bluuebunny/crossref_metadata_2025 huggingface dataset:
Queuing with Preemptive Priorities or with Breakdown
Authors: White Harrison , Christie Lee S.
Published: November 2008

Preemptive priority is defined and contrasted with head-of-the line priority Poisson arrivals at a single server are assumed throughout, and only steady-state solutions are found. The effect on service-time statistics of preempted items re-entering service according to various rules is considered. A formula for the joint probability distribution of queue lengths of two preemptive priority classes is derived assuming negative exponential service statistics. Moments of this queue length distribution are found by a generating function approach. For any number of preemptive priority classes, expected times-in-system are found for a general service time distribution for each class, and for negative exponential service, with the same rate for each class, the generating functions of the delay distributions are also obtained. The similarity of queuing with breakdown to queuing with preemptive priority is pointed out, and two models of breakdown effects are worked out.
Discrete-Time Queuing Theory
Authors: Meisling Torben
Published: November 2008

This paper contains an analysis of a single-server queuing system for which time is treated as a discrete variable. The number of customers arriving within a fixed time interval is assumed to obey a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent but are not otherwise restricted. It is furthermore assumed that customers are served in their order of arrival. Formulas for the mean queue length and the mean waiting time are derived for the general case and it is shown how the previously obtained results for the corresponding continuous-time system may be derived from the results given here by a limiting process. The results are applied to two special cases, (1) a service-time distribution, which has the form of a geometrical progression, and (2) a fixed service-time distribution.
A Discussion of Random Methods for Seeking Maxima
Authors: Brooks Samuel H.
Published: November 2008

In the design of experiments for the purpose of seeking maxima, random methods are shown to have an important place in the consideration of the experimenter. For a rather large class of experimental situations, an elementary probability formulation leads to an exact statement for the number of trials required in the experiment. The rationale, application, and relative merits of random methods are discussed.
A Target-Assignment Problem
Authors: Manne Alan S.
Published: November 2008

This paper is concerned with a target assignment model of a probabilistic and nonlinear nature, but nevertheless one which is closely related to the “personnel-assignment” problem. It is shown here that, despite the apparent nonlinearities, it is possible to devise a linear programming formulation that will ordinarily provide a close approximation to the original problem.
A Practical Guide to the Dual Theorem
Authors: Wagner Harvey M.
Published: November 2008

A summary of the important variations on the simplex method is presented, with an emphasis placed on the connection between these techniques, the revised simplex method, and the dual theorem. Only elementary matrix algebra is employed to enable the nonmathematician to utilize the various algorithms. Specifically, the dual simplex algorithm, parametric programming, and techniques for additional and secondary constraints, and for upper bounded variables are discussed.
Letter to the Editor—Optimum Preventative Sampling Via Dynamic Programming
Authors: Kalaba Robert
Published: November 2008

In an interesting paper entitled “Optimum Preventative Sampling,” Whittle (Whittle, P. 1954. Optimum preventative sampling. J. Opns Res. Soc. Am. 2 197–203.) has discussed the general problem of carrying out a sampling operation—not for the customary purpose of estimating a characteristic of a population but for the purpose of discouraging the arising of defectives. In general the more intense the sampling is, the greater is the deterrent effect on a potential transgressor. We wish to show how the optimization problem to which Whittle's model leads, and which is typical of a large class of related problems, may be treated advantageously by the functional equation technique of dynamic programming (Bellman, R. 1957. Dynamic Programming. Princeton University Press, Princeton, New Jersey.).
Letter to the Editor—Reply: Heuristic Problem Solving
Authors: Simon Herbert A. , Newell Allen
Published: November 2008

According to the preceding letter, Richard Bellman thinks that our predictions about heuristic programming are incorrect, irresponsible, and sensationalist. We should like to comment on these three points in turn.
Two Uses of the Diffused-Target Concept in Aerial Target Analysis
Authors: Thompson W. A.
Published: November 2008

In target analysis, events of interest frequently depend on miss distance in such a way that the event becomes increasingly likely with decreasing miss distance. The most obvious example of such an event is killing the target. In certain cases it is possible to express the relation between miss distance and likelihood of the event in a functional form that leads to particularly simple mathematical expressions. The first section presents an outline of this theory. The second section applies this theory, usually called the diffused target concept, to the problem of studying the adequacy of a fuze under operational conditions. The third section uses the diffused target concept to study the effect of aiming bias on kill probability.
Effectiveness of Troops Exposed to Thermal Radiation from Nuclear Weapons
Authors: Langevin R. A. , Greenstone R. , Elder C.O.
Published: November 2008

