bluuebunny/crossref_metadata_2025 huggingface dataset:
Single-Period Multiproduct Inventory Models with Substitution
Authors: Bassok Yehuda , Anupindi Ravi , Akella Ram
Published: November 2008

We study a single period multiproduct inventory problem with substitution and proportional costs and revenues. We considerNproducts andNdemand classes with full downward substitution, i.e., excess demand for classican be satisfied using productjfori≥j. We first discuss a two-stage profit maximization formulation for the multiproduct substitution problem. We show that a greedy allocation policy is optimal. We use this to write the expected profits and its first partials explicitly. This in turn enables us to prove additional properties of the profit function and several interesting properties of the optimal solution. In a limited computational study using two products, we illustrate the benefits of solving for the optimal quantities when substitution is considered at the ordering stage over similar computations without considering substitution while ordering. Specifically, we show that the benefits are higher with high demand variability, low substitution cost, low profit margins (or low price to cost ratio), high salvage values, and similarity of products in terms of prices and costs.
Myopic Heuristics for the Random Yield Problem
Authors: Bollapragada Srinivas , Morton Thomas E.
Published: November 2008

We consider a single item periodic review inventory problem with random yield and stochastic demand. The yield is proportional to the quantity ordered, with the multiplicative factor being a random variable. The demands are stochastic and are independent across the periods, but they need not be stationary. The holding, penalty, and ordering costs are linear. Any unsatisfied demands are backlogged. Two cases for the ordering cost are considered: The ordering cost can be proportional to either the quantity ordered (e.g., in house production) or the quantity received (e.g., delivery by an external supplier). Random yield problems have been addressed previously in the literature, but no constructive solutions or algorithms are presented except for simple heuristics that are far from optimal. In this paper, we present a novel analysis of the problem in terms of the inventory position at the end of a period. This analysis provides interesting insights into the problem and leads to easily implementable and highly accurate myopic heuristics. A detailed computational study is done to evaluate the heuristics. The study is done for the infinite horizon case, with stationary yields and demands and for the finite horizon case with a 26-period seasonal demand pattern. The best of our heuristics has worst-case errors of 3.0% and 5.0% and average errors of 0.6% and 1.2% for the infinite and finite horizon cases, respectively.
Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power System
Authors: Hobbs Benjamin F. , Ji Yuandong
Published: November 2008

A bounding-based method is developed for estimating the expected operation cost of a multiarea electric power system in which transmission capacity limits interarea flows. Costs include the expense of power generation and losses suffered by consumers because of supply shortfalls, averaged over random generator outage states and varying demand levels. The calculation of this expectation, termed the distribution problem, is a large-scale stochastic programming problem. Rather than solving this problem directly, lower and upper bounds to the expected cost are created using two more easily solved models. The lower bound is from a deterministic model based on the expected value of the uncertain inputs. The upper bound results from a linear program with recourse whose structure permits relatively quick solution by Benders decomposition. The Benders subproblems use probabilistic production costing, which can be viewed as a stochastic greedy algorithm, to consider random outages and demands. These bounds are iteratively tightened by partitioning realizations of the random variables into subsets based on the status of larger generators and a cluster analysis of demands. Computational examples are described and application issues addressed.
Derandomizing Variance Estimators
Authors: Henderson Shane G. , Glynn Peter W.
Published: November 2008

One may consider a discrete-event simulation as a Markov chain evolving on a suitably rich state space. One way that regenerative cycles may be constructed for general state-space Markov chains is to generate auxiliary coin-flip random variables at each transition, with a regeneration occurring if the coin-flip results in a success. The regenerative cycles are therefore randomizedwith respect to the sequence of states visited by the Markov chain. The point estimator for a steady-state performance measure does not depend on the cycle structure of the chain, but the variance estimator (that defines the width of a confidence interval for the performance measure) does. This implies that the variance estimator is randomized with respect to the visited states. We show how to “derandomize” the variance estimator through the use of conditioning. A new variance estimator is obtained that is consistent and has lower variance than the standard estimator.
Rendezvous Search on the Line
Authors: Gal Shmuel
Published: November 2008

We present two new results for the asymmetric rendezvous problem on the line. We first show that it is never optimal for one player to be stationary during the entire search period in the two-player rendezvous. Then we consider the meeting time ofn-players in the worst case and show that it has an asymptotic behavior ofn/2 +O(logn).
The Solution of a Certain Two-Person Zero-Sum Game
Authors: Brown Richard H.
Published: November 2008

