bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Optimality of Pure Strategies
Authors: Wagner Harvey M.
Published: November 2008

In Manne [Manne, A. S. 1960. Linear programming and sequential decisions. Management Sci. (April).] has suggested a linear programming formulation for on optimal steady state solution of sequential decision models. In this note we offer a proof which appeals primarily to the properties of linear programs that an optimal solution exists involving only pure strategies.
Simulation of a Simplified Job Shop
Authors: Baker C. T. , Dzielinski B. P.
Published: November 2008

This is a report of the results of some digital computer simulation studies of a simplified model of a job shop production process. Such factors as the average effectiveness of schedules under the impact of random variations in processing times and the effect of changing operating policies are considered. The average manufacturing times and predictability of completion times were used as measures of effectiveness.
Optimal Policies for a Multi-Echelon Inventory Problem
Authors: Clark Andrew J. , Scarf Herbert
Published: November 2008

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment of stock, this shipment will be delivered in a fixed or perhaps random length of time, but at any rate with a time lag which is independent of the size of the order placed. There are, however, a number of situations met in practice in which this assumption is not a tenable one. An important example arises when there are several installations, say 1, 2, …, N, with installation 1 receiving stock from 2, with 2 receiving stock from 3, etc. In this example, if an order is placed by installation 1 for stock from installation 2, the length of time for delivery of this stock is determined not only by the natural lead time between these two sites, but also by the availability of stock at the second installation. In this paper we shall consider the problem of determining optimal purchasing quantities in a multi-installation model of this type.
Some Team Models of a Sales Organization
Authors: McGuire C. B.
Published: November 2008

The models presented in this paper grew out of an attempt to apply the theory of teams of Marschak and Radner to the organization of the sales force in a typical wholesale bakery. As organizations go, the one we have chosen to analyze is an extremely simple one, even when—as is quite obviously not the case in what follows—it is viewed in its full complexity. At the risk of achieving results of quite limited general interest, a “simple,” easily quantified subject was deliberately chosen as the best place to begin to apply a theory that pretends to prescribe optimum decisions of a team in a precise way.

We shall not here go much beyond a discussion of some mathematical models which deal only with the day-to-day problem a bakery sales force faces in attempting to “properly” supply its regular customers with a single product. Problems of advertising, of price policy, of product design, and of obtaining new customers are ignored. All the reader needs to know, to begin with, is that the sales force consists of truck-driver salesmen who daily visit each of their given customers (i.e. grocery stores) leaving, on consignment, an amount of bread to be decided by the salesman. At the end of the day the salesman returns to the plant and submits an order for the next day. For our purposes here the “organization” is characterized by the way in which these orders are jointly formed. In the last section, after the models have pin-pointed the organization problem, we shall return to a more detailed description of procedures found in practice.
The Balance Delay Problem
Authors: Kilbridge M. , Wester L.
Published: November 2008

Balance delay time is the amount of idle time on production assembly lines caused by the uneven division of work among operators or stations. It is related to the extent and way the total task is subdivided. In this paper the problem of balance delay is treated empirically and analytically. Empirical studies show that high balance delay is associated with a wide range of work-element times and a high degree of line mechanization. The analytical study yields a general algebraic method of minimizing balance delay by the appropriate choice of cycle times. Balance delay functions are drawn and the condition of perfect balance is shown to coincide with the zero points of these functions.
A Model of Customer Behavior for the Task Manufacturing Corporation
Authors: Sprowls R. Clay , Asimow Morris
Published: November 2008

The Task Manufacturing Corporation is a computer-simulated business firm. The objective is to simulate the operations of a real business firm on a greatly contracted time scale for use in education and research. The methodology is to build a business firm from detailed models of its subsystems.

This paper discusses the model of one subsystem, the customer, who is viewed as a participant in an organization and whose behavior involves such participating notions as inducements, contributions, satisfactions, dissatisfactions and searches for alternative sources of supply.
Sensitivity Analysis of Cost Coefficient Estimates: The Case of Linear Decision Rules for Employment and Production
Authors: Van De Panne C. , Bosje P.
Published: November 2008

This paper considers the consequences of errors in the cost function which underlies linear decision rules generally and in particular those developed by Holt, c.s., for the paint factory case. By differentiating the decision rules with respect to the various cost coefficients expressions for the decision errors due to errors in the cost function are obtained. First-period decision errors corresponding to a one per cent error in each of the cost coefficients are given numerically, together with first-period losses. Only infinite horizons are considered.
A Structural Method of Computing Project Cost Polygons
Authors: Prager William
Published: November 2008

