bluuebunny/crossref_metadata_2025 huggingface dataset:
An Approach to Linear Inventory-Production Rules
Authors: Pinkham Roger
Published: November 2008

A method is presented for choosing the constants in a linear production rule so as to achieve an optimal balance between the cost of inventory fluctuation and cost of production-level fluctuation. The central idea is to measure fluctuation by mean-squared error about some level and to give a ready method for computing these “variances” in terms of certain unspecified constants. The constants may subsequently be picked so as to achieve the desired optimal balance. The subject matter of this paper is one of methodology and does not concern itself with a case history.
The Simplex Method for Beginners
Authors: Wagner Harvey M.
Published: November 2008

Although there are many excellent discussions of linear programming and the simplex method, a beginning student or a person whose high school algebra has grown somewhat rusty finds that the tableau presentation and associated notation are difficult to understand, let alone utilize. Related problems of presentation arise if one is a lecturer allotted only a couple of hours to ‘explain linear programming’. I have had some success in overcoming such problems of exposition with the artificial example given below, which—as will be evident to experienced practitioners of the art—is merely the original simplex method without detached coefficients. Perhaps other beginners or lecturers might also find the presentation of help. I have deliberately taken ‘author's liberty’ in selecting an example that avoids certain troublesome details in the application of the simplex method, some of these details are discussed at the end of the paper.
Dynamic Programming and the Reliability of Multicomponent Devices
Authors: Bellman Richard , Dreyfus Stuart
Published: November 2008

In this paper it is shown how the functional equation technique of dynamic programming may be used to treat a class of problems that arise in the construction of multicomponent devices. We are interested in determining the types of components and the quantities that should be used in order to construct the most reliable device possible subject to given cost and weight constraints. A numerical example is given
Effect of Population Mobility on the Location of Communal Shelters
Authors: Alexander Michael N. , Ferebee J. Brooks , Grim Paul J. , Lebow Leonard S. , Senturia Stephen D. , Singleterry Ann M.
Published: November 2008

A method for estimating the size of an area served by a civil defense shelter as a function of building types is developed, walking speeds, warning and reaction times, and percentage of population to be protected are estimated, queuing at shelter entrances is evaluated. The results obtained are applied to the metropolitan area of Washington, D.C.
Nonstationary Queuing Probabilities for Landing Congestion of Aircraft
Authors: Galliher Herbert P. , Wheeler R. Clyde
Published: November 2008

Illustration is made, with reference to a case study of airport landing congestion in the New York area, of how numerical solutions may be easily obtained for the transient behavior of nonstationary waiting lines characterized by Poisson arrivals, constant holding time, and service in order of arrival. In the case study only the mean arrival rate varies as a given function of time, but the methods used as easily provide for variation also of servicing rate and of number of servers. Exact numerical values are sought and obtained only at intervals of the servicing time. While these times were short in the case study, so that little information is sacrificed, the method may be adapted to yield more frequent values in the case of long servicing times. Subject to this restriction, the entire probability distribution of the queue is calculated as the main numerical routine, from which the distribution of waiting time is directly obtained. Use of a stored-program computer is simple, cheap, and especially effective under saturating arrival rates.
An Approach to a Class of Queuing Problems
Authors: Swensson Olle
Published: November 2008

In a variety of situations, the amount of service activity wanted by a queuer is a function of the length of time during which he has had to wait for it. Additional want of service may emerge as a consequence of his own activity. New events may induce him to change the information, which he wants to communicate to somebody else. The latter case may also be regarded as a two-phase queuing problem. This paper considers the queuing problem characterized by Poisson streams of calls for service from the customers, the intensity of the individual rate of calls, and service times, being dependent on the position of the customer. An approximate solution is given for the general case, and special cases are examined with the aid of Monte-Carlo models. The solution covers a range of “machine-interference” problems and provides a pendant, in the range of finite numbers of customers, to the classical Erlangian solution of the infinite population delay system case. The model also accounts for the well-known fact that statistics frequently indicate a longer remaining duration of a telephone conversation, the longer it has been in progress. It remains to study, how the distribution of service times affects the accuracy of the solution.
Errata
Authors: Laurent Andre G.
Published: November 2008

The author thanks Mr. J. H. Ortman of the Applied Mathematics Department, Chrysler Corporation Missile Division, for drawing his attention to an error in the formula that immediately precedes formula (11), page 83, of his paper “Bombing Problems–A Statistical Approach,” Operations Research 5, 75–89 (February 1957).
Scale of Operations—An Empirical Study
Authors: Bowman Edward H.
Published: November 2008