A two-person zero-sum game is specified as follows: Let B be any positive real number, and let θ be a real number between zero and one, exclusive. Player I chooses a number, t1, between 0 and B + 1, inclusive, and player II chooses a number, t2, between 0 and B, inclusive II then pays I the amount ϕ(t1, t2) where [Formula: see text] Best pure strategies do not exist. Let the mixed strategies of I and II be specified by the distribution functions F and G, respectively, and let E(F, G) be the expected value of ϕ. Although ϕ is discontinuous, it is shown that the game has a well-determined value [Formula: see text] where n is the largest integer not exceeding B. Optimal strategies for each player are given explicitly.
The Application of Design of Experiments and Modeling to Complex Weapons Systems
Authors: Biser Erwin , Meyerson Martin
Published: November 2008

This paper presents the conceptual and experimental aspects involved in the construction of a mathematical model to describe and predict the behavior and output of a complex weapons system for a given class of inputs consisting of raid configurations. The weapon system is functionally divided into such activities as detection, weapon-target assignment, tracking, acquisition, firing, and ultimate kill. Time delays, measures of the time intervals corresponding to these functional activities, are given as mathematical functions of input parameters, such as range, radar cross section, velocity, height, etc. The over-all function of the weapon system was partitioned into subfunctions in consonance with the concept of a weapon-complex as a time-response system. The model is to show how the various functions or activities of the weapon system are interrelated and interconnected and how they affect one another. The modeling approach is based upon the conceptual scheme input → system → output. The ultimate aim of the model is to find explicit expressions of the output response in terms of specific raid inputs and to obtain regression equations of kill probabilities in terms of height, velocity, range, concentration of targets, etc. The model contains a flow chart of a computer program that can be coded for any computing machine so that, given the characteristics of a given raid and an assignment procedure, the corresponding system response, in terms of kill probability, can be computed. The techniques used here may be found equally useful in other fields of system research, development, and evaluation.
Letter to the Editor—A Supplementary Bibliography on Linear Programming
Authors: Wagner Harvey M.
Published: November 2008

In the February (1957) issue of Operations Research, F. Virginia Rohde presented an extensive bibliography on linear programming. In my class on “advanced techniques in scientific management,” I also had compiled a list of books and articles on the general subject of mathematical programming. The following bibliography contains over 190 items not included in Rohde's paper. Needless to say, certain significant omissions from the pre-1957 literature have still probably been overlooked.
Mathematical Analysis of an Inventory Case
Authors: Clark Charles E.
Published: November 2008

This paper presents the adjustments in current theory of inventory that were required in a specific case. The demand during lead time was found to be skewed to the extent that it could not be represented by a two-parameter distribution. This skewness was handled by an augmentation of the standard deviation of the lead time demand. The analysis involving runout costs was complicated by the fact that, when one warehouse was short, it was possible sometimes to induce a customer to accept the delay inherent in delivery from another warehouse.
Queuing with Impatient Customers and Indifferent Clerks
Authors: Barrer D. Y.
Published: November 2008

A waiting-line problem in which the arrival and service rates are of Poisson type is considered subject to the additional conditions that (a) each customer is limited to a fixed time during which he is available for service and after which he automatically leaves the system and (b) customers are selected at random from among those in the system rather than on a first-come-first-served basis. The equilibrium distribution of the length of the queue and the expected rate at which customers escape service are obtained. The expected escape rate is plotted as a function of the limited time of customer availability for selected arrival and service rates and compared with the result of Monte Carlo trials of the model.
Queuing with Impatient Customers and Ordered Service
Authors: Barrer D. Y.
Published: November 2008

Two types of customer behavior are considered: (1) if a customer is acquired for service before he has waited a time τ0, he remains in the queue until served irrespective of whether or not his total waiting time exceeds τ0. Only those customers who wait for a time τ0 without being acquired for service become “lost” customers, and (2) a customer whose total waiting time is τ0 becomes a lost customer irrespective of whether he is acquired for service or not.
A Tactical Air Game
Authors: Fulkerson D. R. , Johnson S. M.
Published: November 2008

A discrete, linear model of a tactical air war is formulated as a multi-move game. The symmetric case in which the attrition rates are the same for both sides is solved for both finite and infinite campaigns.
Letter to the Editor—Comment on Dantzig's Paper on Discrete Variable Extremum Problems
Authors: Bellman Richard
Published: November 2008

In his interesting paper on discrete-variable extremum problems, George Dantzig (Dantzig, G. 1957. Discrete-variable extremum problems. Opns Res. 5 266–277.) discusses the “knapsack” problem. He presents two approximate methods based upon linear programming techniques, and an exact solution based upon the functional equation method of dynamic programming (Bellman, R. 1957. Dynamic Programming. Princeton University Press.).
Inadequacy of Cost Per “Kill” as Measure of Effectiveness
Authors: Walsh John E.
Published: November 2008