For a project that consists of numerous jobs subject to technological ordering restrictions the polygon representing project cost versus completion time is to be determined when the normal and crash completion times are known for each job and the cost of doing the job varies linearly between these times. A linear programming formulation of this problem was given by Kelley [Kelley, J. E., Jr. 1961. Critical-path planning and scheduling: Mathematical basis. Oper. Res. 9 296–320.] and a network flow formulation by Fulkerson [Fulkerson, D. R. 1961. A network flow computation for project cost curves. Management Sci. 7 (2, January) 167–178.]. Since the traditional mathematical background of civil engineers includes neither linear programming nor network flow theory, these methods are not as widely used in the building industry as they deserve. This paper shows that Fulkerson's algorithm can be given a structural interpretation using concepts that are familiar to civil engineers.
The Derivation of Probabilistic Information for the Evaluation of Risky Investments
Authors: Hillier Frederick S.
Published: November 2008

The amount of risk involved is often one of the important considerations in the evaluation of proposed investments. This paper is concerned with the derivation of the type of explicit, well-defined, and comprehensive information that is essential for an accurate appraisal of a risky investment. It is shown how, under certain assumptions, such information in the form of the probability distribution of the present worth, annual cost, or internal rate of return of the proposed investment can be derived. The derivation and use of this information is then illustrated by an example.
Indices of the Hierarchical Structure of Industrial Organizations
Authors: Evan William M.
Published: November 2008

A postulate common to both the structural-functional theory of social stratification and to organization theory is that hierarchical organization is functionally necessary. An alternative formulation of this postulate—which is probably more heuristic—is that different degrees of hierarchical organization have different consequences for total and partial social systems.

The present inquiry into the problem of measuring organizational hierarchy begins with the selection of three central dimensions of organization: the hierarchy of skills, the hierarchy of rewards, and the hierarchy of authority. For each dimension an attempt is then made to develop and codify one or more indicators. The question of the empirical application of the indicators of the hierarchical dimensions in turn leads to a consideration of the problems of index construction, analysis of change over time, analysis of causes and consequences of variation in degree of organizational hierarchy, and of comparative research, whether cross-national, cross-organizational, or experimental in character.
A Study of Inventory Theory
Authors: Geisler Murray A.
Published: November 2008

The paper is divided along the following lines. First, I illustrate the inventory models having Deterministic Demand and then consider the class of Probabilistic Demand Models. Within the latter class, I consider the single period steady state case, and then the N-period dynamic inventory model. For the N-period case, I then report results covering non-zero procurement lead time, demand rate varying each period, joint solution of the inventory-control-production scheduling decision, and a multi-echelon model. Finally, since in the previous consideration of probabilistic demand models, knowledge of the demand probability distribution and its parameters were assumed, I discuss a paper dealing with the use of Bayes estimates.
The Effect of Promotional Effort on Sales
Authors: Magee John F.
Published: November 2008

The management of an industrial enterprise is constantly faced with the problem of deciding how much advertising, selling, or promotional effort is economically justified. A reasonable response to this question implies at least an intuitive knowledge of the relation between sales volume and promotional effort. This paper presents a case study of the development of such a relationship.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—Report on the First Summer Program on Operations Research at the Massachusetts Institute of Technology, June 16–July 2, 1953
Authors: Morse Philip M.
Published: November 2008

This 15-day special course in operations research, for persons from industry, government, and the military services, was planned and supervised by the Institute Committee on Operations Research: Prof. Philip M. Morse, Department of Physics, Chairman; Prof. G. P. Wadsworth, Department of Mathematics; Prof. N. C. Dahl, Department of Mechanical Engineering; Prof. M. J. Gordon, School of Industrial Management; Prof. W. K. Linvill, Department of Electrical Engineering; Prof. H. M. Paynter, Department of Civil Engineering; and Mr. A. N. Watson, Research Associate, School of Industrial Management.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Network Dispatching by the Shortest-Operation Discipline
Authors: Conway R. W. , Maxwell W. L.
Published: November 2008

The significance of the dispatching function in production planning and control is discussed and applicable results in sequencing and queuing theory are reviewed. Experimental results for a network of queues representing a small job shop are presented. The investigation involved the comparison of dispatching at random with dispatching in order of increasing processing time under different conditions of shop size, flow pattern, and level of work-in-process inventory. Also considered is the effect of imperfect a priori knowledge of processing times upon the shortest-operation discipline Several modifications of the shortest-operation discipline were also tested one in which the shortest-operation discipline is ‘truncated’ and another in which it is periodically alternated with a first-come-first-served discipline.
Some Problems in Traffic Delay
Authors: Weiss George H. , Maradudin Alexei A.
Published: November 2008