Troops exposed to thermal radiation from nuclear weapons have the possibility of taking evasive action to protect them from burns. A method for predicting the effectiveness of troops attempting such evasion is presented here and it is shown that there is much to be gained by instant evasive action, particularly for the larger yield weapons.
A Failure Model for Equipments Undergoing Complex Operation
Authors: Stoller David S.
Published: November 2008

A simple failure model for equipment undergoing several cycles of operation is given by the expression, 1 − exp(−Λ∑ı=1ı=kτi), where Λ is the failure coefficient, τi is the length of the ıth cycle of operation, and k is the number of cycles. A consequence of this model is that the probability of failure for a given total operating time is independent of the number of cycles of operation. It is shown that, under certain assumptions, a failure model that takes account of the number of cycles of operation, as well as the operating time, is given by the expression, 1 − exp(Λ0∑ı=1ı=kτı + Λ1k). Interpretations of the constants, Λ0 and Λ1, are given. Also discussed is a method for testing the plausibility of the model against failure data.
Letter to the Editor—Application of Operations Research in Farm Operations and Agricultural Marketing
Authors: French Charles E. , Snodgrass Milton M. , Snyder James C.
Published: November 2008

Operations Research, as generally conceived in agriculture, emphasizes interdisciplinary endeavor and quantitative measurement. Farm operations involve a wide range of problems, and agricultural marketing concepts are much broader than those of business marketing. Thus, it is difficult to delineate the area of application of OR in agriculture. Yet, agriculturalists are using OR and this note is an attempt to (a) sketch the historical perspective of quantitative measures in agricultural economics research, (b) catalog recent work of agricultural economists which is considered by them to be OR, (c) list a few problems in application of OR which we feel in a sense to be unique with agriculture, and (d) speculate briefly on the future of OR in agriculture.
In-Process Inventories
Authors: Simpson Kenneth F.
Published: November 2008

Many manufacturing operations can be looked upon as chains of operations separated by inventories. In any real case, there is a question about how inventory investment should be balanced between these various in-process inventories. Investigation of this situation for a very general control system—the base-stock system—leads to some general results which enable one to answer this question by examining a (generally small) finite number of possibilities. The conclusion may be stated “The service time for any inventory should be zero”. An important corollary of the method is that it answers the question of what points in the manufacturing operation should be inventory points and what points should not.
Methods of Sequencing in Job Shops—A Review
Authors: Sisson Roger L.
Published: November 2008

In a job shop the sequence of operations required to process a job lot varies from job to job. At any time there are many jobs in the shop competing for the use of the manufacturing facilities. The problem of sequencing the jobs so as to optimize profits has not been solved. A number of solutions are available for special cases. Simulation appears to be a promising method of study for this problem. This paper reviews the definition of the job shop, the models proposed to date, solutions based on these models, and surveys prospects for the future.
Purchasing Raw Material on a Fluctuating Market
Authors: Fabian T. , Fisher J. L. , Sasieni M. W. , Yardeni A.
Published: November 2008

The essential decision problem in buying on a fluctuating market is the timing of the purchases and the decision of how much to purchase when the time arises. This study presents a solution to the problem of determining inventories of raw material when the price of this raw material fluctuates from period to period. The study is presented in two parts Part II develops a formal dynamic-programming model and its analytic solution under the assumptions that the following data are available for decision making: (a) the existing inventory, (b) the current market price, (c) the cost of holding inventory and the cost of shortage, and (d) probability-density functions for future price and demand of the raw material. Part I presents the results of an actual case study that represents a generalization of the model developed in Part II. In the actual case study, not only was information available concerning the probability-density functions for future price, but price forecasts for the next three periods were also available. Because of the difficulty of solving the original dynamic-programming model developed in Part II when the probability-density functions for future price are dependent from period to period, a surrogate model was developed. This surrogate model combines the analytic solution in its original form with a series of simple decision rules which were easily implemented. Percentage cost savings are also presented in Part I.
The Dynamics of Military Combat
Authors: Brackney Howard
Published: November 2008

In this paper the essentials of warfare are given theoretical treatment in a particularly simple way. A theory of warfare, i.e., a combat dynamics, is derived that is in close agreement with what man has learned about war through his use of it. To the theoretical work of earlier investigators the present study adds a reconnaissance concept and a weapons concept both being stated in explicit mathematical form. The theoretical dynamics appears to be applicable to warfare in the nuclear age.
Traffic Dynamics: Analysis of Stability in Car Following
Authors: Herman Robert , Montroll Elliott W. , Potts Renfrey B. , Rothery Richard W.
Published: November 2008