Cost per enemy “kill” is a commonly used measure for determining the relative worth of competitive components for a defense system. If the defense system components are employed in such a manner that they do not affect each other, this measure of effectiveness appears to be suitable for many situations. If there are interactions among the components of a defense system, however, a comparison based on cost per enemy “kill” which is not obtained from consideration of the over-all defense system can be misleading. This paper presents an analysis which indicates that such misleading situations often exist. To perform this analysis, a somewhat simplified mathematical model is developed to represent the actions and outcomes of an enemy attack against a defense system. The mathematical model permits partial analytical treatment of moderately complicated attack-defense situations and may be useful in many types of military operations-research work.
On the Optimal Allocation of Limited Resources
Authors: Ward L. E.
Published: November 2008

A concave programming problem is presented, which is a model for an operations-research problem arising in both military and commercial applications. It is amenable to linear programming methods and can be solved by a sequence of applications of the simplex algorithm.
Factor Analysis of Personnel Components of Ship Performance
Authors: Glickman Albert S.
Published: November 2008

In the Navy, the ultimate level of performance evaluation at which it is practically possible to obtain quantitative measurements is at the level of the performance of the ship as a whole. This pilot exploration investigated the feasibility of applying factor analysis to ship-performance-evaluation data, as represented by damage-control exercises of the Operational Readiness Inspection. From data obtained on 59 variables for 55 ships of various types, it was possible to demonstrate the presence of six underlying basic dimensions which would account for the common variance of the scores meaningfully and parsimoniously. The implications of the findings are discussed with particular reference to the development of better techniques of personnel selection, training, evaluation, and management.
On a Tactical Air-Warfare Model of Mengel
Authors: Bellman Richard , Dreyfus Stuart
Published: November 2008

This is the first of a series of papers devoted to the computational solution of dynamic programming processes. In it we use the functional-equation approach to treat a tactical air-warefare model that. A Mengel previously has considered by means of classical variational techniques.
A Warehouse-Location Problem
Authors: Baumol William J. , Wolfe Philip
Published: November 2008

This paper describes a method for determining a more profitable geographic location pattern for the warehouses that are employed by a firm in delivering known quantities of its finished product to its customers, where the number of warehouses is also permitted to vary. It is shown that this can normally be expected to be a concave minimization problem. Unfortunately, there are usually no practical computational methods for determining the values of the variables that correspond to the absolute minimum of a concave cost function. However, a local optimum can be determined by a method described in the article. The method involves a sequence of transportation computations that are shown to converge to the solution. An illustrative small scale computation is included. An appendix explains in intuitive terms the nature of the computational difficulties that arise in a concave-programming problem.
Two Queues Under Preemptive Priority with Poisson Arrival and Service Rates
Authors: Stephan Frederick F.
Published: November 2008

This paper extends the work of White and Christie, reported in Operations Research, vol 6, pp 79-95 (January-February, 1958), on preemptive priority queuing. A random walk procedure yields recursive relations between the state probabilities in the steady state. Recursive relations for the moments of the length of the lower priority queue follow. Combined with the use of moment generating functions, this approach provides moments of the waiting time for elements of the lower priority class that arrive when the system is in a given state, i.e., the two queues are of given lengths. The moments of waiting time and time in the system are also obtained recursively for the steady state. Routines for computing and checking are provided.
Letter to the Editor—On “Heuristic Problem Solving,” by Simon and Newell
Authors: Bellman Richard
Published: November 2008

For those who are interested in becoming prophets with honor in their own time and in their own country, there is a fundamental principle which we may call the Principle of Optimism. Never make negative predictions.
Prediction of First-Cruise Reenlistment Rate
Authors: Dailey John T.
Published: November 2008

First-term reenlistment rates were not recorded in the Navy prior to 1953. However, it has been found possible to estimate retention rates for yearly or quarterly entry groups of recruits back to 1936. These rates approximate the reenlistment rates at the end of the first term and vary from a high of 80.8 per cent for 1936 to 1.6 per cent for 1944. However, the number reenlisting each year remains remarkably constant. Thus the reenlistment rate is very heavily influenced by the size of the entry group, since increasing the size of the entry group increases the denominator of the rate much faster than it increases the numerator. A method was developed for removing the effect of the entry-group size, making it possible to extrapolate from one period to another with considerable accuracy. Simple linear projection is subject to very large errors as the uncorrected rate can change tremendously from one year to the next. The corrected reenlistment rate has been remarkably constant for twenty years. It has varied between 12 and 19 per cent except during periods of no Selective Service when it has been as high as 35.1 per cent. The early flood of volunteers after Korea temporarily dropped the rate to as low as 7.9 per cent for the group enlisted during the third quarter of 1950. In years of small quotas, waiting lists are long and there is little active recruiting. Thus, the recruits are largely those strongly enough motivated to come in on their own and wait some time to be accepted Consequently, the group as a whole will have a high degree of career motivation and a high reenlistment rate. In years when quotas are large, active selling and many extrinsic incentives are required to meet quotas, and the additional recruits do not have as much career motivation as those easier to recruit.
A Method for Solving Traveling-Salesman Problems
Authors: Croes G. A.
Published: November 2008