The problems that are considered here concern the delay to a single car waiting at a stop sign for a sufficiently large gap in the oncoming traffic to present itself so that the driver considers it safe to cross the highway. The systematic application of renewal theory techniques offers a method of solving these problems, which is much simpler than the combinatorial solutions published by Tanner and Mayne in the treatment of somewhat simpler versions. It is assumed that successive gaps in the main highway traffic are uncorrelated random variables with known probability density. We treat the case that the probability of crossing the highway is a known function, a(t) rather than a step function. It is shown that the distribution of delay times satisfies a convolution integral equation, and that the moments are easily found using Laplace transforms Integral equations are also found for the delay distribution when the gap distribution is non-stationary, e.g., when traffic light effects are important. Finally the case of semi-Markov correlated gaps are considered, and a formal expression for the delay distribution is given.
Strategy of Data Selection for Adaptive Automation
Authors: Rudd Dale F.
Published: November 2008

The problems of selection of logged process variables by a control computer with limited memory for continuous on-line process automation in the presence of erroneous, erratic and irrelevant data sources are considered from a strategic viewpoint. Markov and simple learning strategies are presented that allow a computer to learn about the current behavior of a process with respect to variable relevancy, resulting in a considerable increase in data selection efficiency over a random selection strategy. The case of single variable selection using a Markov strategy is solved analytically and computer simulation is used to estimate the performance of a simple learning strategy.
Least-Cost Allocations of Reliability Investment
Authors: Kettelle John D.
Published: November 2008

This paper presents two complementary techniques for determining optimal allocation of reliability investment in a multi-stage system. The first is a step-wise dynamic programming algorithm, which has proved to be a simple and direct means for obtaining the exact solution to the basic problem of least-cost allocation of redundancy. The second technique is an explicit solution to the investment allocation problem if the unreliability of each stage decreases exponentially (and continuously) as its cost increases. This solution is based on an inequality, which for reasonably reliable systems justifies minimizing the sum of the stage unreliabilities instead of the system unreliability.
Bombing Problems—A Statistical Approach II
Authors: Laurent Andre C.
Published: November 2008

A continuation of “Bombing Problems, A Statistical Approach,” Opns Res, 5, 75–89 (1957), this paper studies the probability of a hit within a circle centered at a moving target (kill probability) from the viewpoint of statistical inference. The best estimate of such a probability based on results obtained in past experiments, is given when the precision of the bombing apparel is unknown and bombing is performed under already observed experimental conditions. A “predictive” probability is derived in case bombing is performed under new experimental conditions. “Dangerous” regions around the target are discussed. A method is proposed to obtain the best estimate of a hit within a fixed area when the apparent target differs from the unknown true target. Generalizations to three dimensions are outlined.
New Methods in Mathematical Programming—Optimal Flow Through Networks with Gains
Authors: Jewell William S.
Published: November 2008

The special class of linear programs described as network flow problems includes many of the special structure optimization problems in such areas as assignment, transportation, catering, warehousing, production scheduling, etc. Besides the physical motivation of the flow description, this class of problems possesses conceptually simple, and computationally elegant, solution techniques originated by Dantzig, Ford, Fulkerson, et al. This paper describes a generalization of this class of problems to “process-flow networks,” or “flow with gains,” in which flow in any branches of the network may be multiplied by an arbitrary constant, called the branch gain, before leaving the branch and flowing into the remainder of the network. This generalization permits the description of networks in which different kinds of flow may be converted one to another, without “constant returns to scale.” Among other interesting problems, this model includes the metal-processing problem, the machine-loading problem, financial budgeting, aircraft routing, warehousing with “breeding” or “evaporation,” the two-equation capacitated linear program, etc. The solution method here described and proved is a natural extension of Ford and Fulkerson's technique (or specialization of the primal-dual method) and retains much of the physical motivation and easy computational aspect of their technique, a direct starting solution is usually available, and optimization of the imbedded linear program (the restricted primal problem) can be accomplished without the use of the simplex technique. Conceptually, the solution procedure consists of the following steps Find the incrementally cheapest loop in the network that will absorb flow Establish as much additional flow into the network along this route as possible Repeat Steps (1) and (2) until the desired flow is established, or until infeasibility is discovered The solution technique includes a maximal-flow procedure and produces a “min-cut equals max-flow” theorem for networks with gains. Additional features, such as piece-wise linear convex costs, parametric studies, network “tearing,” mixed boundary conditions, etc., may be easily incorporated in the algorithm.
Analysis of a Procedure for Controlling Discrete Stochastic Processes
Authors: Pritsker A. Alan B.
Published: November 2008

