bluuebunny/crossref_metadata_2025 huggingface dataset:
Letter to the Editor—Two Doctrines for the Handling of Two-Priority Traffic by a Group of N Servers
Authors: Helly Walter
Published: November 2008

Two priority classes of customers form inputs to one group of N servers. Each input class offers customers with a Poisson arrival distribution. The holding times of customers in service are drawn from one exponential distribution without regard to priority class. Two service doctrines will be considered.
A Theory of Reconnaissance: II
Authors: Danskin John M.
Published: November 2008

In Part I of this two-part paper, the author considered the one-sided reconnaissance problem, in which the reconnoiterer seeks to maximize the information (minimize the confusion) obtained as a result of the expenditure of a given effort, it being assumed that the side being reconnoitered remains passive. This problem was formulated as a problem in information theory. This part concerns the two-sided reconnaissance problem, in which the side being reconnoitered seeks to minimize the information (maximize the confusion) obtained by the reconnoiterer, while maintaining at least a certain minimum acceptable threat with a fixed budget. This problem, formulated as a zero-sum, two-person game, is solved for one special case (fixed equipment) and it is proved that there exists a solution in mixed strategies for the general case. A model is given for evaluating the effectiveness of a photo-interpreter by separating the confusion caused by the photointerpreter from that caused by the photographs.
Dependability of a Complex System
Authors: Mohan C. , Garg R. C. , Singal P. P.
Published: November 2008

In this paper the behaviour of a complex system consisting of n components of constant failure rates λ1, λ2, …, λn and repair rates pit μ1, μ2, …, μn is examined. The probability that the system is operating at time t is obtained. Also the probability that it is in outage stage i at time t has been determined. At the end, a particular case where μı's are equal is considered.
Some Recent Contributions to the Lanchester Theory of Combat
Authors: Bach Ralph E. , Dolanský Ladislav , Stubbs Harold L.
Published: November 2008

Since the original formulation of Lanchester's equations pertaining to the combat of two opposing forces, the theory has been extended, organized and applied by many writers, including R. H. Brown, J. H. Engel, R. N. Snow, and H. K. Weiss. Certain more recent extensions of this theory, which have been developed under Project NUMERICS (Northeastern University Mathematical and Engineering Research in Complex Systems) will be described in this paper. The model considered is limited to only one kind of combat unit on each side, but operational losses, in general different for each of the two sides, are also included. Under these conditions, certain results were obtained in the following problems. (a) the total losses of the victor as a function of varying amounts of forces included, (b) prediction of outcome from initial performance, when the values of the various attrition rates are not known, (c) analog circuits simulating the performance of the model.
A Single-Server Queue with Recurrent Input and Exponentially Distributed Service Times
Authors: Takács Lajos
Published: November 2008

Combinatorial methods are given for the determination of the distribution of the queue size, the waiting time, the number of customers served in a busy period and the length of a busy period for a single-server queuing process with recurrent input and exponentially distributed service times.
Letter to the Editor—Vitae Faciendo Nemini Timeas
Authors: Paxson E. W.
Published: November 2008

This is a belated memorial to Howard P. Robertson, Professor at the California Institute of Technology, who died in the late summer of 1961 of injuries resulting from a traffic accident. He was 58 years old.
Letter to the Editor—A Comparison of (t, Z) and (z, Z) Policies
Authors: Naddor Eliezer
Published: November 2008

Two widely used inventory policies, the (t, Z) policy and the (z, Z) policy, are compared in this communication. In the (t, Z) policy orders for replenishments are placed at regular intervals t, whereas in the (z, Z) policy the orders are placed only when stocks on hand and on order are equal to or below the level z. In both policies the amounts ordered raise stocks to the level Z. It is shown that in systems in which various items may be separated and analyzed independently the (z, Z) policy is the better policy. However, in other systems the (t, Z) policy may be the optimal policy. This may occur, for example, in systems in which replenishment costs are common to several items.
Letter to the Editor
Authors: Dranoff J. S. , Mitten L. G. , Stevens W. F.
Published: November 2008

In a private communication, Professor R. Aris of the Chemical Engineering Department at the University of Minnesota has raised a significant question concerning our article Application of Dynamic Programming to Countercurrent Flow Processes [Opns Res 9 388–401 (1961)]. His inquiry requests that we define the class of problems for which the application of the “dynamic programming principle of optimality” will yield total returns as high as those achieved by more conventional maximization procedures.
Optimal Capacity Scheduling—I
Authors: Veinott Arthur F. , Wagner Harvey M.
Published: November 2008