This study concerns the optimum size of an ice cream branch plant and territory. The company operated ten plants covering a seven state area. At the time of the study, management was uncertain as to even the approximate size of an optimum plant. The study revealed that about six larger plants would be a better system. The company now operates six plants and is considering cutting this number still further.
The Hub Operation Scheduling Problem
Authors: Minas J. S. , Mitten L. G.
Published: November 2008

This paper treats the problem of scheduling a transportation system consisting of one central terminal and a number of outlying terminals. Commodities are transported between the central terminal and outlying terminals, but not directly between outlying terminals. The immediate demand is probabilistic. The criterion function includes the cost of failure to transport commodities when they are available, and the cost of moving transport equipment empty from one terminal to another. An iterative solution procedure, requiring a precomputable number of steps, is developed and illustrated by examples.
Constructing Maximal Dynamic Flows from Static Flows
Authors: Ford L. R. , Fulkerson D. R.
Published: November 2008

A network, in which two integers tıj (the traversal time) and cıj (the capacity) are associated with each arc PıPj, is considered with respect to the following question. What is the maximal amount of goods that can be transported from one node to another in a given number T of time periods, and how does one ship in order to achieve this maximum? A computationally efficient algorithm for solving this dynamic linear-programming problem is presented. The algorithm has the following features (a) The only arithmetic operations required are addition and subtraction (b) In solving for a given time period T, optimal solutions for all lesser time periods are a by-product (c) The constructed optimal solution for a given T is presented as a relatively small number of activities (chain-flows) which are repeated over and over until the end of the T periods. Hence, in particular, hold-overs at intermediate nodes are not required (d) Arcs which serve as bottlenecks for the flow are singled out, as well as the time periods in which they act as such (e) In solving the problem for successive values of T, stabilization on a set of chain-flows (see (c) above) eventually occurs, and an a priori bound on when stabilization occurs can be established. The fact that there exist solutions to this problem which have the simple form described in (c) is remarkable, since other dynamic linear-programming problems that have been studied do not enjoy this property.
Letter to the Editor—Trends in Operational Research
Authors: Bevan Ronald W.
Published: November 2008

Today, operational research is well-known (by name at least) and a respected activity in many industries and in many countries. The International Conference on Operational Research recently held in Oxford bore witness to the world-wide application of the subject, and there can be no doubt that a great deal of effort is devoted currently to operational research throughout the world.
Letter to the Editor—The Widespread Adoption of an Operational Policy and its Effect on the World as a Whole
Authors: Stewart Robert M.
Published: November 2008

I would like to take this opportunity to point out a potentially deplorable situation that arises because of the indiscriminate and wholesale adoption of an operational scheme, namely, the present policy of most of the world's automobile traffic (that in the U.S.) to drive on the right side of the road. It does not require elaborate statistical considerations to indicate that an average slowing down of the earth results from this practice.
Letter to the Editor—Letter to the Editor of Operations Research
Authors: Brothers LeRoy A.
Published: November 2008

This Letter to the Editor of Operations Research is really a letter to the membership of ORSA. I am writing it as a last duty of the oldest living inhabitant of the Council. Having had the privilege of serving as a Council member continuously since the Society was founded, and having completed my long term as Council member at the May 1958 meeting, I am taking the privilege of reading a lecture to you, the members of the Society.
An Integrated Process Control System at the Cummins Engine Company
Authors: Arnoff E. Leonard , Kania Eugene B. , Day Elizabeth Small
Published: November 2008

This paper describes the efforts of an operations-research team working in the areas of order processing and production and inventory control for an engine manufacturing company. Mathematical models were developed and adjusted to the needs of the company. Results were expressed as decision rules, some of which served as tools for clerical personnel, others of which became the bases of logical decisions for an electronic digital computer. Implementation of results was initiated through training of company personnel and the formation of an ongoing operations-research group within the company.
Optimum Information-Acquisition Systems
Authors: Harris B. , Hauptschein A. , Schwartz L. S.
Published: November 2008

The conditions for optimum information acquisition by means of communication systems involve two basic costs (1) average communication cost and (2) average risk cost. Communication cost is determined by the values of the basic communication parameters, power, bandwidth, and time. It depends on the operational conditions of message density, method of modulation, and the coding technique. Risk cost is the cost of decision and arises in the detection of signals in noise. It is a function of the method of decoding received signals and decreases with increasing reliability of detection. Increases in power, bandwidth, and time decrease risk cost and increase communication cost, respectively Specification of the constraints existing between power, bandwidth, and time in an actual communication system permit risk cost as well as communication cost to be expressed as a function of the three communication parameters. Since a trade-off exists between risk and communication costs, the optimum operating condition for a communication system can be found by solving for the minimum average total cost. This method is applied to a comparative evaluation of binary communication systems using three fundamental means for acquiring information in the presence of noise unidirectional, bidirectional employing information feedback, and bidirectional employing decision feedback.
A Mathematical Model of Terrain Shielding
Authors: Hare R. R.
Published: November 2008