In this paper an analysis is made of a specific procedure for controlling one independent variable described by a discrete stochastic process. Operational or actual tolerances are specified for the variable, that is, a range of acceptable variation is given. The control procedure involves the making of corrective actions to maintain the process within the actual tolerance. To accomplish this, effective tolerance limits (which are smaller than the actual tolerance limits) are set. Corrective actions are then made whenever the process exceeds the effective tolerance limits. A method for setting the effective tolerance limits to minimize the expected equilibrium cost of control per trial of operation is given. The method uses the assumption that corrective actions can be considered as recurrent events. From the theory of recurrent events, expressions for the probabilities of making corrective actions can be developed for inclusion in the equation which relates the cost measure to tolerance setting. By differentiating the cost measure with respect to the effective tolerance setting, a minimum solution can be obtained. The equations for minimization are developed first for general stochastic processes. The recurrent-event method is then extended to processes not necessarily returned to initial conditions by corrective actions. Specific equations are developed which optimize the control of discrete homogeneous Markov Gaussian processes. An example is given in which the optimal control procedure is analyzed as a function of the parameters of such a process.
Kill Probability when the Weapon Bias is Randomly Distributed
Authors: McNolty Frank
Published: November 2008

This paper presents derivations of formulas for the probability of killing a point target and for the expected coverage of a population of targets when the bias of the weapon system is randomly distributed in accordance with a prescribed density function. The paper considers six cases in which the bias distributions are the gamma (2, 3), beta (2, 3), Maxwell-Boltzman (2) and Rayleigh (3), where the numbers in parentheses indicate the dimensionality of the associated kill and coverage problem. The concept of a random bias is important in situations where a unimodal distribution is perturbed by forced scattering (random or deterministic) into a density whose mode lies along a locus of points (2 dimensional) or on a surface (3 dimensional). The notion is also important when a sampling (or an a priori analysis) of the weapon system indicates that the bias is randomly distributed rather than fixed or when the concept of target evacuation is involved, in determining weapon effectiveness. The analysis in this paper is one which employs integration and special functions in the course of deriving kill and coverage formulas. Conceptually, the discussion is based upon extremely rudimentary principles of probability theory and makes no contributions to this latter field.
Differential Calculus in Nonlinear Programming
Authors: Wilde Douglass J.
Published: November 2008

Using only well-known theorems of the differential calculus, we derive necessary conditions for a relative minimum of a nonlinear differentiable objective function of nonnegative variables constrained by nonlinear differentiable inequalities. The results are expressed entirely in terms of partial derivatives, which are subsequently identified with the Lagrange multipliers of the Kuhn-Tucker nonlinear programming theorem. Our conditions may be considered therefore as the Kuhn-Tucker theorem in differential rather than Lagrangian form.
A Missile Allocation Problem
Authors: Piccariello Harry J.
Published: November 2008

The problem of finding the allocation of weapons to a target system that results in the largest payoff is present in almost every war gaming exercise. A technique often employed to find a solution to such a problem is to consider the problem as a continuous allocation process. However, the continuous solution may not furnish the solution to the actual problem, which is a discrete allocation process. This paper presents a solution to a missile allocation problem when the problem is considered in its continuous form. This same problem is investigated in its discrete form and it is shown that the solution in the continuous case is not, in general, a solution for the discrete case. Further, a necessary condition is derived for the existence of a solution for the discrete problem that differs from the solution for the corresponding continuous problem.
Letter to the Editor—Reduction of Letter Delays Between Post Offices
Authors: Samuel Aryeh H.
Published: November 2008

In a paper by Oliver and Samuel (Oliver, R. M., A. H. Samuel. 1961. Reducing letter delays in post offices. Research Report 11, Operations Research Center, University of California, Berkeley, Opns. Res. 10 839–892 (1962).), methods were developed for the minimization of the delay of letters in their flow through a post office in the city of origin. It was shown that this delay is a sensitive function of the time of the dispatch by which they leave the office. We shall now consider briefly an introductory treatment designed to minimize the total letter delay from collection to delivery.
A Decision-Theory Approach to Missile Defense
Authors: Gorfinkel Martin
Published: November 2008

The defense being attacked by a warhead concealed in a cloud of decoys has a problem that belongs in the realm of decision theory. Here it is assumed that the defense gets one measurement on each object, this measurement is subject to error and it, thus considered a random variable. Measurements on decoys come from one distribution, those on warheads come from another. The total cloud is, thus a sample of which one element is the oddball, or outlier. This paper shows how to maximize the defensive probability of hitting the outlier under the two situations first, with the objects strung out so they must be treated sequentially, second, when all the objects appear at once.
Asymptotic Solution of Palm's Integral Equation
Authors: Hellman Olavi
Published: November 2008