Efficient algorithms are developed optimizing an important class of capacity scheduling models. The specific problem considered can be simply described in terms of contracting for warehousing capacity. Contracts must be let for warehouse capacity over n time periods, with the minimum capacity to be provided in each time period being specified. Savings may be achieved by long-term leasing arrangements or by contracting at favorable periods of time, even though this creates idle capacity at certain time periods. A minimum cost solution to this problem is sought. The mathematical model also applies to problems of equipment replacement and overhaul, checkout, repair, and replacement of stochastically failing equipment, determination of economic lot size, product assortment, and deterministic batch queuing policies, labor-force planning, and multi-commodity warehouse decisions. For some of these problems, such as equipment replacement, the computing algorithms presented are even more efficient than schemes heretofore proposed for simpler versions of the same problem.
Optimal Capacity Scheduling—II
Authors: Veinott Arthur F. , Wagner Harvey M.
Published: November 2008

This paper is a continuation of the preceding article. When no special assumption is made about the cost coefficient cij in the capacity scheduling model, it is necessary, as has been shown, to solve the problem by means of a transshipment linear programming model. But for a large class of real situations, the cij can be described in terms of a specific mathematical function that leads to considerable simplifications in the solution algorithm. Here the algorithmic simplifications are explored in detail. The analysis of the capacity scheduling model is also extended to situations in which initial capacities exist, and an application of the model to the multicommodity warehousing problem is given.
Elementary Methods for Some Waiting Time Problems
Authors: Prabhu N. U.
Published: November 2008

Let Wn be the waiting time of the nth arrival in a single server queuing system, and T = min{n ∣ Wn = 0}. The distribution of T is obtained for the system M/G/1, and by applying a duality principle, Smith's theorem for GI/M/1 is deduced. The waiting time distribution in the system Ek/D/1 is also obtained.
Letter to the Editor—The Fiske Model of Warfare
Authors: Weiss Herbert K.
Published: November 2008

It appears that Lanchester's well-known N-square Law, described in his book Aircraft in Warfare (Lanchester, F. W. 1916. Aircraft in warfare the dawn of the fourth arm. Constable and Company, Ltd., London.) and published in 1916, was anticipated at least ten years either by Rear Admiral Bradley A. Fiske. As reported by Robison in A History of Naval Tactics (Robison, Rear Adm S. S. [U.S. Navy (Ret)], Robison, Mary L. 1942. A history of naval tactics from 1530 to 1930. U.S. Naval Institute, Annapolis.), the Naval Institute Prize for 1905 was awarded to Rear Admiral (then Commander) Bradley A. Fiske for an essay titled “American Naval Policy”.
A Note on Fallout Prediction
Authors: Ryan B. A.
Published: November 2008

This paper outlines a study made to determine the requirements of the Army in the field for fallout prediction. A series of operations analyses that depict graphically the fallout event for various yields and wind fields as it develops on tactically deployed Army forces have been performed to (1) confirm countermeasures that minimize the influence of fallout on tactical operations, (2) indicate the predicted information required by tactical commanders to allow effective application of these countermeasures, and (3) determine the accuracy requirements associated with this predicted information. The principal analysis tools used are overlay representations of tactically deployed Army forces, and template representations of the U.S. Naval Radiological Defense Laboratory's Dynamic Fallout Model. The results of application of countermeasures to fallout by tactical commanders have been determined and compared for two conditions (1) No Predicted Information (knowledge only of time and location of burst, and readings from radiac instruments) and (2) Perfect Predicted Information (knowledge of the predicted development of the fallout field in time and space as derived from the USNRDL D-Model). From this comparison, areas are identified where prediction offers a distinct advantage to the tactical commander, the most important elements of the predicted information are deduced, and then prediction accuracy requirements are defined. Finally, an operationally useful prediction concept is suggested.
Cost Minimization Problems Treated by Geometric Means
Authors: Duffin R. J.
Published: November 2008

It is supposed that the cost of an engineering design is a generalized polynomial function in the design parameters. The terms of such a polynomial are products of the parameters raised to powers. Fractional and negative powers are permitted but the coefficients of the terms are taken to be positive. The problem of concern is the adjustment of the parameters so as to minimize the cost. By use of the classical inequality to the effect that the arithmetic mean exceeds the geometric mean it is found that the cost function exceeds a certain function termed the dual. Moreover it is shown that the maximum of the dual function gives the minimum cost. This relation furnishes a simple method of estimating the minimum cost.
Linear Programming in a Markov Chain
Authors: Wolfe Philip , Dantzig G. B.
Published: November 2008

An infinite Markov process with a finite number of states is studied in which the transition probabilities for each state range independently over sets that are either finite or are convex polyhedra. A finite computational procedure is given for choosing those transition probabilities that minimize appropriate functions of the resulting equilibrium probabilities, the procedure is a specialization of the authors' decomposition algorithm for linear programming problems of special structure.
Letter to the Editor—Some Observations on the Routing Problem
Authors: Pandit S. N. Narahari
Published: November 2008

