objects studied, instead of being either materials or machines or people, are the activities of all these together—research into “operations.” To many, operational research conjures up a vision of a busy executive seated at his desk faced with the almost unending problem of making decisions. Everything depends on the speed and correctness with which he makes these decisions, and these in turn depend on the way the facts and factors are presented to him and on his judgment or his ability to weigh them up. Someone tells him about a new tool to help him—the “scientific method.” Finding this tool rather heavy and intricate, he employs specialists to help him, people trained in the scientific method, i.e., scientists. Thus is born an operational research section such as is now to be found in numerous organizations and industries in Britain and the United States.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
The Development of Planning Procedures at Air Proving Ground Command
Authors: Debeau David E. , Porter Robert A.
Published: November 2008

Sophisticated models and complex mathematical formulations are not always necessary for the development of successful planning techniques. Often rather simple and straightforward algebraic statements will serve management's purposes very well. Since planning is in essence prediction, precision of prediction is desirable. Although a relatively simple and direct planning method may lose in precision, it has certain major advantages: (1) timeliness through quick development and application; (2) ease of application; and (3) an understanding of the model on the part of management, who must take action on the basis of the predictions. Often these advantages far outweigh the disadvantages of loss of precision.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Analogue Computations of Business Decisions
Authors: Fair William R.
Published: November 2008

The role of modern computing machinery is a rapidly expanding one with interest being shown in a wide variety of fields. In a sense this arrival of the era of mechanized computation has had a twofold effect. Not only has it meant a release from mathematical drudgery, but it has opened the way for the careful formulation of problems heretofore dealt with in only a qualitative manner or by only the grossest approximation to quantitative reasoning. This paper represents one of the growing number of efforts that start with the assumption that computational ability is not the serious limiting condition that it has been. From there it proceeds to try to answer two questions: How should rational business decisions be made? What kind of computer will be necessary to put the computational problem within reach?

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letters to the Editor—What is the Mission of Operations Research?
Authors: Hitchman Norman
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letters to the Editor—Feedback Control of Continuing Operations
Authors: Camp Glen D.
Published: November 2008

No abstract available.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
State Probabilities in Congestion Problems Characterized by Constant Holding Times
Authors: Evekett John L.
Published: November 2008

This paper presents an alternative method for determining the state probabilities in the multiple-channel case with fixed holding times and random arrivals. This method is considerably less mathematically sophisticated than that given in [Polleczek, F. 1934. Math. Zeits. 38 492–537.] and [Crommelin, C. D. 1932. P. O. E. E. J. 25 (1, April).], but it possesses practical advantages from the point of view of simplicity and convenience.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Combat Problems, Weapon Systems, and the Theory of Allocation
Authors: Karchere Alvin , Hoeber Francis P.
Published: November 2008

In an earlier issue of this journal, Charles Hitch [Charles Hitch. 1953. J. Opns. Res. Soc. Am. 1 87.] discussed the problem of selecting criteria for evaluating the outcome of operations, saying, “The only discipline I know which has made any attempt to explore the characteristics of operations criteria and the intimately related question of the relation between lower and higher level sub-optimization is economic theory.” This paper, following Hitch, uses the standard tools of economic analysis to shed some light on the selection of criteria in operational problems. Some aspects of the military allocations problem are examined. For purposes of illustration the analysis deals with allocation in the army, but it applies equally well to all three armed services.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—New Operations-Research Curriculum at the University of Pennsylvania
Authors: McCloskey Joseph F.
Published: November 2008

As Chairman of the Education Committee, I should like to correct misinformation appearing in the Report of the Education Committee in the last issue of JORSA, and extend the Committee's apologies to the Moore School of Electrical Engineering at the University of Pennsylvania for any embarrassment occasioned by the Report.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Standards on Queue Theory
Authors: Machol Robert E.
Published: November 2008

Is it not time for ORSA (or perhaps IFORS) to adopt standards in such fields as queuing theory just as other professional organizations (e.g., IRE) adopt standards in fields relating to their own competence?
On the Statistical Distribution Function Theory of Traffic Flow
Authors: Anderson Robert L. , Herman Robert , Prigogine I.
Published: November 2008

The homogeneous time-independent solution for a one-car speed distribution function is derived for a Boltzmann-like approach to the statistical theory of traffic flow. Numerical results are discussed for a number of different desired speed-distribution functions. Among these distribution functions, chosen for mathematical simplicity are, for example, the exponential, linear, and parabolic. Flow versus concentration curves and distribution function versus speed curves are given for several of the models.
Distribution of Gaps and Blocks in a Traffic Stream
Authors: Oliver Robert M.
Published: November 2008

