bluuebunny/crossref_metadata_2025 huggingface dataset:
Letter to the Editor—The Distribution of Stock Price Differences: Gaussian After All?
Authors: Brada Josef , Ernst Harry , Tassel John Van
Published: November 2008

In this paper the distribution of stock price differences is studied. Starting from Bachelier's hypothesis regarding the independence of stock price changes a model based on price differences taken across transactions, rather than differences obtained across time periods, is investigated. Using this model the distributions of price changes for a sample of 10 stocks were studied. In contrast to the fat tailed, excessively peaked distributions obtained by differencing across time periods, the distributions obtained by differencing across transactions did not have an excessive number of extreme events, although the center classes continued to be overcrowded. As the number of transactions over which the price differences were taken increased from 1 to n where n is equal to the largest number of transactions over which the price has remained unchanged, the distribution of the ΔP's approached the normal distribution. Thus we conclude that stock price changes are not independent across single transactions, and that stock prices should be differenced across blocks of transactions, rather than time intervals.
A Branch-Bound Algorithm for Plant Location
Authors: Efroymson M. A. , Ray T. L.
Published: November 2008

This paper discusses an integer-programming method for solving a special class of discrete programming problems called plant location. The basic contribution is that the problem is formulated as an integer program in such a way that the associated continuous problem can be efficiently optimized. A branch-bound algorithm is then used to solve the problem. The method discussed in the article has been successfully used to solve “practical” location problems with upwards of fifty plants.
Comparison of Two Scheduling Systems
Authors: Soriano A.
Published: November 2008

The delays that outpatients have to undergo before getting their medical treatment are often excessively long. The most commonly used patterns of scheduling appointments to patients are classified into three categories: (1) Pure Block Appointment systems, (2) Individual Appointment Systems, and (3) Mixed Block-Individual Appointment Systems. Several analytical studies have been concerned with the comparison of some of these appointment systems, and their highlights are described briefly. There are many other possible ways of assigning appointments to patients; one such way, referred to as the Two-at-a-Time Appointment System, is described. The advantages of the Two-at-a-Time Appointment System over any of the commonly used ones are discussed. Finally, the steady-state waiting time distribution functions that will correspond to the Two-at-a-Time Appointment System and the Individual Appointment System, as applied to the Wilmer Outpatient Clinic, have been obtained and are compared.
Optimum Locations on a Graph with Probabilistic Demands
Authors: Frank H.
Published: November 2008

The traffic demands at the stations of a communication network are usually not deterministic. Optimum locations found using deterministic techniques are poor when the random nature of the network traffic is considered. The concepts of absolute centers and medians are generalized to maximum probability absolute centers and medians. Minimum variance points are also considered. Techniques to locate these optimum points are discussed.
A Comparison of Two Methods for Quadratic Programming
Authors: van de Panne C. , Whinston Andrew
Published: November 2008

The paper gives a comparison of Beale's method for quadratic programming and the Simplex Method for quadratic programming as developed by Dantzig and Van de Panne and Whinston. After summary expositions of both methods and a reformulation of Beale's method in the framework of quadratic Simplex tableaux, the relation between the two methods is analyzed. A numerical example is used as illustration.
Observing Stochastic Processes, and Approximate Transform Inversion
Authors: Gaver D. P.
Published: November 2008

This paper describes a method for obtaining numerical information concerning the time-dependent behavior of stochastic processes such as those arising in queuing theory. The method leads to an approximate inverse of the Laplace transform. Examples are given of applications to transforms with known inverses, and the evolution of expected waiting time at a simple single-server queue is illustrated, both when there is a stationary solution and in the saturated case.
Some Queuing Problems with Phase-Type Service
Authors: Chaudhry M. L.
Published: November 2008

This paper deals with steady-state behavior of a discrete-time, single-channel, first-come-first-served, queuing problem where the service is accomplished in phases. Probability generating functions for the number of phases are obtained under two different models each with assumptions that the arrivals at two consecutive time-marks are (i) correlated and (ii) uncorrelated. Special cases of importance are discussed. Finally, mean queue length for each model when the number of phases demanded by an arriving unit is one, is derived.
A Deterministic Multiproduct, Multi-Facility Production and Inventory Model
Authors: Zangwill Willard I.
Published: November 2008