Observation about papers [Pollack, M., W. Wiebenson. 1961. Comments on ‘The shortest route problem’ by Peart, and others. Opns Res. 9 411; Peart, R. M., P. H. Randolph, T. E. Bartlett. 1960. The shortest route problem. Opns Res. 8 866–868; Pollack, M., W. Wiebenson. 1960. Solutions of the shortest route problem—a review. Opns Res. 8 224–230.]. Here the following two aspects of the problem—(a) allowing the link distances to be negative, and (b) searching for maximal routes—are considered.
Letter to the Editor—Comments on a Paper by Kettelle
Authors: Proschan Frank
Published: November 2008

A simpler derivation of the solution to the problem considered in “Least-cost allocations of reliability investments” by John D. Kettelle, Jr. Operations Research Vol. 10, 261–262 (1962).
Safety Levels in Military Inventory Management
Authors: Alt Franz L.
Published: November 2008

A suitable objective function is derived for inventory problems involving stocks of several commodities with interdependent optimal stock levels. To this end the effect of inventory levels on the activities served by the inventory is derived, and the expected utility of these activities is used as the objective function, to be maximized by choice of stock levels. In the case of several activities jointly served, where it may be difficult to choose a joint utility function for these activities, the proposal is made and argued to approximate this function by the sum of the marginal costs of the separate activities.
A Lanchester Model of Guerrilla Warfare
Authors: Deitchman S. J.
Published: November 2008

A variation of the Lanchester equations is applied to exploration of the force ratios required to win in guerrilla-counterguerrilla warfare. It is shown that an attacking guerrilla force can, by using tactics that compensate for its weaknesses, defeat a force of defending regulars that has over-all superiority in numbers and weapons. The defenders can win by appropriate selection of weapons, countertactics, and group sizes for individual engagements. In general, however, the high over-all ratios of defending regulars to attacking guerillas that have characterized recent warfare of this kind in which the defense has been successful are extremely difficult to reduce.
Defense and Development in Less Developed Countries
Authors: Wolf Charles
Published: November 2008

A method is described for examining the question of how military assistance programs in less-developed countries, and their defense forces and budgets, can be modified so as to yield about equivalent military effectiveness, and yet generate improved economic and political side-effects. Research concerned with applying this method to case studies in Viet-Nam and Iran is summarized. The research suggests ways in which program improvements with enhanced side-effects may be made. Qualifications are warranted because of the uncertainties connected with the game-simulation technique for estimating military effectiveness, and the method of judging political side-effects, used in the study.
Letter to the Editor
Authors: Danskin John M.
Published: November 2008

Some years ago I sought to publish another version of the paper, A Game Theory Model of Convoy Routing, now published in this issue of Operations Research, under a disguise.
Letter to the Editor—Critical Path Planning—PERT Integration
Authors: Bildson R. A. , Gillespie J. R.
Published: November 2008

The Critical Path Programming System, even though restricted to project planning situations in which network structure and activity statistics are invariant during reduction of project duration, is proving to be a practical and useful technique. In fact, the efficiency of the algorithm developed by Kelley (Kelley, James E., Jr. 1961. Critical-path planning and scheduling: mathematical basis. Opns Res. 9 296–320.) for project time reduction permits one to adjust rapidly and inexpensively to changes in network structure or activity time-cost estimates as these changes develop. However, the effects of random variations in activity time estimates on earliest event occurrence time and project duration are not evaluated in the basic model described by Kelley, and the incorporation of the PERT procedure provides additional information concerning these effects.
Letter to the Editor—Attempts to Validate Certain PERT Statistics or “Picking on PERT”
Authors: Grubbs Frank E.
Published: November 2008

This letter indicates the restrictions on the Beta Distribution that are required to validate the use of PERT means and variances. The conditions appear to be rather restrictive, thereby limiting the generality of application in computing PERT probabilities. The subjective nature of the PERT estimation problem is also discussed.
A Problem of Optimizing a Collecting Reservoir System
Authors: Avi-Itzhak B. , Ben-Tuvia S.
Published: November 2008

The paper deals with the design of a collecting reservoir system on the lower reaches of a river. The daily input into the reservoir is approximated by the negative exponential distribution and the output is continuous, the water being pumped to another existing reservoir. The problem is how big a reservoir to build and what should the pumping capacity be, such that the cost per cubic meter of water pumped is a minimum. A solution, subject to local cost considerations, is given for any feasible quantity of water exploited. The model described and analyzed here can also be used as an inventory model.
Cost-Effectiveness Evaluation for Mixes of Naval Air Weapons Systems
Authors: Albert Bernard S.
Published: November 2008