This paper studies some of the theoretical questions of large openings or gaps in a single stream of traffic. A gap in the traffic stream is defined as a headway between vehicles greater than or equal to some minimum size—say x. Several authors have studied the probability distribution of the wait that a randomly located observer must endure before he finds a gap. This paper, while briefly reviewing the solutions of this well-known problem, is primarily concerned with expressions for (i) the distribution of gap sizes, (ii) the distribution of spacings between vehicles and gaps, (iii) the mean and variance of intervehicle and intergap spacings, (iv) the stationary flow rates of gaps, and (v) the distribution of blocked and unblocked periods. It is assumed that the origin of measurements may be located (i) with the passing of a vehicle, (ii) at the beginning of a gap, or (iii) at random. It is also assumed that the distribution of intervehicle spacings are independently, but identically, distributed random variables.
Letter to the Editor—Comments on a Paper by Yarnold and Nehnevajsa
Authors: Steger Wilbur A.
Published: November 2008

I would like to comment on the Yarnold and Nehnevajsa article (Yarnold, K. W., Jiri Nehnevajsa. 1961. Analytical methods for determination of training-device requirements. Opns Res. 9 535–545.) appearing in the July–August 1961 issue. The comments fall into two categories: first based on the authors' assumption that “training devices” operate by improving the temporal-accuracy performance of a system's human links, and a second set of comments based on another assumption (mine) that humans can be trained by “training devices” continually to make improvements in and better diagnose problems of the entire man-machine system.
Time-Dependent Solution of the Two-Server Queue Fed by General Arrival and Exponential Service Time Distributions
Authors: Arora K. L.
Published: November 2008

In this paper the queuing system GI/M/2 has been studied by using the “Phase” method. The Laplace transform of the time-dependent probability generating function and the steady-state solutions have been obtained. When the arrival time distribution is exponential, the results correspond to those obtained by Saaty (Saaty, T. L. 1960. Time-dependent solution of the many-server Poisson queue. Opns Res. 8 755–772.) for the queuing process M/M/2.
A Decision Problem with a Deadline
Authors: Wagner Daniel H.
Published: November 2008

Dynamic programming is applied to a problem in deciding when to attack, before a specified deadline. The defender has a detection system whose instantaneous failed or operating status and whose stochastic processes of failure and repair are known to the attacker. The issue is essentially for the attacker to decide how long to wait after observing a failure in order to achieve the best assurance that the detection system will remain failed long enough to complete the attack, also taking into account future failures that may be expected before the deadline. Some properties of the optimal policy are developed and in turn applied to a specific example.
A Single-Server Queue with Poisson Input
Authors: Takács Lajos
Published: November 2008

A single-server queuing process with Poisson input and general service time is considered and a simple method is given for the determination of the probability distribution of the queue size and that of the waiting time for a stationary process.
Letter to the Editor—On An Algorithm for Solving Some Network-Programming Problems
Authors: Minty George J.
Published: November 2008

The purpose of this note is to call to the attention of the readers of this journal a unified algorithm (essentially, a modification and extension of the Ford-Fulkerson algorithm) for solving a class of minimization problems.
Monte Carlo Determination of Stock Redistribution
Authors: Berman Edward B.
Published: November 2008

A model was designed for the purpose of studying stock distribution policies in an inventory system consisting of a number of demand points distributed through space. The model is limited to items that are not centrally repaired and that are procured only once for the life of the item, since both centralized repair and recurrent procurement offer opportunities to correct an imbalance in the distribution of stock among bases at little or no cost to the system. Assuming then an initial distribution of stock among bases, an analytical solution to the redistribution of stock between a pair of bases is obtained in each time period of the model, in terms of (1) the cost of transportation, (2) the stock on hand, depletion penalty, and demand probability function at each of the bases, and (3) a controlled variable βt representing the per cent of the transportation cost to be charged in the tth period in the analytical solution. The expected system costs associated with alternative β functions are then determined by Monte Carlo methods, with each function beginning at a value between zero and one in the first period, and rising to one in the last period. The methodology is extended to include the redistribution decision among three or more bases.
The Lethal Radius of a Salvo
Authors: Weidlinger Paul
Published: November 2008