The manner in which vehicles follow each other on a highway (without passing) and the propagation of disturbances down a line of vehicles has been investigated further. Criteria are derived for both local and asymptotic stability in a chain of vehicles. The influence of next nearest neighbors as well as a statistical theory of stability is discussed. “Acceleration noise” is proposed as a parameter that might be employed to characterize the driver-car-road complex under various conditions. Some preliminary experimental measurements of acceleration noise are discussed.
On Optimum Target Assignments
Authors: denBroeder G. G. , Ellison R. E. , Emerling L.
Published: November 2008

This note is concerned with two target assignment models. An optimum assignment is one which maximizes the expected value of targets destroyed. The first model, which admits an explicit solution, associates values only with the number of targets destroyed. An algorithm which enjoys a computational nicety is established when the values of the individual targets are assumed known. This latter model is a special case of Flood's target-assignment model.
Dynamics of Two Classes of Continuous-Review Inventory Systems
Authors: Galliher H. P. , Morse Philip M. , Simond M.
Published: November 2008

The classes of inventory systems studied in this paper involve random, captive demand and assume continuous review of inventory and replenishment of stock in lots of size Q. The replenishment doctrine is to initiate an order for Q items whenever the sum of stock on hand and stock on order falls below a pre-determined level R. Possible examples are inventories of spare parts for maintenance, of military supplies, or of merchandising stock, so costs of purchase, of storage, and of backordenng are included in the measures of effectiveness. A general relation, between cost of back-orders and minimal-cost probability of stock-out, is derived, similar to that reported earlier [Morse, P. M. 1959. Solution of a class of discrete-time inventory problems. Opns Res. 7 67–78.] for discrete-time systems. For the first class of system studied, demands arrive at random, with a stationary probability distribution of arbitrary form, and all replenishment times are of the same length. For the second class, demand arrivals are Poisson and replenishment times are distributed exponentially. Exact solutions, together with expressions for expected values of operating cost, probability of stock-out, Pout, of stock on hand, etc., are obtained for both classes of system. For the first class, specific formulas are given for the frequently-encountered cases of Poisson and stuttering Poisson demand arrivals. An asymptotic form for these solutions is obtained, valid for both classes of system over the range of parameters of practical interest. In terms of this asymptotic formulation, equations, tables, and graphs are given, from which the re-order level R and replenishment lot size Q can be determined for minimal cost and/or for a pre-set value of Pout, or to satisfy other managerial requirements. For Poisson demand, comparison between the two systems shows that when Q is small, increase in variance of replenishment time makes very little difference in the requirements for R, but when Q is large an increase in variance of replenishment time requires an increase in the value of R, the re-order level, to maintain the optimality of the solution.
A Model for “Real” Poker
Authors: Newman Donald J.
Published: November 2008

A two-person poker game is analyzed and a solution is obtained. The essential difference between this game and those treated in the past is the fact that this one allows arbitrarily high bets. It turns out, curiously enough, that the number 7 is present in an essential way in both plavers' solutions, and furthermore, the value of the game turns out to be 1/7 of the ante. I leave to the numerologists the explanation of this mystical appearance.
A Solution to the Transportation Problem with Nonlinear Costs
Authors: Shetty C. M.
Published: November 2008

In this paper a solution to the generalized transportation problem taking nonlinear costs is given. For the sake of concreteness the problem is discussed in a production and marketing context, though by suitable interpretations it can cover a very wide range of problems. The solution procedure is an iterative method wherein a feasible solution is obtained at each stage, and the value of the criterion function is improved in going from one stage to another.
Reliability of Aircraft Structures in Resisting Chance Failure
Authors: Coleman John J.
Published: November 2008

In this analysis, a measure is developed for the capability of aircraft structures to withstand chance failure, as contrasted to fatigue failure, over the design life of any aircraft system. The measure developed is similar to that for reliability, except the failure rate is specified completely in terms of the power spectral properties of the structural response to the environment. This relation of the reliability to the power spectral parameters enables the reliability of a structure to be predicted. For a given environment and reliability requirement, the analysis could also be used as a basis for determining optimal structural designs.
On Base-Stock Level Inventory Control
Authors: Gaver D. P.
Published: November 2008