An estimate of the effect of terrain irregularities in shielding a target from the burst of a fragmentation weapon is valuable in determining the weapon's effectiveness. In this study a ground-cover function is developed that estimates terrain shielding as a function of burst height, target size, and distance of the target from the burst. This function is then used to examine three representative types of terrain.
The Corporate Planning Process
Authors: Branch Melville C.
Published: November 2008

There is something of a paradox in our use of the word planning. On the one hand, there is widespread agreement that it means looking ahead and is a desirable endeavor. On the other hand, there is considerable confusion concerning just what is implied by the word, and disagreement as to the extent to which planning is a distinctive activity or simply an ordinary aspect of almost everything we do. Thus, we find wide differences and contradictions in the use of the same planning terms, or the assumption they will mean the same thing to different people. Why this confusion and frequent contradiction?
Prediction and Feedback in Business Planning
Authors: McEachron William D.
Published: November 2008

This paper is concerned with how prediction and feed-back fit into business planning. The principal consideration is the integration and interrelation of these three concepts, rather than their separate development.
Joint Optimization of Long-Range Planning and Short-Range Programming
Authors: Verhulst Michel
Published: November 2008

The system of production planning and control described in this paper was devised as a means of stabilizing the inventory level of a ceramics firm that manufactures refractory heat-resistant products such as those used in the linings of blast furnaces.
Letter to the Editor—Commentary on Harling's “Simulation Techniques in Operations Research”
Authors: Moss John Hunton
Published: November 2008

If commentary be construed to include critique, then this commentary must fail in most respects save laudation, should Harling's clearly exposited discussion of points of such manifest pertinence to the area of simulation techniques be considered deficient in any respect, this respect would be brevity. With this in mind, the commentary is directed toward amplification and discussion of points of interest to operations analysts who enjoy the mixed blessing of access to large-scale digital computers.
Errata
Authors: Swensson Olle
Published: November 2008

The author apologizes for the following errors in his paper, “An Approach to a Class of Queuing Problems,” Opns. Res. 6, 276–292 (April 1958).
Optimal Reorder Periods for an Inventory System with Variable Costs of Ordering
Authors: Naddor Eliezer , Saltzman Sidney
Published: November 2008

This paper discusses an inventory system in which the cost per order varies and is dependent on the number of different items listed on the order. The problem is to determine how frequently orders should be initiated and how many different items should be listed on the orders so as to minimize the sum of the costs of carrying inventories and the costs of ordering. An area for application of this study is discussed and models are developed for various ordering policies. Examples are given and the costs associated with each of these policies are compared.
Calculation of Higher Transitions in a Markov Process
Authors: Miehle William
Published: November 2008

The standard matrix method for calculating higher transition probabilities in a Markov process is briefly reviewed in the introduction. This method is extended to path multiplicities. Then a new matrix method for calculating both first arrival probabilities and multiplicities of first arrival paths is presented. The matrix method is also suitable for enumerating paths and for obtaining the diameter of a graph. An example illustrates these methods.
The Value of Irreducibles in the Planning of Service Systems
Authors: Vaswani Ram
Published: November 2008

The research reported in this paper is the result of an attempt to investigate whether analytic techniques can be devised for aiding public administrators in their tasks of making decisions on the design of public service physical facilities. It questions the current practice of using prescriptive formulas that do not explicitly take into account the needs of a community on whose behalf the decisions are made. Then it proposes methods for quantifying decisions currently made and for improving these decisions. Specifically, the paper treats the problem of a criterion that is a two-dimensional vector function with each dimension considered as a measure of a resource expended for the provision and use of a service facility. The quality of service rendered by the facility is a function of the quantity of each one of these two resources used. Since, in general, each community needs, or can afford, a different quality of service, the optimum combination of resources employed will vary from one community to another. The methodology developed in this paper proposes that the actual decisions made by public administrators in regard to the design of service facilities be used as a basis for making commensurate the two dimensions of the cost criterion. It then proposes techniques for aiding administrators in improving their decisions. The proposed methodology is intended to be applicable within the framework of the current value systems of public administrators and it recognizes the limits on their computational capacities and access to information.
Letter to the Editor—Graphical Selection of Military Supply Tables
Authors: Sutherland William H.
Published: November 2008

The writer has had occasion to make certain of the computations referred to in Geisler and Karr's paper on “The Design of Military Supply Tables for Spare Parts,” published in the August 1956 issue of the Journal (vol. 4, pp. 431–442). A somewhat unusual graphical method of making the trial and error computation discussed as Method I of the paper was devised and found to reduce considerably the amount of labor required for the computation. The graphical method is the subject of this letter.
Errata
Authors: Stephan Frederick F.
Published: November 2008