The asymptotic solution of Palm's nonlinear integral equation is obtained, valid for channels sufficiently far away from the first channel. It is shown how the asymptotic formula may be applied, in certain cases, for the determination of the number of channels sufficient to serve a given Poisson input.
The Dynamics and Statistics of Exponential Smoothing Operations
Authors: Morris Robert H. , Glassey C. Roger
Published: November 2008

Certain of the dynamic and statistical properties of exponential smoothing operators are investigated primarily by means of the differential equations appropriate to their continuous analogues. Particular attention is given to Brown and Meyer's estimator of the current mean value of a time series exhibiting a quadratic trend.
Output Distribution of a Single-Channel Queue
Authors: Chang Wei
Published: November 2008

The interdeparture-time distribution of a single-channel queuing system with general arrival and service time distribution is derived by applying the complex-variable theory. It is important in studying the queues in series, since the output from one channel comprises the input into the subsequent channel. An example is given on the exponential channel. This shows that the output from such a system with a Poisson input is itself a Poisson. The interdeparture times fail to be statistically independent if the interarnval times and the service times are other than exponentially distributed.
A Stochastic Transportation Problem
Authors: Williams A. C.
Published: November 2008

When the market demands for a commodity are not known with certainty, the problem of scheduling shipments to a number of demand points from several supply points is a stochastic transportation problem. If the dynamic aspects of the problem may be neglected, i.e., if the effects of “stock outs” and “inventory carry-overs” can be reflected in terms of linear penalty costs (in the case of undersupply) and linear salvage values (in case of oversupply), one obtains a convex nonlinear programming problem. We show that the author's algorithm for the case of known demands can be generalized to obtain a solution algorithm for this stochastic problem. In case the joint cumulative distribution function for the demand is continuous, however, the algorithm is better described as a special (constructive) case of Dantzig's general method for convex programming. Each of these methods is, in turn, based on the decomposition algorithm. No assumptions are made as to the independence or dependence of the probability distributions of the various demands. If F(ξ1, …, ξn) is the joint cumulative distribution function for the demands, we assume only that each of the first moments of F exist (are finite), and that F is regular enough for the integration by parts formula to be valid. The analysis here is applicable (subject to a qualification) to the case of indivisible commodities, as well as the case of infinitely divisible ones.
Expected Retaliatory Capabilities of Launch Control Networks
Authors: Argabright L. , Ahlin A. C.
Published: November 2008

This paper presents a method for analyzing a launch control network in order to determine its expected retaliatory capability, that is, the expected number of operable missiles which are still electrically connected to at least one launch control center after an enemy attack has taken place. The key to the method is to look at a launch control network as a switching circuit and thus represent it by means of a Boolean matrix. Combinatorial techniques are then used to derive a symbolic representation of all possible paths by which a given launch site is connected with some launch control center. These expressions are then used to compute the individual launch probability of each missile in the network. The expected number of launchable missiles is equal to the sum of these individual launch probabilities.
Letter to the Editor—Note on a Paper by C. W. Marshall
Authors: Kaplan Seymour
Published: November 2008

In a paper by C. W. Marshall (“Full Service Probability for Regular Arrangement,” Opns Res. 9 186–199 (1961).), an error is made that, although not fundamental to his results, should be pointed out.
Letter to the Editor—Some Remarks on Server Breakdown
Authors: Eisen M. , Leibowitz M.
Published: November 2008

A single queue with a Poisson input and arbitrary service time is considered. We suppose that the server is subject to random breakdowns that have an arbitrary distribution. The distribution of the queue length at the end of a normal and breakdown period is determined. From this the distribution at a randomly chosen time is found.
A Theory of the Diffusion of Traffic Platoons
Authors: Grace Muriel J. , Potts Renfrey B.
Published: November 2008

A theoretical investigation is made of the diffusion of a traffic platoon as it moves down a road. The basic assumption of the mathematical model is a kinematical one—that the speeds of the cars in the platoon are distributed normally. The parameters of this distribution are related to a diffusion constant that measures the spreading of the platoon. For certain assumed initial conditions, analytical and numerical solutions of the model are presented and applied to the problem of the coordination of two successive traffic lights.
Critical Path Analyses Via Chance Constrained and Stochastic Programming
Authors: Charnes A. , Cooper W. W. , Thompson G. L.
Published: November 2008

Chance-constrained programming methods are applied to examine some statistical properties of PERT networks. Using duality, the PERT method is shown to be equivalent to use of the crudest linear decision rule and the confidence (or lack thereof) in meeting constraints is explicitly presented. The distribution of completion times (= Tintner's stochastic programming) follows easily and may often be multimodal, contrasting with (erroneous) central limit theorem usages in the literature. Possible extensions and developments of PERT using more adequate chance-constrained models and techniques are suggested and will be presented elsewhere.
Letter to the Editor—Note on the Combat Value of Intelligence and Command Control Systems
Authors: Schreiber Thomas S.
Published: November 2008