A deterministic multiproduct, multifacility, multiperiod production planning model is analyzed. The model considers concave production costs, which can depend upon the production in several different facilities, and piecewise concave inventory costs. Backlogging of unsatisfied demand is permitted. After determining the general form of the minimum cost production schedule, algorithms to calculate the minimum cost schedule explicitly in certain specific cases are presented.
Dimensions in Operations Research
Authors: Naddor Eliezer
Published: November 2008

The methods of dimensional analysis, which are used in the physical sciences, can also be used to advantage in operations research. The basic classes of dimensions in operations research are those of time, quantity, and money. In this paper we describe the dimensions of quantities in probability distributions, inventory, linear programming, and in queuing. Some illustrations are given on the use of dimensional analysis in O.R.
Letter to the Editor—Age Replacement with Discounting
Authors: Fox Bennett
Published: November 2008

We consider age replacement with discounting. For known failure distribution, our principal results are for the case when the failure rate is continuous and strictly increasing to ∞. We also show what happens for small discount rate. For unknown failure distribution, we give the mini-max strategy.
The Synchronization of Traffic Signals by Mixed-Integer Linear Programming
Authors: Little John D. C.
Published: November 2008

Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. A mixed-integer linear program is formulated for the following arterial problem: Given (1) an arbitrary number of signals, (2) the red-green split at each signal, (3) upper and lower limits on signal period, (4) upper and lower limits on speed between adjacent signals, and (5) limits on change in speed, find (1) common signal period, (2) speeds between signals, and (3) the relative phasing of the signals, in order to maximize the sum of the bandwidths for the two directions. Several variants of the problem are formulated, including the problem of synchronizing a network of signals. Branch-and-bound algorithms are developed for solving the mixed-integer linear programs by solving sequences of ordinary linear programs. A 10-signal arterial example and a 7-signal network example are worked out.
A Generalization of Linear Car-Following Theory
Authors: Lee Gentry
Published: November 2008

The linear theory of single-lane traffic flow is generalized by using an integral transform technique well-known in other branches of applied science. This technique introduces the idea of a memory function that describes the way in which a driver processes the information he receives from a lead vehicle. Several analytical examples are computed and the earlier linear model is discussed as a special case of the more general theory.
Networks and Basic Solutions
Authors: Johnson Ellis L.
Published: November 2008

A labeling procedure which could be used to carry out the steps of the simplex algorithm for a network flow problem is given. A modification of the simplex algorithm for the maximum flow problem is suggested which is equivalent to the Ford-Fulkerson algorithm if the solutions are kept basic in the latter. A procedure to keep the solutions basic in the Ford-Fulkerson algorithm is given. An example of a flow with gains problem with integer capacities and gains is given for which the usual labeling procedure may not lead to an optimum solution if the solutions are not kept basic. Extension of the network flow techniques to flows with gains is discussed.
On Finding a Maximal Assignment
Authors: Yaspan A.
Published: November 2008

An algorithm is presented and justified for finding a feasible assignment of the largest possible size among the zero elements of a matrix consisting partly of zeros and partly of nonzero elements. The problem comes up at each stage of the Hungarian method for solving the assignment problem. The solution differs from other published versions following the same principle in that it is elementary yet completely specific.
The M-Server Queue with Poisson Input and Gamma-Distributed Service of Order Two
Authors: Shapiro Saul
Published: November 2008

Analysis is made of the multiserver-queuing systems with Poisson input and service times distributed according to a second order gamma distribution. A set of difference equations involving the time-invariant state-probabilities is derived and a unique solution of these equations is found. The method used is that of treating the gamma-distributed service times or order two as the sum of two independent and identically distributed service times, which are exponentially distributed. It is shown that the time invariant probability of n customers being in the system is of the form, Pn = ∑i=0i=mCiβin, where m is the number of servers, and a method for finding the Ci's and βi's is given.
Branch-and-Bound Methods: A Survey
Authors: Lawler E. L. , Wood D. E.
Published: November 2008