The vulnerability of a target subjected to a series of repeated shots is examined. It is shown that properly designed elasto-plastic structures are capable of surviving the cumulative effects of repeated blasts if each blast is less intense than a destructive single blast. The blast intensity of a small number of repeated shots need not be significantly smaller than the intensity of a single destructive blast to permit the survival of most structures. The probability of kill, taking into account the cumulative effects of a series of blasts, is determined and it is shown that it is not significantly higher than the probability of kill obtained by neglecting cumulative damage.
Letter to the Editor—Priority Traffic with at Most One Queuing Class
Authors: Burke Paul J.
Published: November 2008

Load-service relations are derived for three types of preemptive priority traffic, in which a call of any class displaces a call of a lower class (the lowest one present, if any) with the single exception in (b) below. These may be briefly characterized as follows (a) calls of all classes are cleared when blocked, (b) calls of the highest class queue, calls of all other classes are cleared, and calls of the second highest class are not displaced by preemption, and (c) calls of the highest class queue and those of all lower classes are cleared. [Doctrine (b) without its last condition ]
Operations Research in the Health Services
Authors: Flagle Charles D.
Published: November 2008

Some problems of the nation's health services—having to do with providing adequate care, maintaining hospital staff and facilities, and preserving or restoring financial stability—are described and classified according to social, economic, and organizational characteristics. The problems are then reformulated into areas for research. The research program formulation is based on the concept of a system in which a flow of demands arising from illness and accident is matched by a flow of specialized human and physical resources. Relating demands and resources gives rise to other problem areas of communication and organization. General references are made to current efforts of operations analysts in the health field, with examples of contributions from these efforts to the general body of knowledge in stochastic systems and decision processes.
Density Oscillations Between Lanes of a Multilane Highway
Authors: Gazis Denos C. , Herman Robert , Weiss George H.
Published: November 2008

The interchange of traffic density between lanes moving in the same direction is investigated on the basis of a simple mathematical model. Emphasis is placed on the question of stability, i.e., attenuation of disturbances from an “equilibrium density distribution.” A solution is obtained for a system of differential difference equations with a time lag corresponding to the interaction of two lanes. This solution is directly applicable to other problems described by similar equations, such as the follow-the-leader problem. The solution is generalized to n lanes, and it is found that the inherent instability is twice as great for n approaching infinity as it is for two lanes.
Some Properties of Redundant Constraints and Extraneous Variables in Direct and Dual Linear Programming Problems
Authors: Charnes A. , Cooper W. W. , Thompson G. L.
Published: November 2008

Model equivalences may sometimes be used to replace “realistic” but unwieldy initial formulations with simpler counterparts. This can involve sophisticated uses of prototypes, quasi models, etc., or it may involve only simpler ideas of redundancy elimination, removal of extraneous variables, etc. In either case questions can arise concerning the properties of these models when further analyses are to be conducted via parameterizations, duality, etc. These topics are examined in the general context of direct and dual linear programming problems with special reference to boundedness properties of the associated solution sets. It is shown that a bounded solution set in one problem implies an unbounded solution set in the dual problem, unless both are one-point sets. The ideas of projection equivalence are then developed to suggest a possible route for utilizing these one-point solution properties for analyzing or solving linear programming problems. These possibilities might prove useful when, for example, it is desired to simplify an initial formulation while achieving a solution that has additional properties—e.g., boundedness—that are also considered desirable.
Letter to the Editor—Comments on a Paper on “Allocation of Stocks to Warehouses”
Authors: White D. J.
Published: November 2008

Comment about the article “Allocation of Stocks to Warehouses” by K. F. Simpson, published in Operations Research, Vol. 7, 797–805 (1959).
A Game Theory Model of Convoy Routing
Authors: Danskin J. M.
Published: November 2008

This paper considers a nonlinear two-person zero-sum game in which one of the players plays over the direct product of two spaces. In fact he allocates ships and escort vessels, separately, to various routes, and his antagonist allocates submarines to the various routes. Its interest lies first in the methodology connected with the curious nature of the one player's space, and second in its conclusions and some economic considerations related to them, for example the “virtual cost” of a route. The paper is a much condensed version of a paper done in 1953 for the Operations Evaluation Group of the Navy Department. The lengthy discussions and numerical computations in that paper have been deleted here, and the loss function taken slightly less general than there. The solution techniques are essentially the same.
Determining Optimum Ship Routes
Authors: Faulkner Frank D.
Published: November 2008