In my article, “Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates,” in the May–June 1958 issue of Operations Research (vol. 6, pp. 399–418), there are several errors that should be corrected.
Operational Analysis of a Traffic-Dynamics Problem
Authors: Chow Tse-Sun
Published: November 2008

The purpose of this paper is to provide a solution to a linear difference differential equation with time lag which governs the motion of a line of traffic. The idea of using operational calculus in solving such types of equations is not new, but the result may be of interest. In addition, a special problem is considered and some consequences derived from the solution.
A Dynamic-Programming Computational Procedure for Optimal Manpower Loading in a Large Aircraft Company
Authors: Bishop Albert B. , Rockwell Thomas H.
Published: November 2008

A dynamic-programming model is developed for the determination of optimal manpower schedules in a large aircraft plant. The basic model consists of a cost equation representing the weekly costs of obtaining, utilizing, and disposing of various categories of personnel. Losses in efficiency in weeks following transfers among jobs or hiring of new men are included. The optimum schedule is that which minimizes the sum of the weekly costs over an arbitrary scheduling period for a given forecast demand. Computation of the minimum-cost schedule is accomplished by use of dynamic programming. This formulation of the problem (a) leads directly to the optimum solution, (b) is independent of the functional form of the cost equation, (c) can utilize tabular data directly without the necessity of curve-fitting, (d) permits ready adjustment for changes in process parameters and demand forecasts, and (e) is readily programmed for computer solution, but, if need be, it can be earned out manually with some simple computational aids. The procedure is illustrated for a hypothetical demand curve and a representative cost equation.
Waiting-Time Distributions for Application to a Series of Service Centers
Authors: Nelson Ross T.
Published: November 2008

The method described in this paper is a result of analyzing job shop production processes as a network of waiting lines at machine (production) centers. The waiting time distribution for a series of N work centers, P[∑j=1j=N Xj ≦ τ], is derived as a function of the waiting-time distributions at the individual work centers, P[Xj ≦ τ], j = 1, 2, …, N, where the cumulative waiting-time probability distribution at each work center is of the form P[Xj ≦ τ] = l − Kj exp(Cjτ), with Cj and Kj constant. The resulting formula for total waiting time is amenable to desk computation and may be useful in estimating job flow time distributions in production control applications for which the first-come, first-served, steady-state model described below is applicable. Also, the method of proof may suggest an approach for convolution in other waiting-line models.
Letter to the Editor—Comments on the Preceding Comments
Authors: Votaw D. F.
Published: November 2008

Author's comment about Fulkerson, D. R., D. Gale. 1958. Letter to the Editor—Comments on “Solution of the quota problem by a successive-reduction method”. Oper. Res. 6 874–875.
Letter to the Editor—A Variant on the Shortest-Route Problem
Authors: Minty George J.
Published: November 2008

The shortest-route problem has been treated by Dantzig [1] with the simplex-method, by Bellman [2] with ‘dynamic programming,’ and by the author with a simple analog computer [3] and with an algorithm derived from a hydraulic analog (unpublished). There is a simple variant on this problem the solution of which is obvious, and yet it does not fit into the formal structure of any of these theories. I present the problem and its solution less for their intrinsic interest than because they may suggest other solvable problems.
Letter to the Editor—The Progress-Curve Computer
Authors: Eisemann Doris M.
Published: November 2008

In the aircraft industry, costs are generally expected to decrease as experience in production increases. To take account of this relation between the quantity produced and the cost of production, the theory of the progress curve was developed which states that within limits there tends to be a linear relation between the percentage increase in output and the percentage decrease in price. Thus costs may be represented by a straight line on a logarithmic grid.
On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem
Authors: Dantzig G. B. , Fulkerson D. R. , Johnson S. M.
Published: November 2008

This paper elaborates a method of attack on traveling-salesman problems, proposed by the authors in an earlier paper, in which linear programming is used to reduce the combinatorial magnitude of such problems. To illustrate the method, a step-by-step solution of Barachet's ten-city example is presented.
Some Differential Games of Tactical Interest and the Value of a Supporting Weapon System
Authors: Weiss Herbert K.
Published: November 2008

The synthesis of weapon-system complexes often involves consideration of tactical models in which combat extends over a period of time with choices of tactics available to both sides and subject to change with time. This leads naturally to the formulation of the problems as differential games. A tactic that lends itself to analysis is the determination of which of several available targets a weapon should choose. This tactic is incorporated in a combat model that includes a primary and supporting weapon system on each side. Optimum tactics are determined, and the implications on force structure determined depending upon the weapon range, cost, and parametrically specified performance.
An Approach to Linear Programming under Uncertainty
Authors: Elmaghraby Salah E.
Published: November 2008