The essential features of the branch-and-bound approach to constrained optimization are described, and several specific applications are reviewed. These include integer linear programming (Land-Doig and Balas methods), nonlinear programming (minimization of nonconvex objective functions), the traveling-salesman problem (Eastman and Little, et al. methods), and the quadratic assignment problem (Gilmore and Lawler methods). Computational considerations, including trade-offs between length of computation and storage requirements, are discussed and a comparison with dynamic programming is made. Various applications outside the domain of mathematical programming are also mentioned.
Combat Models and Historical Data: The U.S. Civil War
Authors: Weiss Herbert K.
Published: November 2008

Doubt has recently been cast on the applicability of mathematical models in general and Lanchester-type equations in particular to real combat. A comparatively small amount of effort has been spent in the past in testing theory against data, and so the general validity of such modeling largely remains to be demonstrated. In this paper, combat data on the U.S. Civil War is examined to determine the extent to which it can be explained by-simple mathematical relations, and some support, as well as problems, for such modeling is developed. A model for probability of winning is developed, depending solely on the ability of each force to continue to fight after sustaining specified fractional losses. Distributions of parameters describing battles, force ratios, and loss ratios are derived. Limited applicability of Lanchester-type equations is indicated. It is concluded that although these hundred-year-old battles may have limited application to future combat, the possibilities of deriving improved combat models by analyzing real life data are essentially unlimited, and that fact differs sufficiently from theory to make it unlikely that pure conjecture will hit upon the proper form for a combat model structure.
Time-Dependent Delays at Traffic Merges
Authors: Gaver D. P.
Published: November 2008

The expected wait of a side-road driver at an unsignalized intersection or merge point is investigated. The method is that of numerical inversion of the Laplace transform of the time-dependent expected wait in a simple queuing model. The effect of various operational factors, such as mix of “fast” and “slow” side-road drivers, upon approach to conventional steady-state values is exhibited. The development of waits when the intersection is saturated is also illustrated. An approximation procedure is suggested; numerical evaluation suggests that it will often be adequate.
The Double-Ended Queue with Bulk Service and Limited Waiting Space
Authors: Kashyap B. R. K.
Published: November 2008

The double-ended queue involving taxis and customers at a taxi-stand has been considered under the assumption that there is limited waiting space both for customers and for taxis, and that the taxis “serve” the customers in bulk. The arrivals of customers and taxis are taken as general and Poisson respectively. Two separate probability generating functions have been defined for the cases when (i) taxis are waiting and (ii) when customers are waiting and their Laplace transforms (L.T.'s) as well as that of the probability for empty state have been obtained by using the supplementary variable technique. Cases of Erlangian and Poisson arrivals of customers and of single-seated taxis are considered as particular cases.
Some Stochastic Properties of a Compound-Renewal Damage Model
Authors: Morey Richard C.
Published: November 2008

The compound-renewal process is investigated as a model of cumulative damage. The component is assumed to function until the cumulative wear exceeds some critical threshold, in general a random variable, at which time the component is assumed useless. It is this first passage time until breakdown which is of prime interest. Rather than focusing the attention on a certain selected compound-renewal process governed by mathematically convenient distributions, a class of compound-renewal processes involving the nonparametric, physically appealing assumption of a monotone failure rate is studied. Since the assumptions are nonparametric, the results for the most part manifest themselves in the form of useful bounds.
The Routing Problem with “K” Specified Nodes
Authors: Saksena J. P. , Kumar Santosh
Published: November 2008

The functional equation technique has been employed to solve more general “routing” problems, when the route must pass through a number of specified nodes. The method is illustrated by an example.
Damage to a Circular Target by a Gaussian Distributed Warhead with Uniformly Distributed Bomblets
Authors: Jarnagin M. P. , DiDonato A. R.
Published: November 2008

A derivation is given for an analytic expression representing the expected damage to a circular target of uniform value by a cluster of N bomblets. These bomblets are scattered by the detonation of a larger bomb. Each is considered to have a circular lethal area of specified radius, the same radius for all bomblets. The impact point of the large bomb is governed by a circular normal distribution with its mean at the target center. The bomblets are assumed to be independently dispersed under a uniform distribution over a prespecified circular area, known as the warhead-effects field, having its center at the impact point of the large bomb. Typical graphical results are included.
A Method for Solving Discrete Optimization Problems
Authors: Lawler E. L. , Bell M. D.
Published: November 2008