A method is given for determining optimum ship routes on a digital computer. A ship is assumed to be in a fallout field whose intensity is a known function f(x, y, t) of position and time. A typical problem is that of choosing a route to a point where f ≦ fm, the maximum intensity that can be tolerated indefinitely. The route is to be such as to minimize the dose z = ∫0Tfdt, the termininal time and point are not specified. The problem of sending the ship to a given point with z minimized is also discussed. These are equivalent to corresponding problems of choosing a route to minimize the probability of detection while going through a region where the probability of detection is a known function of position and time.
Expected Critical Path Lengths in PERT Networks
Authors: Fulkerson D. R.
Published: November 2008

A method of obtaining a fairly good lower approximation to the expected duration time of a project whose individual job times are discrete random variables is described. It is assumed that jobs that immediately precede any given job may have a joint distribution of times, with independence between immediate predecessors of different jobs. The method provides an estimate that is usually much better, and never worse, than the one obtained by replacing each random job time by its expected value. An application to expected minimal path lengths in networks whose arc lengths are random variables is discussed.
Reducing Letter Delays in Post Offices
Authors: Oliver Robert M. , Samuel Aryeh H.
Published: November 2008

This paper reports a number of mathematical models and experiments that have been designed for the analysis and evaluation of delays of first-class letter mail in a post office. The flow pattern of mail consists of a number of serial and parallel processing stages. A letter takes a particular path through this flow network, which depends on its final destination, consequently, the delay of letter mail depends on its address as well as the inventories of other mail and the processing rates met enroute. While mail flow into a post office may contain many random elements, it is generally the case that input rates are predictable and strongly time-dependent. Scheduling policies must take into account the peak flows that temporarily exceed available processing rates and, in addition, must observe certain specified restrictions on the cost of processing, sorting, and storage operations. The effect of various transportation facilities between processing stages and from one post office to another must also be considered. The mathematical analysis deals with the minimization of letter delay through a network of processing and storage stages where there are capacity restrictions on individual and/or serial and parallel stage combinations. Analytical and graphical procedures are developed and numerical results are reported. The paper also reports a series of full-scale experiments performed at one of the larger United States Post Offices where theoretical procedures and decision rules were applied and tested. Delay reductions for first-class letter mail are believed to be of the order of 25 per cent.
Letter to the Editor—The Report of the 1961 Lanchester Prize Committee
Authors: Ernst Martin , Gomory Ralph E. , Lathrop John B.
Published: November 2008

The 1961 Lanchester Prize Committee continued to follow the procedures developed by previous Committees. ORSA members selected for their knowledge of various fields of operations research were invited to select “… the best paper on operations research or reporting on an operations-research study, identified as such”. This year, 56 publications were examined for prizeworthy papers by 95 screeneers.
Letter to the Editor—Comments on a Paper by H. K. Weiss
Authors: Engel Joseph H.
Published: November 2008

In H. K. Weiss' letter to the Editor (“The Fiske Model of Warfare”, Opns Res. 10, 569–571 (1962).), Weiss pointed out that Rear Admiral Fiske, USN, seemed to have foreshadowed by 11 years the developments that have come to be known as Lanchester's Square Law. Weiss stated that Fiske appears to have been the first to observe publicly that, when the damage each of two forces can inflict on the other is proportional to its own size, the change of size of each force was geometric rather than arithmetic.
Letter to the Editor—A Conjecture Concerning the Smallest Bound on the Iterations in Linear Programming
Authors: Saaty T. L.
Published: November 2008

In solving linear programming problems accurate estimates of the number of iterations needed to reach the optimum are important to have. It has been mentioned in the literature that computing experience indicates this number of iterations to be of the order of twice the number of constraints. We have been informed by two computing groups that a number of large linear programming problems have been left unsolved because, after many hours of machine operation, it was not known how much longer the process would continue. Here through heuristic arguments based on what appears to be a reasonable conjecture we give an upper bound to the number of iterations for algorithms which change one vector at a time, such as the simplex process.
Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints
Authors: Charnes A. , Cooper W. W.
Published: November 2008

Chance constrained programming admits random data variations and permits constraint violations up to specified probability limits. Different kinds of decision rules and optimizing objectives may be used so that, under certain conditions, a programming problem (not necessarily linear) can be achieved that is deterministic—in that all random elements have been eliminated. Existence of such “deterministic equivalents” in the form of specified convex programming problems is here established for a general class of linear decision rules under the following 3 classes of objectives (1) maximum expected value (“E model”), (2) minimum variance (“V model”), and (3) maximum probability (“P model”). Various explanations and interpretations of these results are supplied along with other aspects of chance constrained programming. For example, the “P model” is interpreted so that H. A. Simon's suggestions for “satisficing” can be studied relative to more traditional optimizing objectives associated with “E” and “V model” variants.
Analytic Expressions for the Probability of Penetrating a Point Defense
Authors: Ordway Girard L. , Rosenstock Henry M.
Published: November 2008