The traveling-salesman problem is a generalized form of the simple problem to find the smallest closed loop that connects a number of points in a plane. Efforts in the past to find an efficient method for solving it have met with only partial success. The present paper describes a method of solution that has the following properties (a) It is applicable to both symmetric and asymmetric problems with random elements (b) It does not use subjective decisions, so that it can be completely mechanized (c) It is appreciably faster than any other method proposed (d) It can be terminated at any point where the solution obtained so far is deemed sufficiently accurate.
The Distribution and Effects of Fallout in Large Nuclear-Weapon Campaigns
Authors: Everett Hugh , Pugh George E.
Published: November 2008

The purpose of this paper is to provide a simple way of evaluating the consequences of radioactive fallout from a large nuclear-weapon campaign without resorting to detailed map studies. Simple analytic formulas based on numerical data in Rand Memorandum RM-1969 are presented that enable one to make rapid statistical estimates of the distribution of fallout and its effects on a population, as well as the consequences of changing the total delivered yield or the targeting doctrine. The method was checked against a detailed map study, using the same parameters, and was found to be in excellent agreement with its results. A method of optimally distributing weapons among large areas in order to maximize radiation casualties is deduced on the basis of the formulas, and curves are exhibited expressing the casualties produced as a function of total yield delivered. The achievement of optimized attacks does not require a delivery accuracy with probable error less than about a hundred miles. In addition, the formulas are applied to a number of other targeting doctrines, and the resulting curves of casualties versus total delivered yield are presented.
Optimal Inventory Control Decision Rules for a Large Supply System
Authors: Davis R. H.
Published: November 2008

Mathematical decision rules for the control of inventories in a large supply system are derived. These rules allow the minimization of total system shortages where this minimization is subject to specified system expenditures. Alternatively, the rules permit the minimization of system expenditures for a given level of system shortages. The mathematical model used to derive these rules includes the features random demands, random lead times, set-up and order costs, interest costs, obsolescence costs, physical holding costs, item unit costs, relative essentialities of items, and a measure of shortage costs which takes into account the durations that shortages persist. Derivation of the optimal rules employs an iterative solution of a nonlinear programming problem. Comparisons with presently-used decision rules for a large supply system indicate that significant improvements in system effectiveness can be obtained by the use of the optimal rules.
Letter to the Editor—An Approximation to Distributions of Summed Waiting Times
Authors: De Baun R. M. , Katz S.
Published: November 2008

The present note offers a readily computable approximate solution to the problem discussed in Nelson [Neslon, R. T. 1958. Waiting-time distributions for application to a series of service centers. Opns Res. 6 856–862.].
Letter to the Editor—Bulk-Service Queuing Problem
Authors: Jaiswal N. K.
Published: November 2008

Bailey [Bailey, N. T. J. 1954. On queuing processes with bulk service. J. Roy Stat. Soc. B 16 80–87.], using the “imbedded-Markov-chain” technique devised by Kendall [Kendall, D. G. 1951. Some problems in the theory of queues. J. Roy Stat. Soc. B 13 151–185; 1953. Stochastic processes occurring in the theory of queues and their analysis by the ‘imbedded Markov chain’. Ann. Math. Stat. 24 338–354.] presented a mathematical investigation of the type of queuing problem, in which customers arrive at random, form a single queue in order to arrival, and are served in batches, the size of each batch being either a fixed number s of customers or the total number in the queue, whichever is less. In the following note, the same problem has been solved by a different method.
Letter to the Editor—A Graphical Tool for the No-Queue Model
Authors: Doeh Giyora
Published: November 2008

The accompanying chart was originally constructed to enable solutions for the optimum spares inventories of aircraft components.
A Managerial Game for an Insurance Company
Authors: McGuinness John S.
Published: November 2008

A managerial game based on a property and liability insurance operation instead of a manufacturing operation is described. It is designed primarily as a training device for middle-management and higher executive levels, but it is also capable of refinement into a detailed tool for planning and budgeting and of expansion to all types of insurance. In addition to the mathematical model on which it is based, sufficient references are listed to provide any individual company with most of the essential data needed for actually setting up its own game.
Sampling and Persuasion
Authors: Churchman C. West
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. Late in 1950 several of us undertook to study one of the most troublesome problems of railroad accounting—the settlement of interline accounts. Here a brief description of the problem and our proposed solution will suffice.
Unsuccessful Case Studies and Why
Authors: Ackoff Russell L.
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.
Letter to the Editor—A Generalized PERT
Authors: Freeman Raoul J.
Published: November 2008