Mathematical models are used to discuss the following inventory situation customer demands on the warehouse stock of an item fluctuate independently and randomly during successive discrete time periods (e.g., weeks), demands that cannot be satisfied from stock on hand are “lost,” e.g., are satisfied elsewhere. There is a one-period lag in warehouse replenishments, and a base-stock-level policy determines the sizes of warehouse replenishment orders. Under these conditions available stock at the beginning of a period is a Markov chain, of Morse [Morse, P. M. 1959. Solutions of a class of discrete-time inventory problems. Opns Res. 7 67–78 (in particular pp. 76–78).]. This chain is discussed, and its probabilities are used to evaluate stock-out and inventory carrying costs associated with the end of a period. The above costs are also evaluated for the easily analyzed case in which disappointed demands backorder. A numerical example indicates that optimum base-stock-levels determined on the backordering assumption may be nearly identical with those determined assuming impatience.
A Theory of Allocation of Stocks to Warehouses
Authors: Simpson Kenneth F.
Published: November 2008

An allocation problem that frequently arises in large industrial and military supply systems is this a certain quantity of material has just been received, or is about to be received by a central agency, and another quantity is expected to be received at a known time in the future. The material must be distributed, now, to a number of peripheral activities that we can think of as warehouses. The statistics of consumption at each warehouse are known, and the problem is to allocate the material to the warehouses in a manner that optimizes some management objective. In this paper, a model for the two most common management objectives is proposed, and in each case, a basic theorem is proved that tells how the allocation should be performed. An approximation leads to a final formula that is simple and practical enough to be used in allocating large numbers of items, with either computer or hand computation.
Decomposition Principle for Linear Programs
Authors: Dantzig George B. , Wolfe Philip
Published: November 2008

A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn (from its optimal basic feasible solutions) new activities (columns) for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs (using new proposals and earlier ones) consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.
The Problem of the Amber Signal Light in Traffic Flow
Authors: Gazis Denos , Herman Robert , Maradudin Alexei
Published: November 2008

A theoretical analysis and observations of the behavior of motorists confronted by an amber signal light are presented. A discussion is given of the following problem when confronted with an improperly timed amber light phase a motorist may find himself, at the moment the amber phase commences, in the predicament of being too close to the intersection to stop safely or comfortably and yet too far from it to pass completely through the intersection before the red signal commences. The influence on this problem of the speed of approach to the intersection is analyzed. Criteria are presented for the design of amber signal light phases through whose use such “dilemma zones” can be avoided, in the interest of over-all safety at intersections.
Measures of Dependability
Authors: Hosford John E.
Published: November 2008

This paper defines dependability as the probability that a system will be able to operate when needed. There are many possible measures of dependability. Three of the most important are pointwise availability—the probability that the system will be operable at a specified instant of time reliability—the probability that the system will not fail during a given interval of time, and interval availability—the expected fraction of a given interval of time the system will be operable. The probability that the system is operable at the start of the interval must be determined to evaluate reliability or interval availability. If the system's failure and repair rates do not change, this probability is easily determined. However, most systems are not required to perform their duty constantly, therefore, the system has a different set of failure and repair rates depending upon whether the system is performing its duty, is off, or is warming up. An equation is given to determine the probability that the system is operable at the start of an interval if the system repeats the series of different intervals (duty, off, warming up, etc.) in identical form.
Optimum Preventive Maintenance Policies
Authors: Barlow Richard , Hunter Larry
Published: November 2008

Two types of preventive maintenance policies are considered. A policy is defined to be optimum if it maximizes “limiting efficiency,” i.e., fractional amount of up-time over long intervals. Elementary renewal theory is used to obtain optimum policies. The optimum policies are determined, in each case, as unique solutions of certain integral equations depending on the failure distribution. It is shown that both solutions are also minimum cost solutions when the proper identifications are made. The two optimum policies are compared under certain restrictions.
Brand Preferences and Simple Markov Processes
Authors: Maffei Richard B.
Published: November 2008

Brand preference information combined with a simple two-dimensional Markov process can be used to study characteristics of market dynamics. Advertising activity can be used to alter temporarily the brand preference structure of the consuming public. Such changes generate interesting transient conditions that can be studied mathematically. Discussions of time relations, period-to-period changes in market shares, gains and losses resulting from promotional activity and rapidity of convergence to new steady-state values are all considered. In a concluding section, sensitivity characteristics of the relations are commented upon.
On the Job-Shop Scheduling Problem
Authors: Manne Alan S.
Published: November 2008