The problem for solution was to develop a method for determining cost and a means for employing cost together with effectiveness in the determination of the next generation attack air weapon system for the Navy. A number of factors in this problem are different from the usual cost-effectiveness problem, some aircraft being procured today will still be in use, Naval aircraft have multiple mission capability (both strategic and tactical), the ships being built now or already commissioned are those from which next generation aircraft will operate and aircraft carriers have a fixed area for accommodating aircraft and relatively fixed personnel accommodations. In addition, when we consider a decision that must be made in the relatively near future, we must allow that not only is the total Naval budget limited, but that each kind of major procurement appropriation (for aircraft, missiles, ships, etc. ) is also limited. These considerations led to the formulation of a weapon system costing methodology that was tailored to Naval operating characteristics, and the development of a cost-effectiveness evaluation methodology by way of linear programming to include the various restrictions cited.
On a Problem in Naval Defense
Authors: Mohan C. , Arora S. D.
Published: November 2008

This paper deals with analytical study of the encounter of home submarines with the incoming fleet of enemy destroyers. A stochastic model is framed with a view to describing the situation and ascertaining the probabilities of hit under different conditions. In the end a particular case is deduced, and the mean time for n hits has been ascertained.
A Problem in Optimum Allocation
Authors: Srikantan K. S.
Published: November 2008

In this paper we have developed an iterative process for obtaining, in a stratified sampling design, optimum allocation of the total sample to the various strata in order to secure minimum variance at a given cost and, at the same time, provide strata estimates with variabilities not exceeding specified levels. The process has been illustrated and generalized. The application of the extended procedure has been discussed.
Operations Research and Industrial Engineering: The Applied Science and its Engineering
Authors: Barish Norman N.
Published: November 2008

Programs of education in industrial engineering, operations research, and management science should be based upon definitions of the respective fields, upon a concept of the present and future scopes and limitations of professional activity in these fields, as well as upon an evaluation of what academic disciplines provide the most suitable preparation for the respective professional activities. This paper examines these subjects and concludes that educational programs for these professions should have much in common and that, although a wide variety of quite different types of educational experience can provide the basis for professional work in industrial engineering and in operations research, these educational programs should emphasize the system and the decision-making approaches to the science, engineering, and practice of management.
An Allocation Problem with Applications to Operations Research and Statistics
Authors: Zahl Samuel
Published: November 2008

A considerable number of problems in operations research and statistics have the following form maximize ∫ f[x, y(x)] dx subject to ∫ g[x, y(x)] dx = constant with respect to bounded y(x). We give a necessary and sufficient condition for a maximizing function under fairly weak restrictions and prove its existence. The solution is applied to a general version of B. O. Koopman's search problem, and to the Neyman, Pearson lemma of statistics. We also show that in the discrete version of this problem, where x is replaced by an index and sums replace integrals, our condition is sufficient but not necessary and give, as illustration of the sufficiency, a solution to an assignment problem.
Letter to the Editor—A Note on Highway Transparency
Authors: Weiss George
Published: November 2008

Comparison of two different approaches to the concept of highway transparency.
Equipment Maintenance Procedures
Authors: Buzzanca Victor , Goldstein Marvin H.
Published: November 2008

A model of equipment failure and repair in which failures are not assumed to be instantly recognized is investigated. Two maintenance procedures are analyzed within this model with the assumption of independent and exponential failure and repair rates. The first considers continuous monitoring of the spares, the second no monitoring. Equations for the pertinent probabilities are derived together with loss equations for comparing the two procedures. Examples and curves are included to demonstrate the results.
A Note on the “Explosion” and “Netting” Problems in the Planning of Materials Requirements
Authors: Elmaghraby Salah E.
Published: November 2008

The “explosion” problem is the problem of determining the required components from knowledge of demand for finished products. The “netting” problem is the problem of determining the net requirements of these components, for purposes of production or procurement from outside the firm, based on available inventory. This paper presents a simple algorithm which yields the “netted explosion.” The algorithm is suitable for digital computation in case of large inventories.
Preemptive Repeat Priority Queues as a Special Case of the Multipurpose Server Problem—II
Authors: Avi-Itzhak B.
Published: November 2008

In this part of the study it is assumed that the servicing rate of the station is constant and the variability of service time is caused by the differing service requirements of the customers. Some characteristics of the model, such as the expected queue length and queuing time are derived. The effect of the type of service time variability upon the expected queue length is illustrated by a numerical example. The preemptive repeat priority problem, analogous to this model, is solved as a special case. Some other special cases are discussed in the paper.
Letter to the Editor—The Growth of Operations Research in Italy
Authors: Stoller David S.
Published: November 2008

The past and present extent of operations research activities in Italy are discussed. Several factors related to the growth of operations research activities in the educational, industrial, governmental, and military sectors of the Italian economy are identified. The future prospects for the operations-research profession in Italy are evaluated.
A Sampling Study of Minimum Absolute Deviations Estimators
Authors: Ashar V. G. , Wallace T. D.
Published: November 2008