I read with interest the article “Application of a Technique for Research and Development Program Evaluation” by Malcolm, Roseboom, Clark, and Fazar in the September–October, 1959, issue of Operations Research (vol. 7, pp. 646–669). It seems to me that the next step in the development of the network technique, PERT, described therein, is its generalization to include resources and technical performance as well as ‘time’ (presently the only measure of effectiveness considered). To this end, I should like to make a few comments.
Optimum Size and Hardness of Sites for Storage of Nuclear Weapons
Authors: Dobbie James M.
Published: November 2008

A study is made of the optimum size and hardness of sites for the storage of a certain portion of the national stockpile of nuclear weapons. These weapons can be stored in existing nuclear sites, nonnuclear sites converted for the storage of nuclear weapons, and new sites built for this purpose. The principal questions considered are. To what extent should existing and converted sites be used for this purpose? Should unoccupied sites be used as decoys? What are the optimum size and hardness of new sites? Should the sites be compact or dispersed over large areas? Methods are developed to answer these questions under certain limitations. The rough estimates obtained from this analysis would need to be adjusted to allow for variations from the average conditions at the individual sites.
Letter to the Editor—On Pulse-Type Arrivals to a Queue
Authors: Heyne Jay B. , Brotman Lewis
Published: November 2008

A population of N units is assumed to arrive simultaneously at a service facility at time t = 0. A number, n0, of these units is postulated as having failed. The service channels are capable of exponential service, each having a mean rate μ. The number of channels, k(=1, 2, 3, …) will affect the rate at which service is to be performed.
Letter to the Editor—Comments on a Paper by Karush
Authors: Vazsonyi Andrew
Published: November 2008

In the paper, “A Queuing Model for an Inventory Problem,” that appeared in Operations Research, volume 5, pages 693–703 (October 1957), William Karush solved an important inventory-control problem. The purpose of this note is to present a chart depicting a graphical form of Karush's distribution function of the inventory replenishment time.
Letter to the Editor—Digital Simulation of a Massed-Bomber, Manned-Interceptor Encounter
Authors: Brotman Lewis , Seid Barry
Published: November 2008

This letter is a report on a method which was devised for simulating on the IBM-704 digital computer the performance of an advanced-type, manned-interceptor weapon system against a massed raid of enemy bombers. The program can accommodate a maximum of 250 interceptors and 500 bombers.
Sequential Analysis of the Reliability of an Antitank-Mine Simulator System
Authors: Kurlat S. , Springer M. D.
Published: November 2008

This paper discusses the development of an antitank-mine simulator system and the evaluation of the reliability of the system. The reliability of the system must be at least 75 per cent in order to be acceptable to the military. To achieve this degree of over-all system reliability, one must impose specifications upon each component of the system. More specifically, variations in the pressure at which the mine simulator actuates must be within prescribed bounds. Likewise, the strength of the electromagnetic signal emitted from the mine simulator must be reasonably consistent. The receiver must operate at a level of sensitivity that will assure a high probability of response to an electromagnetic signal issuing from the mine simulator and at the same time will rarely result in a triggering of the stopping mechanism by spurious electromagnetic signals from sources other than the mine simulator. The reaction time of the mine simulator must be such that actuation will occur under one of the first three roadwheels when the tank is traveling at speeds up to 20 miles per hour. Statistical methods utilizing efficient experimental design are employed to analyze component reliability and the reliability of the system as a whole.
Letter to the Editor—The Use of Row Values in Solution of the Transportation Problem
Authors: Niederjohn James A.
Published: November 2008

A computational procedure for solving the transportation problem by hand that ordinarily has been overlooked is one involving only the computation of row values (or column values if fewer columns than rows) after each iteration instead of both row and column values as required by Dantzig's method [Dantzig, G. B. 1951. Application of the simplex method to a transportation problem. Chap 23 in Koopman's Activity Analyses of Production and Allocation. Wiley, New York.].
Queuing Systems in Which the Discipline is “Last-Come, First-Served”
Authors: Wishart David M. C.
Published: November 2008

In this paper we compare the waiting-time distributions under different queue disciplines of customers in a single-server queuing system with Poisson input and general (independent) service time. To make the comparison it is necessary to know the distribution of the unexpended service time at a moment of arrival, and the distribution of busy periods. These are discussed and it is shown that the variance of the waiting-time distribution when the queue discipline is “last-come, first-served” is greater (whatever the service-time distribution) than the corresponding variance when the queue discipline is “first-come, first-served.” The same comparison is also discussed (and is shown to be simpler) for the system with general independent input and negative exponential distribution of service times.
Simulation of Air Operations with the Air-Battle Model
Authors: Adams R. H. , Jenkins J. L.
Published: November 2008