This is a proposal for the application of discrete linear programming to the typical job-shop scheduling problem—one that involves both sequencing restrictions and also noninterference constraints for individual pieces of equipment. Thus far, no attempt has been made to establish the computational feasibility of the approach in the case of large-scale realistic problems. This formulation seems, however, to involve considerably fewer variables than two other recent proposals [Bowman, E. H. 1959. The schedule-sequencing problem. Opns Res. 7 621–624; Wagner, H. 1959. An integer linear-programming model for machine scheduling. Naval Res. Log. Quart. (June).], and on these grounds may be worth some computer experimentation.
Transient Behavior of Single-Server Queuing Processes with Recurrent Input and Exponentially Distributed Service Times
Authors: Takács Lajos
Published: November 2008

Customers arrive at a counter at the instants τ1, τ2, …, τn …, where the inter-arrival times τn − τn−1(n = 1, 2, …, τ0 = 0) are indentically distributed, independent, random variables. The customers will be served by a single server. The service times are identically distributed, independent, random variables with exponential distribution. Let ξ(t) denote the queue size at the instant t. If ξ(τn − 0) = k then a transition Ek → Ek+1 is said to occur at the instant t = τn. The following probabilities are determined [Formula: see text] Gn(X) = the probability that a busy period consists of n services and its length is at most x, and further the distribution of the number of transitions Ek → Ek+1 occurring in the time interval (0, t).
Finite Queues and Cyclic Queues
Authors: Koenigsberg Ernest
Published: November 2008

The finite queue problem, for which tables exist [Peck, L. G., R. N. Hazelwood. 1958. Finite Queuing Tables. ORSA Publications in Operations Research No. 2. Wiley, New York.], is a special case of the cyclic queue [Koenigsberg, E. 1958. Oper. Res. Quart. 9 22–35]. We consider a closed system with two stages, the first a repair stage and the second an operating stage. There are N machines in the system, of which a maximum of A can be operating or productive at any one time (A operators). When breakdowns occur at a mean rate μ2 the machines enter the repair stage which has M parallel servers (M repairmen), who service the machines at a mean rate μ1. If μ1 and μ2 are defined by an exponential distribution, then the numbers N, A, M, and μ2/μ1 define the output of the system. When A = N the problem is identical to the Swedish Machine problem for which tables are already available [Peck, L. G., R. N. Hazelwood. 1958. Finite Queuing Tables. ORSA Publications in Operations Research No. 2. Wiley, New York.].
The Use of Wye-Delta Transformations in Network Simplification
Authors: Akers Sheldon B.
Published: November 2008

In network problems such as the maximum-flow problem and the minimum-route problem, it is often desirable to attempt to simplify the given network before applying the various algorithms available for its solution. This is especially true when the maximum flow (or minimum route) between a number of different pairs of points is desired. Various transformations are discussed that can lead to considerable simplification. In particular, it is shown that wye-delta transformations analogous to those used with electrical networks are available. The application of these transformations to the maximum-flow problem (both with and without node capacities) is discussed and it is shown that for the minimum-route problem dual transformations apply. The effect of the topological properties of a network on the usefulness of these transformations is examined briefly. The application of the transformations to two networks in the literature is shown.
Optimal Composition and Deployment of a Heterogeneous Local Air-Defense System
Authors: Leibowitz Martin L. , Lieberman Gerald J.
Published: November 2008

A point target is threatened with attack by a raid of enemy aircraft. The enemy has a spectrum of attack tactics at his disposal, each tactic being defined in terms of speed, altitude, bomber cross-section, and raid size. The defense consists of a deployment of missile batteries surrounding the target. There are several types of missile batteries, each having a characteristic cost and a characteristic capability against a given attack tactic. The problem is to determine the optimal mix of missile batteries, and the deployment of that mix, so as to obtain the best defense against the entire spectrum of attack tactics. Although a general approach is outlined, the model is developed and the solution obtained for the special case in which the measure of effectiveness is linear with respect to both raid size and the number of defense units.
Optimal Persistence Policies
Authors: MacQueen J. , Miller R. G.
Published: November 2008

This paper deals with the problem of whether or not a search activity should be started and, if started, whether or not it should be continued. This problem suggests a model that is described. The model gives rise to a general functional equation for which existence and uniqueness conditions are given. Several examples are discussed, solutions to the specific functional equations appropriate to the examples are given, and the optimal policies are characterized.
Assembly-Line Balancing by Linear Programming
Authors: Bowman E. H.
Published: November 2008

Linear-programming solutions to the assembly-line balancing problem are offered in two forms. Feasible solutions depend on work recently presented on integer solutions to linear-programming problems. As yet, the computation involved for a practical problem would be quite large.
The Properties of Recurrent-Event Processes
Authors: Jewell William S.
Published: November 2008