A method is developed for computing the probability that an air attack will penetrate a point defense made by a surface-to-air missile system. Analytic expressions are obtained from a model for the probability of penetration by at least one of k attackers, as a function of k and of the spacing between successive attackers, the number of shots that can be made at an approaching attacker, and the single-shot kill probability of the defensive missiles. The mean number of attackers required for penetration can be approximated very closely by a formula that is valid throughout the range of tactical interest.
Addendum to “Cost-Effectiveness Evaluation for Mixes of Naval Air Weapons Systems”
Authors: Jones George P.
Published: November 2008

The method described in the paper to which this article is an addendum forms the basis of the selection procedure used in the Navy Attack Study contract number NOa(s) 59-6074c. Because of time and money limits, revisions were made to the full method. The extent of the revisions will be obvious by comparing the discussion of the procedure actually used with that described by Mr. Albert in the previous paper.
Duration of a Countdown when Considered as an Interrupted Service Process
Authors: Firstman Sidney I.
Published: November 2008

A countdown (and other kinds of service processes) could be interrupted by several kinds of problems, and, following each interruption, it could continue according to one of several policies, seven such policies are considered in this paper. The problem addressed is that of accounting for the randomly occurring problems and the time required to deal with them when estimating the distribution of interrupted countdown durations. The countdown is considered as an interrupted service process, and expressions are derived from which the moments of the interrupted countdown duration distribution can be obtained. The first two moments are derived explicitly. Although the results are derived in a countdown context, they appear applicable to other kinds of service processes that are subject to randomly occurring interruptions.
Use of Linearized Nonlinear Regression for Simulations Involving Monte Carlo
Authors: Walsh John E.
Published: November 2008

The material presented furnishes an extension of regression analysis in two respects. First, a type of nonlinear regression function is developed that seems to (1) have substantial curve-fitting flexibility, (2) be satisfactorily determined from an acceptably small number of observations, (3) permit isolation of important combinations of effects, and (4) be computationally manageable. Second, in conjunction with this general type of regression function, a probability model is developed that is applicable under exceedingly general conditions. Namely, each of the independent observations utilized can be from a different statistical population and the shapes of these populations are not necessarily restricted or related in any specific manner. An important aspect of the model is selection of the kind of “average” that the regression represents Estimates, tests, and confidence intervals are developed for investigating the regression coefficients. The methods and results presented are especially useful for Monte Carlo type simulations that are performed by use of a computer. This paper represents a report of research in progress, since many additional results should be obtainable on the basis of the concepts and methods that are presented.
The Distribution of the Virtual Waiting Time for a Single-Server Queue with Poisson Input and General Service Times
Authors: Takács Lajos
Published: November 2008

A single-server queuing process with Poisson input and general service times is considered and an elementary method is given for the determination of the distribution function of the virtual waiting time.
Some Queuing Problems with the Service Station Subject to Breakdown
Authors: Avi-Itzhak B. , Naor P.
Published: November 2008

A number of situations is considered where the single service station is incapacitated from time to time to render service to the incoming (stationary) Poisson stream of customers. Five models are presented Model. A deals with the situation in which the service interruption is brought about by a Poisson process homogeneous in time. The preemptive priority queuing model is shown to be a special case. Model B is concerned with the case in which breakdowns occur only while the station is giving service. In Model C it is assumed that the repair process cannot start without customers at the station. Model D describes a situation in which the repair of the station starts at the initiative of a customer who wishes to improve the standard of service. In Model E the assumption is that the station can break down only while no customer is being serviced. In all models it is assumed that service times and repair times possess arbitrary distribution functions each having a density and finite second moment. The expected queue lengths and related operating characteristics of the various systems are derived using relatively simple mathematical methods.
On Poisson Queue with Two Heterogeneous Servers
Authors: Krishnamoorthi B.
Published: November 2008

A Poisson queue with two heterogeneous servers has been considered. Some objections to the use of classical queue discipline are raised, chief among them being the violation of the “first-in first-out” principle, because of heterogeneity of servers. Two alternative queue disciplines are considered, one with a slight and the other with a greater modification of the classical one. The second one takes care of the objections raised against the classical one, while the first is still of interest because of its operational simplicity. Under the first one the steady state and the Laplace transform of the transient state probability distribution of the queue length have been derived. Also different types of busy periods have been defined. Under the second one, only steady-state results have been obtained. An application has been indicated.
Multi-Commodity Network Flows
Authors: Hu T. C.
Published: November 2008