This paper discusses the Air-Battle Model that, with its supporting computer programs, is a device for simulating a large-scale two-sided global war on a high-speed digital computer. The three parts, the Plan Converter, the Air-Battle Model, and the Output Programs, of the Air-Battle-Model System are discussed. Some applications of the Air-Battle Model are shown and the technique of using gross summary measures to obtain a feel for some key conclusions and using detailed studies to determine why some conclusions resulted is demonstrated.
The Nature and Validity of Operations-Research Studies, with Emphasis on Force Composition
Authors: Strauss Walter J.
Published: November 2008

The epistemology of operations research directed at force composition or weapon-system selection is different from that of the physical sciences. Though tests of parts of the operations-research process are possible, and indeed required, no empirical tests of the general recommendations are possible. It is thus found that this type of operations research is not science in the sense of the physical sciences. Hence the philosophical question of the nature and validity of operations-research studies arises. The tests of validity, the criteria for judging quality, involve judgment. Several criteria for judging are presented. In practice a combination of all is required. The methodology of operations research, the subject matter of the problem, and the expertness of the analyst, all play a role in lending credence to the recommendations of a study.
Letter to the Editor—The Bayesian Approach to the Reliability-Confidence Relation for Exponential Failure
Authors: Pugh Edward L.
Published: November 2008

In this paper, Bayes' postulate is applied to a problem whose traditional solution, in the sense of Neymann and Pearson, is readily available. A comparison reveals some interesting differences and similarities of the two solutions. The Bayesian solution is believed to be the more realistic of the two in the particular application studied.
Time-Dependent Solution of the Many-Server Poisson Queue
Authors: Saaty Thomas L.
Published: November 2008

In this paper we obtain the Laplace transform of the transient probabilities of the ordered queuing problem, with Poisson inputs, multiple channels, and exponential service times. Explicit expressions are derived for the two-channel case and known equilibrium conditions are shown to hold. The proof proceeds in two stages. The first obtains the Laplace transform of the generating function of the system and the second solves a first order linear partial differential equation in a restricted generating function introduced to determine the Laplace transform of the probability functions appearing in the first generating function. In the two-channel case the solution is decomposed into two components, one of which is immediately related to the well-known solution of the single-channel queue. We also study the problem with different service distributions for the two-channel case and compute the distribution of a busy period for that case.
A Decade of Military Operations Research in Perspective—A Symposium
Authors: Boldyreff A. W.
Published: November 2008

This all-day Symposium was held at the Fourteenth National Meeting of the Operations Research Society of America, in St. Louis, Missouri, on October 23, 1958. In a new and rapidly developing discipline, it is advisable to assess progress periodically, to examine the record both on the credit and on the debit side, and to look for future trends. It was for this reason that this Symposium was organized.

Six papers were presented by the representatives of the six principal operations-research agencies of the national-defense establishments of the United States and Canada. These were followed by concluding remarks by Omond M. Solandt. Unfortunately Hugh J. Miser's paper, on the work of the Operations Analysis Office of the US Air Force, was not made available for publication herewith.
Letter to the Editor—Correction and Addendum to “A New Measure of Effectiveness for Queuing Problems”
Authors: Rawdin Eugene
Published: November 2008

Dr D. Y. Barrer and Mr. Kenneth W. Webb have called to my attention a fault in my Letter to the Editor, “A New Measure of Effectiveness for Queuing Problems,” Opns. Res. 8 278–280 (March–April 1960) and have presented constructive criticism regarding the matter. Briefly, the fault resides in the fact that equations (8) and (9) do not recognize the effect of the servers upon the impatience of the customers, and that the subscript n in these equations refers to the number of customers in the system, not only in the queue.
A Study of Optimum Assembly Runs
Authors: Mills Edwin S. , McClain Hartsel G.
Published: November 2008

This paper reports on the formulation and application of a mathematical model of optimum assembly runs. The study was conducted in a large manufacturing firm and was concerned with the assembly and storage of expensive electronic equipments for use in commercial aircraft. The principle costs pertaining to this study involved the purchase of parts, internal parts fabrication, final assembly and inventories of raw materials, goods in process and finished goods. The most detailed consideration was given to assembly costs and these were derived directly from learmng curves which had been estimated from time-card records. Consideration was given to the effects on costs not only of varying the run size but also of varying the rate of assembly by altering the assembly time cycle. Thus the model includes as decision variables both the length of the run and the rate of assembly. It is formulated so that these decisions can be made simultaneously in a routine, clerical way. Finally, some remarks are made concerning the practical use of the model in the manufacturing operation.
The Greatest of a Finite Set of Random Variables
Authors: Clark Charles E.
Published: November 2008