The theory of recurrent events is often used in operational models to describe the stochastic repetition of a certain event—for instance, customers arriving at a queue. This paper explores in some detail the relation between the distributions of (1) the spacings between the events, and (2) the cumulative number of events that occur in a given time interval. It is shown that different results are obtained for the second class of distributions (called the state probabilities) and their averages, depending upon the location of the origin of the measurement interval relative to the process. Two situations of interest—starting after an event has occurred, and starting “at random”—are explored, and various asymptotic results are obtained. Special results for the Poisson, Erlang, and Stuttering-Poisson processes are presented. A condition for the asymptotic normality of the state probabilities is also found.
Waiting Lines with Heterogeneous Servers
Authors: Gumbel Harold
Published: November 2008

A “multiple-booth” server system with nonhomogeneous servers is analyzed under the assumption of Poisson distributed arrivals and exponential service time with different individual mean service rates for each server. Explicit expressions for the state probabilities are obtained in closed form under “steady-state” conditions and the expected length of the waiting line is derived therefrom. It is shown that an “equivalent” system with homogeneous servers does not exist. The error incurred in assigning each server the arithmetic mean of the service rates of all of them is analyzed and illustrated if expected number in the system is used as a criterion of comparison.
The Economical Planning Period for Engineering Works
Authors: McDowell Ian
Published: November 2008

In certain important situations, the observed nature of the growth of demand for service that must be met by engineering capital works is exponential in form. Plant to meet this demand is provided in instalments, each of which is usually kept in service for a much longer period than that which elapses before the next instalment is required. The problem is, what is the optimum length of the first and subsequent planning periods for various types of plant under different rates of interest and growth? Solutions are presented in this paper. Even though in practical cases the requirements of expediency must be met, it is still helpful to know what is best.
Effects and Causes of Discrepancies in Supply Operations
Authors: Rinehart R. F.
Published: November 2008

A matter that has received scant attention in the literature of operations research is the role of discrepancies between physical stocks and stocks of record in a supply operation. Discrepancies not only exert a deleterious effect on the performance of the supply function, but may have a serious effect on the realization of benefits to be derived from implementation of theoretically optimal methods of inventory control and procurement or production scheduling. The present paper reports on a case study of discrepancies and their causes in a supply facility of an agency of the Federal Government. Contrary to the general expectation that the massive and complex paper work system connected with processing of issues and receipts was the principal source of discrepancies, it was possible to determine that about 80 per cent of the discrepancies were caused by the discrepancy-correcting procedures themselves. As a result two principal targets for further study are clearly delineated, (1) the inventorying process and (2) the stock balance adjustment procedures. Even on the basis of preliminary study some ameliorating recommendations were possible.
Allocation of Two Types of Aircraft in Tactical Air War: A Game-Theoretic Analysis
Authors: Berkovitz L. D. , Dresher Melvin
Published: November 2008

The problem of allocating two types of aircraft (bombers and fighters) among three different air tasks (counter air, air defense, and support of ground operations) in a multistrike campaign is analyzed as a two-sided war game. It is assumed that a bomber can be used in either the counter-air or ground-support operations, while a fighter can be used in either the air defense or ground support roles. That is, bombers and fighters have one task—ground support—in common. Optimal employment during the last strikes of the campaign consists of a concentration of all resources in support of ground operations. Optimal employment during the early strikes of the campaign requires randomization by both sides.
Probabilistic Model of System Operation with a Varying Degree of Spares and Service Facilities
Authors: Ashar Kanu G.
Published: November 2008

The techniques for evaluating the probabilistic properties of systems having identical operational and spare units with different facilities for repairs are discussed in this paper. The important properties studied are (a) Reliability and transient behavior of systems, (b) the expected values of times to failures and the measure of variations from the distributions of system failures, and (c) asymptotic or steady-state probability of such a system being in unavailable state. The general expressions are obtained for many cases, while the methods are illustrated by a simple practical example.
Letter to the Editor—The Maximum Capacity Through a Network
Authors: Pollack Maurice
Published: November 2008

The maximum capacity route is defined to be the route between any two given cities (nodes) that allows the greatest flow. This differs from the maximum capacity problem[1] in that only the single best route is desired, in the maximum capacity problem, the object is to find the maximum flow between two nodes using as many different routes as needed. The maximum capacity route problem arises in automatic teletype networks where, for any given origin-destination pair, there is only one route specified.
The Distribution of Radial Error and its Statistical Application in War Gaming
Authors: Edmundson H. P.
Published: November 2008