A network is a set of nodes Nı connected by arcs with nonnegative arc capacities bıj which indicates the maximum amount of flow that can pass through the arc from Nı to Nj. Given all bıj, there is a maximum flow from Nı to Nj using all arcs. Under the assumption that bıj = bjı, the present paper generalizes the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and gives an algorithm similar to the labelling method for constructing the two flows.
A Note on Exponential Smoothing and Autocorrelated Inputs
Authors: Cohen Gerald D.
Published: November 2008

This paper considers the use of exponential smoothing to forecast time series which are compound processes containing both deterministic and random components. Recognition is given to the fact that modifications made in the simple smoothing formula to correct for one assumed component in the input series, such as a trend, interacts with the other series' components, and the total forecast error may be increased. The mean squared forecast error, using exponential smoothing, is compared when the random inputs are independently distributed and when they are autocorrelated. The latter case being commonly encountered in sales series. The characteristics of the smoothing procedure is examined when the input time series is geometrically autocorrelated and the range of values of the smoothing constant to minimize the forecast error is calculated.
Further Results for the Queue with Poisson Arrivals
Authors: Prabhu N. U. , Bhat U. Narayan
Published: November 2008

Transition probabilities are obtained for the queue length in the single-server system with Poisson arrivals and arbitrary service time distribution. The method used is applicable to systems with batch arrivals and balking, discussed respectively by D. P. Gaver and Lajos Takács.
Letter to the Editor—A Simple Proof of a Theorem in Exponential Smoothing
Authors: Dobbie James M.
Published: November 2008

A simple proof is given of a theorem in exponential smoothing that is sometimes referred to as “the fundamental theorem”. This theorem states that a polynomial, of degree N at most, minimizes the exponentially-discounted sum of squares of the errors if and only if it satisfies the set of N + 1 equations obtained by equating the ith iteration of the exponentially-discounted average of the sequence to the corresponding average of the polynomial, i = 1, 2, …, N + 1.
The Sorting of Sawmill Lumber
Authors: Clapham J. Charles , Lambe T. A.
Published: November 2008

The cost of sorting lumber is a major expense at all sawmills. It is a relativey inefficient process by present methods, but it has received little analytical study. A model is developed here to show how the manpower requirements vary with the relevant parameters for any particular sawmill sorting-chain. This relation is useful in determining the best manual sorting system and in determining the most profitable sorts to mechanize. A questionnaire survey of sawmills in British Columbia and the Western United States shows a considerable scope for improvement by application of the technique developed. Specific applications have already been made to some sawmills and the predictions of the theory validated.
A Gambler's Ruin Type Problem in Queuing Theory
Authors: Keilson Julian
Published: November 2008

The Takács process, X(t) describing the virtual waiting time or server backlog for a single-server queue with Poisson arrivals and general service time distribution, is discussed with two absorbing boundaries. The process terminates at x = 0 when the server becomes idle or at x = T when a given backlog level is exceeded. The probabilities ΓT(x0) that absorption will occur at x = 0 if the process starts at x0, and ΓT(x0, t) that absorption will occur at zero before time t, are exhibited. The process is also of interest to the theory of collective risk.
The Effectiveness of Mobile Logistic Support
Authors: Danskin John M.
Published: November 2008

A fundamental question in long-range planning for the logistic support of an ocean area is the size and location of bases. The present paper proposes a measure of effectiveness, called the “logistic effectiveness,” for a given set of bases supporting the region. This is done by a maximizing process Then the sizes of the bases are varied, subject to a budgetary constraint, and an “optimal base structure” found. For small numbers of bases, for instance three bases, the calculations may be done by hand. Two numerical examples are presented. The paper is intended as a contribution to theory and not for immediate practical application.
Preemptive Repeat Priority Queues as a Special Case of the Multipurpose Server Problem—I
Authors: Avi-Itzhak B.
Published: November 2008