Small sample properties of minimum absolute deviations estimators were studied via a simulation model. A four-parameter model of full rank was proposed and 50 random samples were drawn consistent with this model. Results indicated that, for this experiment, m a d estimators were about 20 per cent efficient compared to minimum variance estimators, using Aitken's concept of generalized efficiency. No significant biases were found in the experiment.
Letter to the Editor—Use of OR in a Data-Processing Operation (A Case History)
Authors: Smith R. L. , Schwartz B. L.
Published: November 2008

An OR type procedure for developing decision criteria is presented, the criteria determine whether to reprocess data through an automatic digital computer or use error-correction routines to modify incorrect results. Error correction routines refer to procedures by which results could be modified without completely duplicating the original computer processing. Conclusions, surprisingly enough, show that the use of error-correction routines is often no more economical than reprocessing even a relatively large set of data.
Letter to the Editor—Monte Carlo Methods and the PERT Problem
Authors: Van Slyke Richard M.
Published: November 2008

Many planning problems can be represented as a network in which the arcs represent “activities” with lengths equal to the time required for the activities performance and the nodes represent “events,” marking the beginning and ending in time of activities. For fixed activity durations, a very simple algorithm gives the length of time required for the total project as well as indicating the activities which are particularly obstructive, those on the “critical path” “PERT” generalizes the above model to recognize uncertainty in the activity durations by allowing them to be random variables. A relatively crude solution to this problem is obtained by reducing the problem back to the first case, by means of appropriate approximation. In this paper the results of a Monte Carlo simulation of PERT networks are given. First the concept of using Monte Carlo methods to give solutions to PERT problems under less restrictive assumptions is discussed. Results are given for the accuracy obtainable, for the computing time required and devices for reducing computation are developed. Finally a “critically” index is defined for each activity. This index is simply the probability that the activity will be on the critical path. The ramifications and uses of this parameter, which is not available using current techniques, are developed.
Letter to the Editor—A Limiting Distribution of an Estimate of Mean Queue Length
Authors: Gebhard Richard F.
Published: November 2008

This letter presents a limiting distribution of an estimate of mean queue length when such estimate is based on a tune series sample taken from a queuing system adequately represented by the M/M/1 model with a first-come, first-served discipline. The results obtained are of use in simulation, model validation, and queuing process control.
Forecasting Periodic Trends by Exponential Smoothing
Authors: Dobbie James M.
Published: November 2008

Some commodities are known to have periodic trends, through seasonal variations and other variations that are repetitive. In forecasting these trends it is desirable to use a set of periodic functions. A method is obtained for the computation of the required coefficients in exponential smoothing when the set of fitting functions consists of a finite number of sine and cosine functions, or such functions multiplied by exponential functions. Explicit expressions are derived for some particular cases.
Queues with Finite Waiting Time
Authors: Ghosal A.
Published: November 2008

The paper considers a single-server queuing system in which a customer does not wait more than a fixed time k, so that if he does not get his service within this time, he departs. Some results are obtained by applying the theory of storage.
Stochastic Variations in Queuing Processes
Authors: Eisen M. , Tainiter M.
Published: November 2008

In this paper we consider a queuing process in which there are two mean arrival and service rates. Not only does the system randomly change from one mode of service and arrival to the other, but units arrive at random and require varying amounts of service. Analytic expressions are obtained for the generating functions, the mean queue length, and the mean waiting time. Several practical illustrations are given.
Markov-Renewal Programming. I: Formulation, Finite Return Models
Authors: Jewell William S.
Published: November 2008

A special structure in dynamic programming which has been studied by Bellman, Blackwell, D'Épenoux, Derman, Howard, Manne, Oliver, Wolfe and Dantzig, and others is the problem of programming over a Markov chain This paper extends their results and solution algorithms to programming over a Markov-renewal process—in which the intervals between transitions of the system from state i to state j are independent samples from a distribution that may depend on both i and j. For these processes, a general reward structure and a decision mechanism are postulated, the problem is to make decisions at each transition to maximize the total expected reward at the end of the planning horizon. The paper is divided into two parts. This part describes the properties of Markov-renewal processes, the reward structure, and the decision process. Algorithms for finite-horizon, and infinite-horizon models with discounting are presented. The second part will investigate the models that have infinite return.
Letter to the Editor—Accuracy, Precision, and Reliableness in Operational Research
Authors: Mayne John W.
Published: November 2008