An idealized model of a battle is formulated and analyzed enabling the efficiency of the intelligence and command and control systems to be quantitatively related to firepower and numerical strength. The analysis is based on a pair of differential equations analogous to Lanchester's equations. Some indicative numerical results are given that show that an increase in the efficiency of an intelligence and command and control system can be equivalent to a substantial increase in numerical strength.
Discrete Time Queues at a Periodic Traffic Light
Authors: Kleinecke D. C.
Published: November 2008

The response delay in clearing the queue of automobiles waiting at a traffic light can be modeled by allowing one car to leave at the end of each of a series of discrete intervals in time. The steady-state queue formed at a cycle traffic light is discussed for general stationary arrival processes. A method of solution for the case where arrivals are Poisson is described. General formulas are given for the probability of not clearing the queue during a cycle and for the expected wait at the light.
Algorithm for Traffic Control
Authors: Dunne Michael C. , Potts Renfrey B.
Published: November 2008

A linear control algorithm is proposed for the computer operation of a signalized traffic intersection. A theoretical analysis of the algorithm under the assumption of constant vehicular arrival and departure rates shows that the control is stable under unsaturated conditions, and with proper choice of control constants usually gives a rapid convergence to a limit cycle that minimizes the average delay.
Reduction Methods for Tandem Queuing Systems
Authors: Friedman Henry D.
Published: November 2008

A tandem stage queuing system has n stages A1, A2, …, An in series, where stage Ai consists of mi parallel channels each having the same constant service time si . In addition, one of the stages may be a single-channel stage Aj having variable service times that are always ≧si/mi for i ≠ j. Customers arrive at the first stage and proceed through the stages, in order, on a first-come, first-served, unlimited queuing basis. For any sequence of customer arrival times, the time spent in the system by each customer is independent of the order of the stages. It follows that certain steady-state and time- and customer-dependent problems for the system and for its stages, involving waiting time, queue length, and busy period, can for any interarrival distribution be reduced to corresponding problems for a system of fewer stages, possibly a single stage.
A Theory of Cost-Effectiveness for Military Systems Analysis
Authors: Fox Peter D.
Published: November 2008

This paper presents a theoretical basis for cost-effectiveness analysis. It is argued that, frequently, a range of effectiveness or cost levels may be acceptable to whoever must ultimately decide which military system (if any) should be acquired. The function of the analyst is to present a schedule of alternatives and not to optimize in the sense that he recommends the selection of a particular alternative. The formulation of the schedule is discussed where the cost and effectiveness associated with each alternative are viewed as random variables. The paper concludes with some general observations relating to military system selection.
On Monte Carlo Methods in Congestion Problems: I. Searching for an Optimum in Discrete Situations
Authors: Page E. S.
Published: November 2008

The crude Monte Carlo method is inefficient when searching for extreme points since it uses none of the information gained from earlier samples. If the possible situations are the permutations of a number of items, a method called Chain Monte Carlo is suggested that needs a measure of distance between two permutations. Examples are given and in some scheduling problems substantial savings in computation are observed.
Letter to the Editor—Some Characteristics of a Special Joint-Order Inventory Model
Authors: Silver Edward A.
Published: November 2008

Joint ordering strategies are of extreme importance in many inventory control situations. This paper considers a situation involving two items having identical characteristics including unit Poisson demand. The joint ordering rule is to order both items up to a level Q each time the level of either of them drops to zero. Expressions for the probability mass function of the remnant stock, the expected value of the remnant stock, the expected time between orders, and the long-run cost per unit time are shown. The joint ordering strategy is compared with the situation where the two items are treated independently. When the cost of placing an order for two items is equal to that for a single item, it turns out that it is never preferable to use the independent strategy.
Problems of Statistical Inference for Birth and Death Queuing Models
Authors: Wolff Ronald W.
Published: November 2008

A large sample theory for birth and death queuing processes which are ergodic and metrically transitive is applied to make inferences about arrival and service rates. Likelihood ratio tests and maximum likelihood estimators are derived for simple models. Composite hypotheses, for example that the arrival rate does not vary with the number in the system, are considered. A numerical example illustrating these results, based on data generated by simulating a known model, is presented, which includes the testing of both true and false composite hypotheses.
Reliability of Spare Part Support for a Complex System with Repair
Authors: Goodwin James M. , Giese Erich W.
Published: November 2008