A solution is given to a programming problem under uncertainty when the distribution function of demand is discrete and the cost structure assumes a certain type. The resulting objective function is convex, but not necessarily separable. With a rather simple change in variables, the solution of the stochastic problem is shown to be equivalent to the solution of a linear program.
A Vulnerability Model for Weapon Sites with Interdependent Elements
Authors: Firstman Sidney I.
Published: November 2008

This paper describes a simple “counting” model, employing overlays and probability-grids, which aids in the determination of the trade-offs, measured in survival probability, between site dispersal and hardening for a weapon complex composed of several interdependent elements, separated by distances of less than two lethal radii. The survival-probability expressions are obtained through the use of Markov chains. An example of vulnerability estimation by the use of the model is discussed and referenced.
Coefficient Perturbation of a Constrained Extremum
Authors: Saaty Thomas L.
Published: November 2008

A schedule of allocating labor (in a shipping operation) whose available amount is a function of time, to different tasks, in order to minimize the total cost, is given. The problem is cast in linear-programming form in which all the coefficients are parameterized. An illustration is given followed by a general discussion of the use and limitation of this method, which yields a correspondence between optimal solutions and ranges of time values. The dependence of the optimal value on the parameterized coefficients leads to a sensitivity study.
Parametric Programming and the Primal-Dual Algorithm
Authors: Kelley J. E.
Published: November 2008

This paper studies the close relation between the Gass-Saaty parametric programming algorithm and the “primal-dual” procedures recently exploited by Dantzig, Fokd, and Fulkerson. It is shown that the two procedures are equivalent. The possibility of eliminating the two-phase character of the simplex method using these techniques is discussed. Finally, the application of the techniques to problems with special structure is considered.
On the Allocation of Effort Among Deterrent Systems
Authors: Dobbie James M.
Published: November 2008

A study is made of the allocation of a fixed effort among several deterrent systems. The capability to retaliate should war be initiated by our enemy is used as the deterrence criterion. Assuming that the enemy's blunting effort can be allocated among our deterrent systems with full knowledge of our distribution, what is the best allocation of our effort? This problem is solved in detail for the case in which the alternatives consist of a system of fixed bases and a system of mobile units, such as the land-based titan and the submarine-based polaris. The results are illustrative only.
Letter to the Editor—Comments on “Economic Lot Sizes with Seasonal Demand”
Authors: Wagner Harvey M. , Whitin Thomson M.
Published: November 2008

In an article in the January–February 1959 issue of Operations Research, Mark B. Schupack has supplied harmonic analysis to the problem of determining economic lot sizes in the face of seasonal demand. While the paper is a contribution to the theoretical analysis of the problem, it seems of limited use from a practical point of view.
A Comparison of Maximum-Seeking Methods
Authors: Brooks Samuel H.
Published: November 2008

The steepest ascent, univariate, factorial, and random methods for seeking maxima were compared by trying versions of them in several two-factor situations, with and without experimental error. Of the two sequential methods, the steepest ascent was better than the univariate. Of the nonsequential methods, the factorial was better than the random. The sequential methods were superior to the nonsequential.
Stationary Single-Server Queuing Processes with a Finite Number of Sources
Authors: Harrison Gerald
Published: November 2008

Some basic relations are obtained that apply to finite single-server stationary queuing processes. These relations depend only on the mean service time and mean source idle time and not on the form of the distributions. When the source idle time follows a negative exponential distribution, the service time distribution being arbitrary, the length of the waiting line at instants of completion of service is a Markov chain. Its distribution as well as the waiting-time distribution is obtained. The results are specialized to the cases of negative exponential and constant service times.
An Optimum Policy for Detecting a Fault in a Complex System
Authors: Gluss Brian
Published: November 2008

Consider a complex system consisting of N modules containing n(1), …, n(N) items or sub-circuits. A very simple device of this nature, for example, would be a hi-fi set, where the amplifier, the cartridge, the speaker(s) and the turntable could be considered to be the modules, and the various parts of each as the basic items in which faults could occur. A more realistic application of the results obtained might be to a radar-missile system, in which surveillance radar, tracking radar, communications system, computer, missile launcher and missile, or parts of them, represent the modules. When the system breaks down, the procedure for detecting the breakdown and hence repairing the system will determine the time taken to repair it. Assuming two different possible models, equations are developed for the optimum policy, i.e., the policy which minimizes the expected amount of time consumed or penalties paid, and these equations are solved for the first model. Model I assumes that over-all tests of each module may be performed, and individual item tests within modules, model II assumes that over-all module tests are not possible, and that penalty costs must be paid whenever the search moves from one module to another. In both models, penalty costs—in time, for example—are associated with the testing of each item and module.
Car-Following Theory of Steady-State Traffic Flow
Authors: Gazis Denos C. , Herman Robert , Potts Renfrey B.
Published: November 2008