There appears to be a singular lack of information and discussion concerning accuracy, precision, and reliableness in the practice of operational research. Attention is drawn to this lack and some suggestions are made for overcoming it. Examples are given to show how failure to consider accuracy and reliableness may lead to erroneous conclusions and that it is as important to take account of accuracy and reliableness as it is to have valid models. The two salient points emphasized are that some measure of the accuracy and reliableness of quantitative results should always be given in operational research work and that such measures should be objective rather than subjective. It is hoped that the paper will serve to stimulate discussion on how checks for precision, accuracy, and reliableness can best be made and reported.
Letter to the Editor—An Approximate Method for a Queuing Process with a Randomly Deteriorating Server
Authors: Eisen M.
Published: November 2008

Herein we are concerned with the following situation. A server processes similar items in order of their arrival. The service time is exponentially distributed, however, the mean varies randomly with time and depends upon the state the server as in. Approximate expressions are derived for pertinent parameters—for example, the mean queue length and the mean time spent in each state by the server.
An Outline for Research in Penology
Authors: Roy Robert H.
Published: November 2008

The concept of the “indeterminate sentence” as it is applied to those defined as “defective delinquents” in the State of Maryland is presented in some detail, and a contrast is drawn between the Patuxent Institution, which functions on this basis and conventional penal institutions from which inmates are released after the service of fixed sentences. A research proposal, based upon a cost model, is then presented for the purpose of exploring the desirability of extending the indeterminate sentence concept to a larger fraction of the prison population.
The Primal-Dual Method for Bounded Variables
Authors: Eisemann Kurt
Published: November 2008

This paper presents an extension of the primal-dual method to linear programming problems with bounded variables. Moreover, an attempt is made to give an expository description of the ideas and motivations underlying the computational steps of the primal-dual method.
A Sequential Approach to the Feed-Mix Problem
Authors: Swanson Leonard W. , Woodruff James G.
Published: November 2008

A solution to the feed-mix problem is presented that treats the problem as a part of a decision-making system. Three basic approaches are utilized to solve the problem of continual reformulation of many feeds in order to follow market price fluctuations. The resulting system can produce 20 to 30 new formulations in an hour on an IBM 650. Extension of the system to faster computers would make the system more flexible and responsive to grain market fluctuations.
Trunking Problem
Authors: Hellman Olavi
Published: November 2008

The infinite system L1, L2, …, Lr, … of parallel channels is receiving traffic by a Poisson input. Each call enters at L1, proceeding, if L1 was occupied, along the line of channels until it arrives at an unoccupied channel. Palm has solved the case of identical exponential channels. In what follows we shall consider identical channels with an arbitrary service-time distribution.
The Distribution of the Maximum Length of a Poisson Queue During a Busy Period
Authors: Neuts Marcel F.
Published: November 2008

In the design of waiting facilities for the customers in a queue, it is of interest to know probability distributions of extremal values of the queue length. In this paper we propose to calculate explicitly the probability that [Formula: see text] for all t in [0, t), in which Zt denotes the queue length at time t. This is the probability that in a Poisson queue the server remains busy throughout the time interval [0, t) without ever having as many as b customers in line. We express this probability in terms of the taboo-probabilities with taboo-states 0 and b for a finite continuous time random walk. As an incidental result we obtain new expressions for these taboo-probabilities. It is routine to determine the distribution of the maximum queue length before the next emptiness from our results.
A New Derivation of the Kuhn-Tucker Conditions
Authors: Bernholtz B.
Published: November 2008

The Kuhn-Tucker necessary conditions for a local maximum of a differentiable function subject to differentiable inequality constraints, are derived by showing that the classical necessary conditions for a local maximum of a differentiable function of N variables subject to less than N equality constraints, are also meaningful when there are N or more equality constraints, if appropriate assumptions, similar to Kuhn and Tucker's “constraint qualification,” are made.
Approximate Solutions to the Three-Machine Scheduling Problem
Authors: Giglio Richard J. , Wagner Harvey M.
Published: November 2008

This paper summarizes experimental results from applying several computational methods for solving the classic three-machine scheduling model. The basic mathematical problem is to select an optimal permutation of n items, where the objective function employed is the total amount of processing time elapsing for the completion of all n items on three machines. The methods tested are integer linear programming, ordinary linear programming with answers rounded to integers, a heuristic algorithm, and random sampling. Throughout the experimentation n = 6. A dual integer programming code is tested on six trial problems. Consideration is given to studying the phenomenon of input-form sensitivity. The results are not encouraging and confirm previous experimental evidence as to the strong effect of varying the input form. However, the addition of a powerful bound on the objective function has a significant beneficial effect on the convergence of the dual algorithm. A sampling study of the statistical characteristics of this model is made with 100 sets of data randomly generated. Frequency distributions of minimum and mean total processing time are tabulated and analyzed. On this same set of problems, a linear programming approach is examined for effectiveness in producing nearly optimal schedules. Such an approach tends to give answers that are better than would be obtained by a single permutation drawn at random, but the LP rounded solutions average about an 11 per cent increase over the optimal processing time. A heuristic algorithm based on Johnson's method is tested on 20 of the 100 cases and gives excellent results. Finally attention is turned to the method of randomly sampling the permutations, possibly applying a simple heuristic gradient method to improve each sampled schedule. A feature of this method is that elementary probability theory can be applied to yield corresponding statements about the accuracy guaranteed by the approach.
An Application of Symbolic Logic to a Selection Problem
Authors: Root James G.
Published: November 2008