A single station provides service to customers who arrive in a Poisson stream with constant intensity. All the customers require an equal and fixed amount of service but the servicing rate of the station varies randomly, and thus the resulting service time is randomly distributed. The service station itself is subject to random breakdowns rendering it inoperative for random periods of time during which repairs take place. The service of a customer, displaced by a breakdown, is repeated from the beginning as boon as the repair process is completed. The service given to the customer prior to his displacement is wasted. It is shown that this model describes a situation where displacement is not necessarily a result of breakdowns, but may well be caused by other, more urgent, tasks which have to be performed by the station. Some characteristics of the model, such as the expected queue length and queuing time are derived. A solution is given for the preemptive repeat queuing problem as a special case of this model.
Simple Machine Interference with Two Types of Failure
Authors: Jaiswal N. K. , Thiruvengadam K.
Published: November 2008

This paper deals with the simple machine interference problem when each machine is liable to two types of failure whose repair times are distributed according to general distributions. One type of failure is assumed to have the “head-of-the-line” priority over the other type. Using the supplementary variable technique, the steady-state probabilities for the number of machines running, have been obtained.
Modular Design—A Special Case in Nonlinear Programming
Authors: Evans David H.
Published: November 2008

The optimal design of a module under a special set of circumstances is considered. These circumstances prevail in the design of a module for logistical applications and sometimes in modular equipment design in electronic technology. Mathematically, the problem considered is given Rαβ ≧ 0, find positive Bα, mβ such that Bαmβ ≧ Rαβ, α = 1, 2, …, n, β = 1, 2, …, k and such that W = ∑βmβ∑αBα is a minimum. It is attacked by first examining the primal problem, then finding a dual problem, and finally finding an algorithm for solving the dual.
Letter to the Editor—Apportionment of the U.S. House of Representatives: A Minimum Range, Integer Solution, Allocation Problem
Authors: Burt Oscar R. , Harris Curtis C.
Published: November 2008

The following allocation problem was encountered in considering optimal distribution of the 435 members of the U.S. House of Representatives among the 50 states. It is impossible to have perfect equality of representation because fractional representation is not allowed, consequently, there has been a long history of controversy over criteria of equality.
Letter to the Editor—Corrigendum to “The Loading Problem”
Authors: Pandit S. N. Narahari
Published: November 2008

The abstract of S.N.N. Pandit's paper [Opns Res. 10, 639–646 (1962)] makes a reference to a bracketing bound technique, while the paper does not present the technique. The original version of the paper did include this technique but considerations of space forced the omission of the relevant sections of the paper. By oversight, corresponding modifications were not carried out in the abstract. The numerical illustration is condensed and an explanatory foot note, referred to on page 642, is also omitted. The author regrets these errors and wishes to refer the readers interested in the bracketing bound technique to a forthcoming paper, “An Enumerational Approach to Integer Programming Problems.”
Forest Fire Problems—A Progress Report
Authors: Jewell William S.
Published: November 2008

Forest and wildland fires in the United States of America destroy about 4 million acres annually, at an estimated direct cost of about $350 million. In the state of California alone, about 270,000 acres of timber, recreation, and watershed values are destroyed yearly. Under a cooperative agreement with the U.S. Department of Agriculture Forest Service, a research group at the Operations Research Center, University of California, Berkeley, has begun a program to study the application of operations research to forest fire control systems, this paper is a progress report on that program Problem areas that have been explored to date are (1) Initial attack planning, (2) man and equipment mobilization, (3) economics of detection systems, (4) fire camp organization, and (5) fire agency communications. Although it is still too early to provide definite recommendations in these areas, certain approaches appear very promising. One of the present limitations to OR studies is a lack of fundamental knowledge about (1). The macro-physical behavior of fire, and (2) the effect of varying suppression tactics upon this behavior. Nevertheless, the problems of forest fire control provide an exciting and worthwhile area for future research.
Stock Levels Generated by a Controlled-Variability Arrival Process
Authors: Govier L. J. , Lewis T.
Published: November 2008

Controlled-variability arrivals are of widespread occurrence, and a model for discrete controlled-variability arrivals, called the (a, b) process, has been discussed in the literature. This paper considers the marginal distribution of stock levels generated by (a, b) arrivals of equally sized cargoes, assuming that discharge into stock is instantaneous and that offtake from stock is at a continuous uniform rate equal to the mean rate of planned arrivals. It is shown that, provided the arrival pattern is not too close to regularity, the resulting distribution of stock levels is effectively normal and has a standard deviation that can be simply expressed in terms of the parameters of the (a, b) process. The paper also discusses some aspects of the use of this result for the justification of storage facilities in some real systems.
On the Optimum Location of Checking Stations
Authors: Young Henry A.
Published: November 2008