The steady-state flow is examined for a car-following model in which the acceleration at time t of a car attempting to follow a lead car is proportional to the relative velocity at a time t − Δ and in which the sensitivity λ is no longer taken constant as in previous work but is inversely proportional to the car spacing. The characteristics of the steady-state flow for this model are described and compared with experimental data.
On Optimal Redundancy
Authors: Black Guy , Proschan Frank
Published: November 2008

A complex system is to be placed in the field for a fixed period. During the period only the spares initially provided may be used to replace components that have failed. Independence of failures is assumed among the essential components considered. Given the cost of components, the number of like components of each type simultaneously operating, the length of operation scheduled for each component, the failure distributions of components, a general mathematical solution is obtained for the composition of the spare parts kit which maximizes assurance of continued operation during the period, subject to a fixed budget for spares. Explicit formulas are obtained in the case of exponential failure distributions, constructive procedures in the case of monotone likelihood ratio densities. Fortunately, the identical mathematical model is applicable in determining the optimal allocation of redundancy in designing system reliability under a weight or cost restraint.
Optimum Search for Objects Having Unknown Arrival Times
Authors: Blachman Nelson , Proschan Frank
Published: November 2008

In defense against missiles, early detection is crucial. This is the motivation for the mathematical solution of the following general search problem. Objects arrive in accordance with a Poisson process. Having arrived, the object appears (and remains until detected) in box i with probability pi. A single scan of box i costs Ci (possibly including the cost of false alarms), takes time ti, and, if the object is present in box i at the beginning of the scan, will detect it with probability Pi. The resultant gain gi(t) is a nonincreasing function of t, the delay between arrival and the beginning of the detecting look, i = 1, 2, …, n. An asymptotically optimum search procedure is obtained. A number of particular cases of interest are solved.
The Time-Dependent Problem for a Queue with Preemptive Priorities
Authors: Heathcote C. R.
Published: November 2008

Use is made of the Laplace transform to study the two-dimensional preemptive priority queuing problem with exponential arrival and service times. The method of generating functions is used to solve the difference equations so obtained. In the section “The Differential-Difference Equations for the System” the transform of the generating function of the queuing process is given and the moments of the distribution of the nonpriority queue length derived from this. An explicit solution is given only for the case of equal service rates, the general case requiring only additional calculation. The distribution of the length of a busy period for the nonpriority queue is studied later.
A Safety Index for Traffic with Linear Spacing
Authors: Kometani Eiji , Sasaki Tsuna
Published: November 2008

The authors have tried to improve the traffic dynamic theory of Professor Pipes and have found the fundamental equation of traffic dynamics for a case in which the velocity of the following vehicle is determined not only by the space between following and lead cars but also by the velocity of the lead car. The safety of the following car with respect to rear end collision when the lead car is in sinusoidal motion is quantified by introducing a safety index. At the same time, the authors describe the stability of the indicial response of the following car, and the stability of the propagation of a sinusoidal disturbance down a line of cars.
A “Monte Carlo” Approach to Evaluate Multimoded System Reliability
Authors: Curtin Kenneth M.
Published: November 2008

A mathematical model of a multimoded system is presented and a Monte Carlo technique is used to predict and evaluate system reliability.
Mechanisms for Linear Programs
Authors: Sinden Frank W.
Published: November 2008

Linear programs can be represented by simple mechanisms compounded of strings and rods. In schematic form these are useful because they render many of the facts about linear programs, especially those related to duality, immediately evident. It is shown, for example, that the Dantzig-Ford-Fulkerson primal-dual algorithm has a particularly simple interpretation in terms of a mechanism. Some of the mechanisms lend themselves well to physical realization. A small, homemade model of one for the transportation problem is described in the last section.
Development and Application of a Terminal-Air-Battle Model
Authors: Taylor James L.
Published: November 2008

The development and applications of a terminal engagement model of a Monte Carlo type fighter-bomber battle is presented. Sequential progression and sampling techniques are applied to the fighter-bomber duel, allowing realistic evaluation of the effects of airborne vehicle and equipment characteristics, bomber countermeasures, fighter tactics and counter tactics, and fighter-bomber intelligence exchange upon the outcome of a terminal air battle. Possible extensions and refinements of the model are also presented.
Letter to the Editor—Comments on “Brownian Motion in the Stock Market”
Authors: Laurent A. G.
Published: November 2008