The variables ξ1, …, ξn have a joint normal distribution. We are concerned with the calculation or approximation of max(ξ1, …, ξn). Current analyses and tables handle the case in which the ξı are independently distributed with common expected values and common variances. This paper presents formulas and tables for the most general case with n = 2. When n > 2, the problem becomes cumbersome. This paper presents formulas and tables that permit approximations to the moments in case n > 2. The moments are approximated by iteration of a three-parameter computation or, alternatively, through successive use of a three-parameter table, which is given. Recent applications of the theory are described.
Allocating for Acceptable Risk Instead of Expected Value
Authors: Bennett William S.
Published: November 2008

Allocation of inventory, spares, or redundancy in reliable systems often seeks to maximize expected orders filled or hours until failure (assuming known distributions). Often there is no opportunity for an averaging process to permit this expectation to materialize. Each operation of the system may be critical, instead of the average of many, or the first shortage may terminate the whole operation. Predictable adequacy of each operation is attained by considering the full distribution, e.g., of operating hours before failure, instead of just the mean (expected) value. Distributions with small standard deviations permit more precise prediction of probable time before failure (shortage). Plans based on marginal utility concepts tend to avoid the expected-value trap but do not necessarily minimize the appropriate risk of shortage. Operating characteristic curves, like those used in quality control, allow intelligent consideration of the risks involved in choosing among alternate allocation plans. Allocation of a small number of stock items is used to illustrate the criterion.
Military Operations Research—A Personal Retrospect
Authors: Whitmore William F.
Published: November 2008

Several instances, drawn from personal experiences since 1945, are presented in which military operations research has had an impact on national policy decisions. An attempt is made to identify instances of failure to influence higher authority, as well as admitted successes. Failures to transmit past experience are noted, with resultant need for rediscovery of results and tactics. The predominant point of view is that of the “scientific analyst,” working as liason with operational staffs, as opposed to that of the worker in large OR teams. Admittedly, these latter provided the analyst with his working capital, but the personal relation between analyst and operational commander is frequently decisive for the acceptance of the work of the larger group.
Letter to the Editor—A Letter of Resignation
Authors: Shortley George
Published: November 2008

To the Council of the Operations Research Society of America. I should like to submit my resignation, as Editor of the Society and Chairman of its Publications Committee, effective as of the Ninth Annual Meeting in May 1961 or as soon thereafter as arrangements can be completed for providing a successor.
Letter to the Editor—Comments on a Paper by Bowman
Authors: White William W.
Published: November 2008

In the paper, “Assembly-Line Balancing by Linear Programming,” that appeared in Operations Research 8, 385–389 (1960), E. H. Bowman presented two linear program formulations for the assembly-line balancing problem. These two formulations are referred to as the First Linear Program and the Second Linear Program, respectively. The following are comments about, and a reformulation of, the First Linear Program.
Letter to the Editor—Comment on Vazsonyi's Comments on a Paper by Karush
Authors: Benson F.
Published: November 2008

A comment of the paper Vazsonyi, A. 1960. Comments on a paper by Karush. Opns Res. 8 418.
Comments on the Preceding Paper
Authors: Clark Charles E.
Published: November 2008

We wish to indicate how the PERT team faced the problem discussed in Captain Healy's interesting paper.
The Probability Law of the Busy Period for Two Types of Queuing Processes
Authors: Takács Lajos
Published: November 2008

A simple combinatorial method is given for the determination of the joint distribution of the length of the busy period and the number of customers served during this period for two types of single-Berver queuing processes. (1) Customers arrive at a counter according to a Poisson process and the service times have a general distribution, (2) customers arrive at a counter according to a recurrent process and the service times have an exponential distribution.
Letter to the Editor—Comments on a Paper by McDowell
Authors: White D. J.
Published: November 2008

Ian McDowell's paper on “The Economical Planning Period for Engineering Works” [Opns Res. 8 533–542 (1960)] discusses a problem that can be fruitfully investigated with Bellman's dynamic-programming approach.
On a Problem of Preemptive Priority Queuing
Authors: Avi-Itzhak B. , Naor P.
Published: November 2008

A priority queuing system is considered possessing the following properties. There exist two populations of potential customers. One population of regular customers is infinitely large and its arrival characteristics are well-represented by a Poisson stream of constant intensity. The other population consists of a relatively small number of extraordinary customers. The arrival of each of these extraordinary customers is governed by an individual constant Poisson intensity. Service is given at a single station and regular customers on service are preempted by any arriving extraordinary customer. The expected value, the variance, etc., of the queue of ordinary customers is derived. Various relations given by previous authors are shown to represent special cases of the model discussed in this paper.
Cost Functions for Systems with Spare Components
Authors: Morrison Donald F.
Published: November 2008