Given a set of jobs that must be performed, although not necessarily concurrently, a set of resources to perform the jobs, a set of cost measures for the resources, and a set of restrictions on the resources that may be used, the selection problem is to find a least-cost subset of resources that satisfies the restrictions and is capable of performing all the jobs. This selection problem is generalized into minimizing a linear function of Boolean variables subject to Boolean restriction equations. A “smallest” complete set of solutions is found that contains all optimal solutions.
On Single-Server Bulk-Queuing Processes with Binomial Input
Authors: Bhat U. Narayan
Published: November 2008

In this paper, treating time as a discrete variable, we study the transient behavior of a bulk-service queuing system in which the number of customers arriving within a fixed time interval follows a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent. The busy period and queue length distributions have been obtained in terms of probability generating functions.
Scheduling of Vehicles from a Central Depot to a Number of Delivery Points
Authors: Clarke G. , Wright J. W.
Published: November 2008

The optimum routing of a fleet of trucks of varying capacities from a central depot to a number of delivery points may require a selection from a very large number of possible routes, if the number of delivery points is also large. This paper, after considering certain theoretical aspects of the problem, develops an iterative procedure that enables the rapid selection of an optimum or near-optimum route. It has been programmed for a digital computer but is also suitable for hand computation.
Sensitivity Analysis of Multiterminal Flow Networks
Authors: Elmaghraby Salah E.
Published: November 2008

Given an undirected flow network with finite arc capacities, an algorithm is developed for the determination of the effect of a reduction (or increase) in the capacity of any arc on the maximum flow between any two nodes of the network. The algorithm is based on the Gomory-Hu construction of “cut-trees.”
Planning by Resource Allocation Methods—Illustrated by Military Applications
Authors: Taylor James L. , Walsh John E.
Published: November 2008

This paper is concerned with resource allocation problems of a somewhat general nature. For presentation convenience, the material is stated in terms of military planning, where this planning refers to the production and use of types of weapons that have already been developed. The situation can be conveniently phrased in terms of resource allocation with respect to some specified types of weapons that are to be used to attack some given targets. Consider all combinations of target and type of weapon. The problem is to distribute the total available resources (for production and use of weapons) among these combinations in such a manner that the value of the targets surviving the attack is minimized. A deterministic model of an exceedingly flexible nature is developed for representing situations of this nature. Despite the generality allowed, an elementary iterative method is obtained for solving the allocation of resources problem. These results are computer oriented and should be feasible for application even when the model is of an exceedingly complicated nature.
A Queuing Approach to Logistics Systems
Authors: Mirasol Noel M.
Published: November 2008

This paper deals with tradeoffs and major interactions among the different activities in logistics systems. Specifically, the problem of “interchange-ability” between maintenance and supply, embodied in the question of “subassembly vs. piece-part replacement,” is considered. The approach presented consists of a novel method of systems representation: A basic model, which is fundamentally a multistage circular queuing system, is developed for each of the units (assemblies, subassemblies, etc.) that constitute an equipment system. These elementary systems are then connected together with the pattern of linkage made to correspond to the technological breakdown of the over-all system. An interesting result of this approach is that the important measure of effectiveness for any unit is not only its unavailability (probability of stockout), but also the duration of unavailability. Iterative solutions in the case of linear cost functions, a total cost constraint, and the usual exponential assumptions are also presented.
Letter to the Editor—The Incorporation of Step Functions and Ramp Functions into a Linear Programming Model
Authors: Schoomer B. Alva
Published: November 2008

There exist a number of algorithms for solving linear programming problems in which some or all of the variables are required to have integer values. This paper describes a method for solving programming problems in which some of the variables are step functions of other variables that may themselves be continuous or constrained to take only integer values. The method reduces the latter problem to an integer or partial integer programming problem that can be solved by existing algorithms.
The Highway Merging and Queuing Problem
Authors: Evans David H. , Herman Robert , Weiss George H.
Published: November 2008

This paper presents a study of several aspects of the theory of car queues. In it we consider a situation in which there is traffic on a main highway and a queue of cars on a side road waiting to merge. First we consider a case in which the lead driver chooses to merge on the basis of whether the gap in main highway traffic exceeds a service time that is chosen from a probability density. An expression for the generating function of the steady-state distribution and the waiting-time distribution are derived. Secondly, the critical input to the side road is determined such that for all larger inputs the queue is transient. In particular we consider the effect of the move up time (of the second car in a queue) on this parameter. Finally, we present the results of a study by simulation techniques for the analysis of traffic queuing models. A discussion of the use of importance sampling in improving simulation studies is given, and a comparison made between theoretical and simulation results.
Forced Merging in Traffic
Authors: Jewell W. S.
Published: November 2008