In this paper an expression is derived for the probability that a given number of spares for each element of a complex system will be sufficient to ensure continued operation without requiring a spare (for replacement of a failed part) when none is available. Each part of the system being considered is subject to failure according to Poisson statistics, and may be subject to repair in some fixed time. The probability (that the number of spares will be sufficient) for nonreparable parts is obtained as a special case of the result for reparable parts. The probabilities are obtained for a single part by the construction of an artificial model, which differs from the case being considered, allowing the deviation to shrink to zero. Samples of the results obtained are included for several values of the various parameters. The results are generalized to include a variety of parts, both identical and different, and to include the effects of passive redundancy.
Letter to the Editor—Another Formulation of the Inventory Problem
Authors: Sudderth William D.
Published: November 2008

The past decade has given rise to a considerable amount of research in the fields of inventory control and production planning. One of the most useful mathematical models originated with the paper of K. D. Arrow, T. E. Harris, and J. Marschak, “Optimal Inventory Policy,” Econometrica 19, 250–272 (1951). This model was further improved in Richard Bellman's book, Dynamic Programming, pp. 152–182, Princeton University Press, Princeton, New Jersey, 1957. In the present paper, another formulation of the same problem is exhibited. The attentive reader will observe many similarities to the dynamic programming formulation.
Selecting the Best Lengths to Stock
Authors: Wolfson M. L.
Published: November 2008

A compact method has been developed for solving the following frequently occurring inventory problem: Given a list of lengths and either the known or the expected demand for each length (because of storage limitations or manufacturing economies, only a few of these lengths are to be made and stocked). Any required length not in stock will be cut from the next longer length, with an attendant cutting loss. Select that particular set of R lengths that will minimize the cutting losses. The method actually finds the minimum cutting loss for an entire range of R's. By weighing the cutting loss for each additional stored length against the added manufacturing and storage cost, management can better determine how many and which lengths to stock.
Preemptive Priority Queues
Authors: Chang Wei
Published: November 2008

Customers of different priorities arrive at a counter in accordance with a Poisson process. The customers are served by a single server in order of priority and for each priority in order of arrival. Preemptive discipline is assumed. Three service policies are considered: (i) preemptive-resume, (ii) preemptive-repeat-identical, and (iii) preemptive-repeat-different. The time-dependent solutions for these priority systems are very complicated. However, the problem can be simplified in case of stationary solutions. In this paper, a step-by-step method is proposed to find the stationary distributions of the queue sizes, the waiting times, and the busy periods of each priority class.
Modular Design, Generalized Inverses, and Convex Programming
Authors: Charnes A. , Kirby M.
Published: November 2008

It is shown that the modular design problem [Formula: see text] can be transformed into a problem of minimizing a separable convex function subject to linear equality constraints and nonnegativities. This transformation is effected by using a generalized inverse of the constraint matrix. Moreover the nature of the functional and the constraints of the separable problem are such that a good starting point for its solution can be obtained by solving a particular transportation problem. Several possible methods for solving the separable problem are discussed, and the results of our computational experience with these methods are given. It is also shown that the modular design problem can be viewed as a special case of a large class of general engineering design problems that have been discussed in the literature.
The Number Served in a Queue
Authors: Greenberg Harold , Greenberg Irwin
Published: November 2008

A single-server queue with Poisson arrivals and exponential service is studied to obtain the joint probability distribution of the number in the system at time t and the cumulative number already served at time t. The probability that k are served in time t is then determined.
Interpolation of the Renewal Function
Authors: Ehrenfeld Sylvain
Published: November 2008

Some useful conditions are explored for determining a renewal process from knowledge of the renewal function H(t) at values H(h), H(2h), … for some h > 0. Furthermore, these conditions are used for expressing H(t) as an infinite interpolation series involving H(h), H(2h), …. The results are useful for estimation problems in replacement and reliability involving attribute observations of renewal processes.
Observations on the Theoretical Basis of Cost-Effectiveness
Authors: Heuston M. C. , Ogawa G.
Published: November 2008

This paper presents some observations on the theoretical foundation of cost-effectiveness analysis. It describes the results of continuing research to develop a comprehensive and rigorous description of the important elements of cost-effectiveness as used by the aerospace industry for military and commercial systems planning. The primary objective is to utilize basic mathematical and statistical theory to construct the rules, properties, and hypotheses that are needed to satisfy the contractual requirements imposed by various government customers.
An Alternative Proof of a Theorem of Takács on the GI/M/1 Queue
Authors: Neuts Marcel F.
Published: November 2008

An analytic proof is given of the fact that the stationary distribution for the imbedded Markov chain in a GI/M/1 queue is geometric. A generating function for the stationary transition probabilities is obtained as the unique solution to an integro-differential equation, which may be solved by reduction to a Wiener-Hopf equation.
An Interval Estimate of System Availability
Authors: Jacobson Harold I.
Published: November 2008