Comments on the paper “Brownian Motion in the Stock Market” [Osborne, M. F. M. 1959. Opns Res. 7 145–173.].
Letter to the Editor—High-Level Operations Research Activity in the U.A.R.-Egyptian Region
Authors: Saaty T. L.
Published: November 2008

In March of this year I visited the United Arab Republic-Egyptian Region, to look into mathematical and operations-research progress for the Office of Naval Research. I met several people in research, learned about their activity and gave lectures in operations research and mathematics both at the University of Cairo and at the National Planning Committee, which is in the ideal position of being able to examine problems arising on a national scale in Egypt.
Letter to the Editor—Selection of an Initial Solution for the Traveling-Salesman Problem
Authors: Dacey Michael F.
Published: November 2008

The present writer has developed a procedure that is not iterative and that rapidly selects a single solution. Experience in solving a number of problems by this method discloses a persistent, though not necessary, tendency for these solutions to approach optimum.
Letter to the Editor—Design of Threat Models
Authors: Tombach Harold
Published: November 2008

The purpose of this Letter is to formalize an approach to threat model design that provides the model builder with criteria for selecting, from the universal set of all possible threat models, a limited subset of models that are realistic, usable, and useful. It is believed that this approach will contribute to the elimination to a large degree of the arbitrariness that often accompanies the design of the more complex threat models. It is realized, however, that consciously or subconsciously many a threat model designer is likely to have used in his work some or all of the principles discussed in this letter.
Computing Tetraethyl-Lead Requirements in a Linear-Programming Format
Authors: Kawaratani T. K. , Ullman R. J. , Dantzig George B.
Published: November 2008

There are some types of nonlinearities that are difficult to incorporate into a linear-programming model. One of these occurs in the scheduling of refinery operations where linear-programming methods are widely used. The specific problem is the one of simultaneous determination of the quantities of various components of gasoline and tetraethyl lead to blend to form regular or premium type gasolines. It is believed the general approach can be used for other nonlinear situations. Linearization is accomplished by viewing the lead requirements of a blend first as a known general function of two variables each of which is a linear function of the quantities in the blend. The general function is then approximated by a convex linear combination of a mesh of representative points.
System Reliability as a Function of System Age; Effects of Intermittent Component Usage and Periodic Maintenance
Authors: Flehinger Betty J.
Published: November 2008

This paper is concerned with the analysis of the reliability of complex systems in which components are used intermittently and which are maintained in operating condition by component replacement. The idea that a failed component causes system failure only when it is called into use is expressed mathematically. Based on component failure distributions and usage properties, the system reliability and expected time to system failure are derived as functions of system age for two different maintenance policies. With both policies, a component is replaced whenever it causes system failure. In the first, this is the only maintenance, while in the second, system check-outs are conducted at fixed intervals and all components which have failed without causing system failure are replaced. The two policies are compared and, for the second, the dependence of system reliability on the maintenance interval is determined.
A Forecasting Method for Management of Seasonal Style-Goods Inventories
Authors: Hertz D. B. , Schaffir K. H.
Published: November 2008

Because of high obsolescence costs, optimum decisions on the amounts of highly seasonal, styled items to place into inventory in anticipation of customer orders hinge primarily on the probabilities of selling these amounts before the end of the season. In a study of the operations of a textile manufacturer, methods, were developed for determining (based on sales data) the duration and timing of the selling seasons, and for forecasting total sales for the season for each individual item in the line, at different probability levels. From these, criteria for weekly re-evaluation of inventories are established.
Diffusion Attrition Model
Authors: Ash Milton
Published: November 2008

In attempting to investigate the attrition of a large target complex (raid) caused by attacking manned or unmanned interceptors, the analogy to the diffusion of electrons or neutrons in suitable media, or similarly, radiation transport in a stellar atmosphere, suggests itself. The interceptors correspond to the diffusing particles while the target complex corresponds to the transporting medium. The particles undergo absorption and elastic scattering in the transport medium, while the interceptors “lock-on” to and destroy targets (absorption), or “break-lock” and possibly seek new targets (scattering) in the target analogue medium. Depletion of the target medium as a result of attrition, which does not usually occur in particulate diffusion, must be taken into account in the target medium analogue. Consideration of the usual interceptor capabilities usually leads to a target medium with “heavy absorption” and “light scattering” properties. The above analogue is used to determine the attrition in target number density in time and space. This is accomplished by finding solutions to the transport equation for the interceptor flux density in the target medium. Solving this integro-differential equation comprises the central effort, since analytical solutions are known exactly only in an isolated number of cases. The transport equation in the interceptor flux and an equation obtained for the target medium density constitute a pair of simultaneous equations. Eliminating the interceptor flux density between these equations yields the sought for expression of time and space history of attrition in the target medium. An illustrative problem is given with an outline of its solution.
Choice of Pay-Offs for Military Operations of the Future
Authors: Brooks Douglas L.
Published: November 2008