This paper describes a simple, easily-programmed method for solving discrete optimization problems with monotone objective functions and completely arbitrary (possibly nonconvex) constraints. The method is essentially one of partial enumeration, and is closely related to the “lexicographic” algorithm of Gilmore and Gomory for the “knapsack” problem and to the “additive” algorithm of Balas for the general integer linear programming problem. The results of a number of sample computations are reported. These indicate that the method is computationally feasible for problems in which the number of variables is fairly small.
Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method
Authors: Kaplan Seymour
Published: November 2008

A specific type of all-integer integer programming problem which seems to arise frequently in capital budgeting and other areas involves a zero-one restriction on the problem variables. Approaches to solutions to such problems by the General Lagrange Multiplier Method are discussed. This procedure, because of its relative simplicity, has certain advantages over other direct methods such as the use of integer programming algorithms, especially in areas such as capital budgeting where the constraints are usually not binding to the degree indicated by the problem statement. Throughout this paper, the Lorie-Savage problem in capital budgeting is used as a basis for the discussion.
Allocating Weapons to Target Complexes by Means of Nonlinear Programming
Authors: Day Richard H.
Published: November 2008

The paper presents a three-stage method of assigning weapons to targets and illustrates its application with a small sample problem. The method decomposes the general allocation problem into a set of targeting problems in the small and a targeting problem in the large. The former are solved by a sequential optimizing method that provides information for solving the latter by nonlinear programming. The discussion is not advanced and illustrates a basic feature of applied operations research: the combination of existing operational methods to achieve approximative solutions to complicated problems. The study may have some added interest because of its relation to problems of decentralized planning.
Queues with State-Dependent Stochastic Service Rates
Authors: Harris Carl M.
Published: November 2008

The standard M/G/1 queuing system is generalized so that the service time parameter becomes a stochastic process, {Mn, n = 1, 2, …}, indexed on the length of the queue at the moment service is begun. The service time, Ti, of a customer entering into service when a total of i customers are in the system is to be conditioned upon the random variable Mi. Some general theory is developed for the model and three specific cases are explored. For each of the examples, both the conditional service-time distributions, {BTn∣Mn(t∣μn), n = 1, 2, …}, and the prior distributions of {Mn}, {FMn(μn), n = 1, 2, …}, are specified, and results are obtained that characterize queue behavior using the imbedded Markov chain approach. The first case is an illustration of a random, non-state-dependent parameter, while the other two describe different ways a service parameter may be state-dependent. In addition, an industrial example based on the third case is cited.
Letter to the Editor—Computational Experience with the Algorithm of Balas
Authors: Fleischmann Bernhard
Published: November 2008

This note reports on the application of the Balas algorithm for linear programs with zero-one variables on larger problems involving up to 159 variables. Two modifications of the algorithm are discussed. Some information about the machine program and numerical results are given.
Letter to the Editor—Circular Distribution Estimation
Authors: Inselmann Edmund H. , Granville William
Published: November 2008

This note deals with two studies. The first considers an estimate of the probability of being within a given radius. The minimum variance unbiased estimates is derived in this case. The second study considers the estimate of the circular probable error wherein an order statistic estimate is used.
Letter to the Editor—Kill Probability for Multiple Shots
Authors: McNolty Frank
Published: November 2008

A point target is randomly located according to an offset circular normal distribution and remains in its unknown position throughout N independent tosses of a lethal circle. The paper presents integral expressions for the probability of: (1) killing the target at least once in N tosses of the lethal circle; (2) killing the target exactly n times in N tosses; (3) requiring less than or equal to m shots to kill the target exactly once; (4) killing the target at least once in N tosses when the bias (offset distance) is randomly distributed. The paper also presents formulas for the expected number of shots required to kill the target exactly once and the expected number of times the target is killed in N tosses. A simple expression is also given for the single-shot kill probability for an offset ellipsoidal case when the lethal radius of the weapon is variable rather than fixed.
Solving Bicriterion Mathematical Programs
Authors: Geoffrion Arthur M.
Published: November 2008