Cost functions for determining the optimum number of spare elements to be assigned to systems of identical components under a certain replacement scheme are investigated. The properties of one cost function are studied for component life as an exponentially distributed random variable, and tables are presented of the number of spare components that minimize the function for specified cost ratios. The problem of the optimum number of spares is also considered for systems in which unfailed components may be salvaged for use with later systems.
The Future of Arms Control
Authors: Schelling Thomas C.
Published: November 2008

Arms control is based on the recognition that military preparations, and even war itself, are nonzero-sum-game activities, with scope for mutually advantageous accommodation even among potential enemies. It is an extension of traditional strategy in the direction of collaboration with potential enemies in the interest of reducing the likelihood of war, the limitation of war if it occurs, or the costs and risks of preparation for war. But the nature of this relation to potential enemies is still only dimly understood, even the character of the arms control that may be the most promising is hard to predict. It is not even clear that, by some measures, the level of armament is necessarily reduced. Although we have had a great deal of passive arms control, we are in a very exploratory stage with respect to explicit military alliances and understandings with potential enemies. It seems almost certain that the kind of strategic analysis that is needed to arrive at good military policy would also be needed to arrive at good arms-control policy.
Letter to the Editor—The Use of Abstract Manned Simulation to Aid Weapon Planners
Authors: Geisler M. A. , Steger W. A.
Published: November 2008

Modern weapon systems are a complex amalgam of the end item hardware, the support ground operational and support equipment, spare parts, trained operational and logistical personnel, and a set of operational goals with a management system designed to help attain them. Given a choice of a hardware system to be developed into a weapon system, the weapon system's planners are left with an enormous number of choices between competing alternatives before that hardware system is developed into an operational weapon system. This decision-making process may involve several hundred “milestones,” many opinions, more than six years, and several billion dollars.
Double Queues and Impatient Customers with an Application to Inventory Theory
Authors: Sasieni Maurice W.
Published: November 2008

This paper starts by observing that any queuing system can be viewed as two symmetric queues, one of customers in line for service, and one of idle clerks, awaiting customers. Usually at least one of the queues (the idle clerks) has a finite limit, but examples, such as passengers and taxis at a taxi stand, exist where both queues are unlimited. In such cases, if arrival and service rates are independent of queue length, at least one of the queues is unstable and grows indefinitely as time passes. In practice there has to be some factor that limits queue length, and a possible mechanism is to assume that both passengers and taxis become impatient and will leave if, after some fixed amount of time, they have not been “serviced.” The equations governing such a system are developed and steady-state solutions are found. It is shown that steady-state solutions always exist for both queues, the means and variances (which are finite) are given. In the last part of the paper an application to inventory theory is suggested. Here the backlog of orders corresponds to the queue of customers, and items in stock to the idle clerks. It is assumed that orders not filled in a certain time are cancelled and that items are perishable and cannot be sold if stocked too long.
The Distribution of Urban Population and an Application to a Servicing Problem
Authors: Weiss Herbert K.
Published: November 2008

The growth of the urban component of a nation and the shift in population from rural to urban areas in the course of industrial development are processes that show both regularity and predictability. Consequently, it is possible to describe the concentration of population in terms of population density and area by comparatively simple expressions. In this paper expressions are examined for the distribution of people within cities, for the distribution of city sizes within the United States, and for the total population contained within boundaries described in various ways. These generalizations have many applications, both in industrial planning and in civil defense and other military considerations. The paper shows how it is possible to make approximate estimates of the total population serviced by operations of specified types as a function of the cost structure of the operation.
Catalytic behavior of unsupported Co materials in the reformation of ethanol to hydrogen: An in situ diffuse reflectance infrared Fourier transform (DRIFT)-mass spectrometry study
Authors: Martí Salvador , Homs Narcís , Pereira Evandro Brum , Ramírez de la Piscina Pilar
Published: November 2008

New unsupported Co catalysts were studied in the ethanol steam-reforming reaction by in situ diffuse reflectance infrared spectroscopy and on-line mass spectrometry (MS) techniques. The initial ethoxy surface species evolved to surface-acyl species and to acetaldehyde intermediate at temperatures ca. 473 K. The subsequent formation of surface-acetate species occurs at ca. 573 K. Further, the acetate species mainly evolve above 573 K to H2 and CO2 products. The route to ketone formation was inhibited on these materials. The presence of surface-hydroxyl groups, which are probably related to the formation of a CoO phase under the reforming conditions, was determined. Alkaline addition shows a beneficial effect on the ethanol steam-reforming over bulk Co catalysts.