A vehicle waiting at an intersection with a major road makes a merging maneuver into the mainstream traffic, thus possibly requiring oncoming traffic to slow down. This paper examines the resulting disturbance that this forced entry may create in the main stream, assumed to be a renewal process. After showing that the disturbance propagation is formally equivalent to the busy period of a related queuing model, explicit results on the length of disturbance period and the number of vehicles affected are obtained for the case of Poisson traffic. It is shown that there is some minimal main-stream headway which should be forced in order to maximize the rate at which entries can be made from the secondary road. Finally, two measures of accident potential for the merging maneuver are discussed.
Letter to the Editor—Solution of a Combinatorial Problem by Dynamic Programming
Authors: Roberts S. M. , Flores Benito
Published: November 2008

A combinatorial problem to determine the least cost of a matrix configuration is solved by dynamic programming. In particular, the application of an algorithm based on an approximation in policy space yields a least-cost configuration consistent with the initial matrix configuration. While the optimization is local in character because of its dependence on the initial matrix configuration, the optimization may be extended to approach global optimization by consideration of a variety of initial matrix configurations. The method lends itself readily to finding the hierachy of configurations ranging from the least to the most expensive.
Multistage Cutting Stock Problems of Two and More Dimensions
Authors: Gilmore P. C. , Gomory R. E.
Published: November 2008

In earlier papers [Opns. Res. 9, 849–859 (1961), and 11, 863–888 (1963)] the one-dimensional cutting stock problem was discussed as a linear programming problem. There it was shown how the difficulty of the enormous number of columns occurring in the linear programming formulation could be overcome by solving a knapsack problem at every pivot step. In this paper higher dimensional cutting stock problems are discussed as linear programming problems. The corresponding difficulty of the number of columns cannot in general be overcome for there is no efficient method for solving the generalized knapsack problem of the higher dimensional problem. However a wide class of cutting stock problems of industry have restrictions that permit their generalized knapsack problem to be efficiently solved. All of the cutting stock problems that yield to this treatment are ones in which the cutting is done in stages. In treating these practical cutting problems, one often encounters additional conditions that affect the solution. An example of this occurs in the cutting of corrugated boxes, which involves an auxiliary sequencing problem. This problem is discussed in some detail, and a solution described for the sequencing problem under given simplifying assumptions.
Some Discrete Processes in the Theory of Stochastic Duels
Authors: Ancker C. J. , Williams Trevor
Published: November 2008

The duel in which the contestant on each side has a fixed kill probability and a random (continuous) time between firings has been previously considered. By limiting the time between rounds to a constant, certain situations in which strong interactions occur are investigated. The models investigated here are (1) the fundamental (one versus one) duel in which firing times are fixed and their ratio is a rational number; (2) the duel with displacements in which two contestants fire simultaneously at fixed intervals and a near miss causes a contestant to displace (and lose a firing turn); (3) multiple duels in which two versus one or two versus two fire simultaneously at fixed intervals; and (4) the cluster duel in which there are several contestants on each side and firing is simultaneous. In the first three, the probability of a given side winning is obtained. In the last, the probability of m contestants on one side killing v of the n contestants on the other side at a single firing is derived.
Multistage Replacement Strategies
Authors: Naik M. D. , Nair K. P. K.
Published: November 2008

In a system containing a large number of a certain unreliable item the replacement cost per unit may be different because of inaccessibility or unusual expense associated with the failure of certain units. For such a system a generalized theory of multistage strategies is developed showing the exact conditions under which it is more economical than the simple replacement policy. This theory is based on the grouping of units according to replacement cost and on the replacement of failures and of vacancies caused by the transfer of units operating in one stage to the preceding stage. The economy is brought in by transfer of failure rates from groups where replacement cost per unit is large to those where it is comparatively small. Procedure for quick computation of savings is also shown. The method of finding the optimum number of stages for multistage strategies is indicated. In the literature two-stage strategies are available; however, they are of limited advantage and multistage strategies will be more economical in many practical cases. Further, only with the aid of multistage strategies is it possible to arrive at the optimum number of stages. As an illustration, three-stage strategies for certain distributions are worked out and they are found to be more economical than the two-stage strategies described in the literature. Finally, some possible fields of applications are indicated.
On Monte Carlo Methods in Congestion Problems: II. Simulation of Queuing Systems
Authors: Page E. S.
Published: November 2008

The application of antithetic variate techniques is shown to possess advantages for variance reduction in a simple queuing system and its application to more complicated situations is proposed.