It often happens in applications of mathematical programming that there are two incommensurate objective functions to be extremized, rather than just one. One thus encounters bicriterion programs of the form of equation (1), [Formula: see text] where h is an increasing utility function, preferably quasiconcave, defined on outcomes of the concave objective functions f1 and f2, and x is a decision n-vector constrained to the convex set X. It is shown how such programs can be numerically solved if a parametric programming algorithm is available for the parametric subproblem [Formula: see text] A natural byproduct of the calculations is a relevant portion of the “tradeoff curve” between f1 and f2. Outlines of several algorithms for solving equation (1) under various special assumptions and a numerical example are presented to illustrate the application of the theory developed herein. A useful extension is presented that permits nonlinear scale changes to be made on the fı.
Methods for the Solution of the Multidimensional 0/1 Knapsack Problem
Authors: Weingartner H. Martin , Ness David N.
Published: November 2008

In the knapsack problem, given the desirability of each of a number of items, one seeks to find that subset which satisfies a constraint on total weight. The multidimensional variant imposes constraints on additional variables of the items; the 0/1 specification means that an item is either taken or not, i.e., multiples of the same item are not considered, except possibly indirectly. Traditionally the one-dimensional knapsack problem is solved by means of dynamic programming. The multidimensional problem is usually reduced to a one-dimensional one by use of Lagrangian Multipliers that, however, do not generally yield the exact solution to the problem posed. Here some new algorithms are developed that are applied within a dynamic programming framework. Additionally, the methods make integral use of an interactive computer system in which the heuristics of the problem solver are applied and changed as the character of the solution process evolves. The problem arises in the context of capital budgeting, but has obvious applications in a variety of other areas. The methods have been employed for solving numerical problems with as many as 105 items, the parameters having been obtained from industrial applications.
Stochastic Duels with Varying Single-Shot Kill Probabilities
Authors: Bhashyam N. , Singh Naunihal
Published: November 2008

This paper deals with the evaluation of the probability of winning for a duelist when the single-shot kill probability is assumed to depend upon its position in the sequence of the firing pattern. A few examples are discussed.
Nonpreemptive Priorities in Machine Interference
Authors: Hodgson Vincent , Hebble Thomas L.
Published: November 2008

A model of machine interference is studied in which one repairman is assigned to maintain several batteries of machines with a finite number of machines in each battery. The model, which assumes nonpreemptive priorities, random breakdowns, and general repair time distributions, is closely analogous to the classical priority queuing model of Kesten and Runnenburg. A system of equations, for the multivariate binomial moments of the number of machines working in each battery immediately after a repair is completed, is established and solved.
Closed Queuing Systems with Exponential Servers
Authors: Gordon William J. , Newell Gordon F.
Published: November 2008

The results contained herein pertain to the problem of determining the equilibrium distribution of customers in closed queuing systems composed of M interconnected stages of service. The number of customers, N, in a closed queuing system is fixed since customers pass repeatedly through the M stages with neither entrances nor exits permitted. At the ith stage there are ri parallel exponential servers all of which have the same mean service rate μi. When service is completed at stage i, a customer proceeds directly to stage j with probability pıj. Such closed systems are shown to be stochastically equivalent to open systems in which the number of customers cannot exceed N. The equilibrium equations for the joint probability distribution of customers are solved by a separation of variables technique. In the limit of N → ∞ it is found that the distribution of customers in the system is regulated by the stage (or stages) with the slowest effective service rate. Asymptotic expressions are given for the marginal distributions of customers in such systems. Then, an asymptotic analysis is carried out for systems with a large number of stages (i.e., M ≫ 1) all of which have comparable effective service rates. Approximate expressions are obtained for the marginal probability distributions. The details of the analysis are illustrated by an example.
Finite Queues in Series with Exponential or Erlang Service Times—A Numerical Approach
Authors: Hillier Frederick S. , Boling Ronald W.
Published: November 2008