This paper presents a unified treatment of the assumptions and theorems concerning the distribution of radial error, and demonstrates its statistical application in war gaming. The density function and cumulative distribution function of the radial error are derived and graphed for one, two, and three dimensions. For each of these cases, formulas are given for the expectation, standard deviation, and median of the radial error. Tables of pertinent conversion factors are provided. Results are given for the distribution of detonation points in three dimensions that are useful in war games employing atomic rockets or torpedoes.
Reliability Analysis of a One-Unit System
Authors: Barlow Richard E. , Hunter Larry C.
Published: November 2008

This paper considers an electronic system that upon failure is repaired Only two states—the “on” state and the “off” state—are distinguished. The time-to-failure and the time-to-repair are random variables with general distribution functions. The purpose of the paper is to make available, in single unified treatment, mathematical information that is relevant for a reliability analysis of a one-unit system. The following questions are answered (a) What is the probability that the system will be on at any given time t? (b) What is the probability that it will be on t hours or more during a given time interval (0, T)? (c) What is the expected fractional amount of time that it will be on during (0, T)? (d) What is the probability distribution of the number of failures during a given time interval? (e) What is the expected number of failures during a given time interval?. In particular, it is noted that “down” time is approximately normally distributed for large time intervals. The special cases of exponential failure with exponential and constant repair are given as examples.
Nonlinear Effects in the Dynamics of Car Following
Authors: Newell G. F.
Published: November 2008

It is assumed that the velocity of a car at time t is some (nonlinear) function of the spacial headway at time t − Δ, so the equations of motion for a sequence of cars consists of a set of differential-difference equations. There is a special family of velocity-headway relations that agrees well with experimental data for steady flow, and that also gives differential equations which for Δ = 0 can be solved explicitly. Some exact solutions of these equations show that a small amplitude disturbance propagates through a series of cars in the manner described by linear theories except that the dependence of the wave velocity on the car velocity causes an accleration wave to spread as it propagates and a deceleration wave to form a stable shock. These conclusions are then shown to hold for quite general types of velocity-headway relations, and to yield a theory that in certain limiting cases gives all the results of the linear car-following theories and in other cases all the features of the nonlinear continuum theories, plus a detailed picture of the shock structure.
Letter to the Editor—Some Expected Transition Times in Simple Queues
Authors: Jackson James R.
Published: November 2008

The note describes certain phenomena in the behavior of simple queues, and indicates their possible relevance to the design of simulation experiments. Certain generalizations, which seem to be of only marginal interest, are omitted.
An Inclusive Solution to the Inventory Problem
Authors: Yaspan Arthur
Published: November 2008

This paper gives a unified approach to a set of inventory problems subsumed under the classical inventory problem proposed by Arrow, Harris, and Marschak. This set includes those problems with periodic reordering, proportional costs and revenues, fixed time lags in receipt of an order, and a static criterion of optimality. Within this class shortages may be either back ordered or forgotten, the time lag can be any fixed integral number of periods, including zero, and demands in the various periods may follow any known joint distribution. The method yields a solution for the forgotten shortages case with time lag, as well as the familiar results for the instantaneous case and the back-order lag case. The approach can be modified to allow for a setup cost in purchasing.
A Proof for the Queuing Formula: L = λW
Authors: Little John D. C.
Published: November 2008

In a queuing process, let 1/λ be the mean time between the arrivals of two consecutive units, L be the mean number of units in the system, and W be the mean time spent by a unit in the system. It is shown that, if the three means are finite and the corresponding stochastic processes strictly stationary, and, if the arrival process is metrically transitive with nonzero mean, then L = λW.
Letter to the Editor—Conference on Operational Research in the Health Services of Great Britain
Authors: Flagle Charles D.
Published: November 2008

Officials of the Ministries of Health of England, Ireland, and Scotland, along with a number of researchers and sponsors of research, met at Magdalen college, Oxford, in December 1960, to review programs of operational research in health services in Great Britain.
Nonlinear Follow-the-Leader Models of Traffic Flow
Authors: Gazis Denos C. , Herman Robert , Rothery Richard W.
Published: November 2008

A variety of nonlinear follow-the-leader models of traffic flow are discussed in the light of available observational and experimental data. Emphasis is placed on steady-state flow equations. Some trends regarding the advantages of certain follow-the-leader functionals over others are established. However, it is found from extensive correlation studies that more data are needed before one can establish the unequivocal superiority of one particular model. A discussion is given of some ideas concerning the possible reasons for the existence of a bimodal flow versus concentration curve especially for multilane highways.
Letter to the Editor—The kth Best Route Through a Network
Authors: Pollack Maurice
Published: November 2008