A confidence interval estimate for fixed sample size is obtained for the pointwise availability of one of the states in a system that switches at random between two states. The state definitions can be tailored to the problem at hand, provided only that the definitions are pointwise. The interval estimate is exact for all sample sizes, if the durations of both states follow exponential probability distributions. An asymptotic estimate is obtained where the state durations are either exponential or uniform (0, C), where c is unknown. Where the state durations follow other probability distributions, the interval estimate is dependent upon only the coefficient of variation of each state distribution. In these cases, interval estimation is dependent upon a priori estimates made of the two coefficients of variation. This dependence is, however, meaningful in the sense that errors in the a priori estimates are readily put in terms of errors in the interval estimate.
Expected Production of a Single Repairman Machine-Maintenance System with Overnight Repairs
Authors: Elce Ivan , Liebeck Hans
Published: November 2008

Assuming that the repair time and the working time of each machine is exponentially distributed, and that the system operates for a time period of given length starting with all machines in working order, an expression is found for the expected number of machine hours worked. This is proportional to the expected production of the system. The expression is complicated to evaluate, so upper and lower bounds for it are derived, which are of a simpler form.
On Programming under Uncertainty
Authors: Wilson Robert
Published: November 2008

The duality theory of programming under uncertainty is developed for the special case of proportional penalties and normal probability distributions, and from this an approximately optimal sampling plan is determined by the solution to a separable nonlinear programming problem with linear constraints. The duality theory is interesting per se; in particular, it evidences clearly the specific roles of the means and standard deviations in determining the solution. The duality theory of programming under uncertainty has been available for some time, at least in principle, by application of the general theory. It is worthwhile, however, to examine specially structured problems in finer detail, and that is the purpose of this paper.
Letter to the Editor—The Time-Dependent Solution to the Many-Server Poisson Queue
Authors: Jackson R. R. P. , Henderson J. C.
Published: November 2008

An alternative method of obtaining the Laplace Transform of the state probabilities for the many-server Poisson queue to that given by Saaty in an earlier paper in this Journal is obtained. The form obtained is simpler than Saaty's.
Two-Way Traffic on a Single Line of Railway
Authors: Frank Ove
Published: November 2008

In this paper a mathematical treatment of two-way traffic on a single line of railway is given. The traffic capacity, the cycle times of the trains, and the number of trains needed to accomplish the transports are studied for certain regular traffic systems.
Multistage Planned Replacement Strategies
Authors: Marathe V. P. , Nair K. P. K.
Published: November 2008

For failing type of equipment, multistage replacement strategies, available in literature, specify use of the equipment in the system until its failure. The strategies bring economy by transferring failure rate from groups where the replacement cost is higher to those where it is smaller. A large variety of equipment has monotone increasing failure rate and in such cases planned replacement has significance. This paper presents two types of multistage planned replacement strategies, namely, multistage block replacement strategy and multistage planned replacement strategy by age. Each of these is compared with the corresponding single stage strategy available in literature. The comparison provides the condition of economy and the amount of economic gain. Besides their applications, the two strategies are discussed in relation to each other. Certain means for improving the economy of the strategies, and further work in this field are indicated.
The Theory and Computation of Knapsack Functions
Authors: Gilmore P. C. , Gomory R. E.
Published: November 2008

In earlier papers on the cutting stock problem we indicated the desirability of developing fast methods for computing knapsack functions. A one-dimensional knapsack function is defined by: [Formula: see text] where Πi and li are given constants, i = 1, …, m. Two-dimensional knapsack functions can also be defined. In this paper we give a characterization of knapsack functions and then use the characterization to develop more efficient methods of computation. For one-dimensional knapsack functions we describe certain periodic properties and give computational results.
Feasibility of Two Commodity Network Flows
Authors: Rothschild B. , Whinston A.
Published: November 2008

The paper considers the problem of feasibility of integer flows in a two commodity network with integral capacities. The main result of the paper establishes conditions under which, in an Euler network, and for two non-negative integers a and b, there exists a two commodity flow, where the flow of the first commodity is of size a and the second flow of size b. This result is used to find some conditions for the case where a and b are not necessarily even.
Letter to the Editor—Some Invalid Properties of Markov Chains
Authors: Schweitzer Paul J.
Published: November 2008

Let, PA, PB, and PAPB denote the transition probability matrices of finite Markov chains A, B, and the “product chain” AB. It is demonstrated by counterexamples that the sets of recurrent, periodic, and transient states of A and B cannot be simply related to the corresponding sets of AB.