Studies which relate to decisions affecting the course of possible military operations in the distant future face the familiar pitfalls of operations research in a particularly aggravated form, due principally to the broad context in which such decisions typically appear. This paper discusses means for avoiding undesirable suboptimization, for including the effects of feedback and competition, and for introducing the effect of significant constraints when choosing criteria on which to base long-range planning decisions. Several new measures of merit are presented which emphasize the feature of “R and D” leverage over potential enemy countermeasure developments. For decisions affecting possible near-term military operations, it is suggested that operations-research studies can profitably emphasize the optimization of (a) deployment of existing forces, (b) military decision-making processes. These near-term problems, like their long-term counterparts, must also be studied with reference to future goals.
Some Numerical Experiments for an M × J Flow Shop and its Decision-Theoretical Aspects
Authors: Heller J.
Published: November 2008

Numerical experiments for M × J deterministic flow shops performed on an IBM 704 digital computer lead to the conclusion that the schedule times are approximately normally distributed for large numbers of jobs. The meaning of this result in the decision-theoretical problem of sampling for a minimum is discussed. Examples of these results for 10 × 100 and 10 × 20 schedules are given.
The Utility of Statistics of Random Numbers
Authors: Clark Charles E.
Published: November 2008

The utility of tables of random numbers is enhanced when statistics of the numbers are known. Such statistics permit, inter alia, the efficiencies of stratified sampling. This fact is indicated by numerical examples. Computer Monte Carlo is also discussed.
Solutions of the Shortest-Route Problem—A Review
Authors: Pollack Maurice , Wiebenson Walter
Published: November 2008

Several methods are available for determining the shortest route through a network. These methods are described in some detail with added remarks as to their relative merits. Most of the methods are intended for both manual and digital computation, however, two analog methods are included. Brief mention is also made of the duality between the shortest-route problem and the network capacity problem.
Review of Port of New York Authority Study
Authors: Edie Leslie C.
Published: November 2008

One of the papers from the Symposium Case Histories Five Years After, held at the Fourteenth National Meeting of the Society, in St. Louis, Missouri, October 23, 1958.
Computers in Medical Data Processing
Authors: Ledley Robert S. , Lusted Lee B.
Published: November 2008

This paper contains a brief resumé of the ideas inherent in the utilization of digital electronic computers in medical data processing. Concepts associated with the application of a sequential decision theory applied to the analysis of medical diagnosis, and with the accumulation and recall of individual medical records, are discussed. The conclusion is reached that the great significance of a national health computer network cannot be overestimated, both as an aid to increasing individual good health and longevity, and as a vast new source of medical information concerning mankind. Present day computer technology indicates that such a health computer network is entirely feasible.
Efficiency Criterion for Comparing Cargo Aircraft in Deliveries between Two Terminals
Authors: Brady Roy P. , Walsh John E.
Published: November 2008

The ability of a given cargo aircraft and cargo-handling system combination to perform a specified task can be influenced by a large number of factors. This paper identifies the more important of these factors and presents a quantitative criterion for measuring the relative efficiency of combined air-cargo systems of this type. Although developed for the case of only two air-freight terminals, this criterion can be useful for situations involving many terminals.
An Extremal Production-Line Problem
Authors: Supnick Fred , Solinger Jacob
Published: November 2008

Let G1, …, Gr be groups of n1, …, nr workers on a production line, all members of Gi performing identical operations in the time ti on entities drawn (repeatedly) from a pool Pi. When the production line starts all members of G1 are put to work at the time T1, and some time thereafter all members of G2 are put to work at the time T2, etc. We assume that n1/t1 = ⋯ = nr/tr ≡ R. Let dj = g.c.d. (nj−1, nj). We prove the theorem. Let Tj−1 = 0. Then Tj = (nj−1 + nj − dj)/R is the earliest time at which Gj can be put to work so that supply for Gj is at any time greater than or equal to demand (j = 2, …, r).
The Flow of Highway Traffic Through a Sequence of Synchronized Traffic Signals
Authors: Newell G. F.
Published: November 2008

We consider here the delays suffered by a car in passing through a long sequence of synchronized traffic signals, assuming that the density of traffic is low enough that one can neglect the interactions between cars, and that each car has a desired speed which it maintains at all times except when stopped by a traffic light. By considering the special case of equally spaced lights, we conclude that for short distances between lights the relative phase of the traffic lights that gives a minimum average delay per light depends upon the fraction of green time of the traffic cycle. For long distances between lights, it is found that the usual progressive timing of lights may cause greater delays than a random synchronization but in such cases there are other schemes of synchronization that are still better. Finally, some qualitative effects of velocity fluctuations are discussed.