Items move uniformly from the initial to the terminal point of a route. Checking stations that detect and repair imperfect items can be located along the route. If the condition of an item changes from “perfect” to “imperfect,” an operating cost is incurred which increases with the distance traveled in the imperfect condition to the nearest checking station. Given an arbitrary increasing operating cost function, data on the likelihood of failure of an item at any point enroute, the volume of traffic per unit time and the cost per unit time of maintaining a checking station, the dynamic programming technique is used to find the number and placement of checking stations which minimize the sum of operating and checking costs. The model is applicable to the problem of locating “hot-box” detectors along a railroad right-of-way. The analysis of the convex cost functional involved may be of independent interest.
Optimal Scheduling of Replacement and Inspection
Authors: Jorgenson Dale W. , McCall John J.
Published: November 2008

This paper summarizes research on the optimal scheduling of replacement and inspection for stochastically failing equipment, it is assumed that for some parts of the equipment, the state of the equipment—whether good or failed—is not known with certainty. Periodic policies for inspection or replacement of equipment consisting of a single stochastically failing module are discussed, first under the assumption that the distribution of times to failure of the stochastically failing module is known and secondly under the assumption that the form of the distribution is known but that the failure rate is unknown. “Opportunistic” policies for inspection and/or replacement of equipment consisting of more than one stochastically failing module are discussed, for such policies, the action to be taken for a given part may depend on the state of other parts.
Stochastic Duels
Authors: Williams Trevor , Ancker Clinton J.
Published: November 2008

The relative importance of kill probabilities, rates of fire, and other parameters in a duel is considered by examining their effect on the most natural measure of effectiveness, the probability that a given side will win. In the “fundamental” duel, two contestants, A and B, fire at each other until one is killed. The time between rounds fired is a random variable of known but different density function for each, and each has a different known but fixed kill probability. The duel starts with both duelists having unloaded weapons and unlimited ammunition supplies. The general solution is obtained in quadrature form and specific solutions are derived for a particular firing time distribution and for certain variations in initial conditions. Finally, the general solution and a specific example for the duel with random initial surprise are obtained.
Letter to the Editor—Report of the Student Paper Judges
Authors: Hare Van Court , Shortley George , Caywood Thomas E.
Published: November 2008

On Tuesday, May 28, 1963, at the Twenty-third National Meeting of the Society in Cleveland, sixteen students delivered contest papers at Session K in competition for the announced prize round-trip air transportation and appointment as an official delegate to the Third International Conference on Operations Research, Oslo, Norway, July 1–5, 1963.
Letter to the Editor—Multiple Correlation—A Technique for Prediction of Future Hospital Bed Needs
Authors: Beenhakker Henri L.
Published: November 2008

The problem of “prediction of future hospital bed needs” cannot be adequately solved by usual prediction techniques in case of high occupancy rates of a hospital over the past years, since trends are not recognized in this situation. The following method is proposed if the usual prediction techniques do not seem adequate. (1) Relate the number of patients per month to factors that can be predicted by using multiple regression techniques. (2) Predict the number of patients per month with the help of multiple regression equations. (3) Predict the number of beds from the predicted number of patients per month, by multiplication of the predicted number of patients per month by the fraction (predicted average length of stay)/30.5.
A Linear Programming Approach to the Cutting Stock Problem—Part II
Authors: Gilmore P. C. , Gomory R. E.
Published: November 2008

In this paper, the methods for stock cutting outlined in an earlier paper in this Journal [Opns Res 9, 849–859 (1961)] are extended and adapted to the specific full-scale paper trim problem. The paper describes a new and faster knapsack method, experiments, and formulation changes. The experiments include ones used to evaluate speed-up devices and to explore a connection with integer programming. Other experiments give waste as a function of stock length, examine the effect of multiple stock lengths on waste, and the effect of a cutting knife limitation. The formulation changes discussed are (i) limitation on the number of cutting knives available, (n) balancing of multiple machine usage when orders are being filled from more than one machine, and (m) introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts. The methods developed are also applicable to a variety of cutting problems outside of the paper industry.
A Geometric Model and a Graphical Algorithm for a Sequencing Problem
Authors: Hardgrave William W. , Nemhauser George L.
Published: November 2008

A geometric model is given for the problem of scheduling N jobs on M machines so that the total time needed to complete the processing of all jobs is minimized. This model leads to a graphical algorithm, the essence of which is the determination of a shortest path between two nodes in a finite network. Particular attention is given to the case of 2 jobs for which the algorithm developed is simple and efficient. The theoretical analysis is then extended to the general case. Computational problems arise in the general case primarily because of the difficulty of constructing the network.