Determining the shortest route through a network is a problem for which many solutions have appeared. Not so well known, but of equal importance, is the generalized problem of determining the kth best route through a network. The purpose of this Letter is to present a formulation of the generalized problem, to reference several known solutions, and to describe a new simple method of solution which possesses some advantages.
Importance Sampling in Monte Carlo Analyses
Authors: Clark Charles E.
Published: November 2008

Some Monte Carlo analyses require hundreds of hours of high speed computer time. Many problems of current interest can not be handled because the computer time required would be too great. Statistical sampling procedures have been developed that greatly reduce the required computer time. Importance sampling is one of these. This paper is an elementary description of importance sampling as used in Monte Carlo analyses.
The Fundamental Theorem of Exponential Smoothing
Authors: Brown Robert G. , Meyer Richard F.
Published: November 2008

Exponential smoothing is a formalization of the familiar learning process, which is a practical basis for statistical forecasting. Higher orders of smoothing are defined by the operator Snt(x) = αSn−1t(x) + (1 − α) Snt−1(x), where S0t(x) = xt, 0 < α < 1. If one assumes that the time series of observations {xt} is of the form xt = nt + ∑ı=Nı=0 aıtı where nt is a sample from some error population, then least squares estimates of the coefficients a, can be obtained from linear combinations of the operators S, S2, …, SN+1. Explicit forms of the forecasting equations are given for N = 0, 1, and 2. This result makes it practical to use higher order polynomials as forecasting models, since the smoothing computations are very simple, and only a minimum of historical statistics need be retained in the file from one forecast to the next.
Priority Assignment in Waiting-Line Problems Under Conditions of Misclassification
Authors: van der Zee S. P. , Theil H.
Published: November 2008

This article deals with priority assignment in waiting-line problems in case the classification on which the priorities are based is subject to errors. The expected waiting time under this condition is derived for a two-priority single-channel system. The procedure recommended involves the introduction of a “mixed” group for those customers who cannot be classified with certainty in group 1 or group 2, and to allocate such a customer to this group when the probability that he really belongs to group 1 lies in a certain interval, the limits of which are determined by the basic data of the waiting-line problem (mean service times, arrival rates, etc).
Letter to the Editor—Information Theory and Search Theory as Special Cases of Decision Theory
Authors: Mela Donald F.
Published: November 2008

It is the purpose of this note to indicate with some simple examples that the connection between the information-theory approach and the search-theory approach is tenuous and that search problems can better be regarded as an application of the more general theory of statistical decision.
Relationships between serum adiponectin levels versus bone mineral density, bone metabolic markers, and vertebral fractures in type 2 diabetes mellitus
Authors: Kanazawa Ippei , Yamaguchi Toru , Yamamoto Masahiro , Yamauchi Mika , Yano Shozo , Sugimoto Toshitsugu
Published: November 2008

Background

Although, adiponectin might be associated with bone metabolism, the relationships between serum adiponectin and bone mineral density (BMD) as well as vertebral fracture in type 2 diabetes are still unclear.

Objective and methods

We investigated the relationships between each of serum total and high molecular weight (HMW) adiponectin versus BMD, bone markers, and the presence of vertebral fractures in a total of 231 men and 170 post-menopausal women with type 2 diabetes.

Results

Multiple regression analysis adjusted for age, duration of diabetes, BMI, serum creatinine, and HbA1c showed that serum total adiponectin was negatively correlated with BMD at the total, lumbar spine, and femoral neck (r=−0.165, P<0.05; r=−0.187, P<0.05; and r=−0.136, P<0.05 respectively) and positively with urinary N-terminal cross-linked telopeptide of type-I collagen in men (r=0.148, P<0.05), and that serum HMW adiponectin was negatively correlated with BMD at the lumbar spine (r=−0.146, P<0.05). Multivariate logistic regression analysis adjusted for the parameters described above showed that total adiponectin was associated with the presence of vertebral fractures in men (odds ratio (OR)=1.396, 95% confidential interval (CI) 1.020–1.911 per s.d. increase, P<0.05), and both total and HMW adiponectin were associated with moderate or severe vertebral fractures (OR=1.709, 95% CI 1.048–2.787 per s.d. increase, P<0.05 and OR=1.810, 95% CI 1.112–2.946 per s.d. increase, P<0.05 respectively), but not in post-menopausal women.

Conclusions

Serum adiponectin could be associated with BMD and turnover and clinically useful for assessing the risk of vertebral fractures in type 2 diabetic men.