This paper considers a queuing system consisting of N service channels in series where each channel has an exponential or Erlang holding time and (except for the first channel) a finite queue, and where the input process is such that the first queue is never empty. The measures considered are the steady-state mean output rate and mean number of customers in the system (excluding the first queue). First, a procedure is described, for obtaining these measures, that is relatively efficient computationally. Second, an exceptionally efficient procedure is developed for approximating the mean output rate for the case of exponential holding times. It is demonstrated that this procedure provides an excellent approximation for most cases and that it is computationally feasible for large problems. Third, extensive new numerical results are obtained.
Optimum Bribing for Queue Position
Authors: Kleinrock Leonard
Published: November 2008

In this paper we consider that relative position in queue is determined according to the size of a customer’s bribe (which is paid before the customer sees the queue length). Such a policy allows the customer himself to affect his own queue position, rather than the classical approach of assuming that a customer is preassigned to some (possibly continuous) priority class. For the case of Poisson arrivals, arbitrary service time distribution, and arbitrary distribution of customer bribe, we obtain the average waiting time for customers as a function of their bribe. We consider both preemptive and nonpreemptive disciplines. Examples are presented for various bribing distributions, which demonstrate that many well-known priority queuing systems are special cases of this bribing situation. Furthermore, a cost function is defined after we introduce the notion of an impatience factor (which converts seconds of wait into dollars). Conditions for optimum bribing are then determined, where the optimization refers to minimizing the average cost subject to a mean bribe constraint. An example for exponential service and exponential bribing is carried out and the results are plotted.
A Finite Renewal Algorithm for the Knapsack and Turnpike Models
Authors: Shapiro Jeremy F. , Wagner Harvey M.
Published: November 2008

The mathematical and algorithmic connections between the knapsack problem and a fundamental renewal-type problem are established. The renewal point of view leads to an efficient computational result and is based in part on an extension of a turnpike theorem shown by Gilmore and Gomory. The distribution of effort model is examined briefly by means of the renewal approach so as to add new insight to the mathematical structure of this problem.
Letter to the Editor—Nonoptimality of Planned Replacement in Intervals of Decreasing Failure Rate
Authors: Denardo Eric V. , Fox Bennett L.
Published: November 2008

The planned replacement problem assumes a known failure distribution F(t) and that replacement occurs at the earlier of a planned replacement interval (at cost c1) and the time of failure (at cost c2). We show that it cannot be optimal to select a planned replacement interval at a point for which the failure rate f(t)/[1 − F(t)] is decreasing.
The Status of Developments in the Theory of Stochastic Duels—II
Authors: Ancker C. J.
Published: November 2008

This paper contains a brief outline of the history and the principal features of the Theory of Stochastic Duels, as well as the major analytical results to date. Areas for future research and possible fields of application are also considered. The connection with other models of combat, such as Lanchester's equations and games of strategy, is discussed. An annotated bibliography is included.
Sufficient Conditions for Some Optimum-Property Facility Designs
Authors: Francis Richard L.
Published: November 2008

A facility design is considered to consist of n mutually nonoverlapping facilities of known areas. Some problems are considered of finding, from the class of all possible facility designs, facility designs with optimum properties; sufficient conditions are given for certain minimum total cost and minimax facility designs, and examples are considered. Possible facility design applications include those of warehouse design and layout, parking lot design and layout, and stadium design.
An Application of Regenerative Stochastic Processes to a Problem in Inventory Control
Authors: Hurter Arthur P. , Kaminsky Frank C.
Published: November 2008

The theory of regenerative stochastic processes is applied to the problem of finding the limiting distribution of the number of units in storage for a basic single commodity storage system. In this system two modes of replenishment, called random and regular replenishment, are assumed to be available to the stock controller.
Letter to the Editor—Additive Utilities with Incomplete Product Sets: Application to Priorities and Assignments
Authors: Fishburn Peter C.
Published: November 2008

A previous paper discusses the notion of additive utilities in the expected-utility context when the set of consequences X can be written as the product of n other sets: X = X1 × X2 × ⋯ × Xn. The present paper continues this investigation for cases where X is a subset of the product of n other sets: X ⊂ X1 × X2 × ⋯ × Xn. Under a finiteness restriction, an additivity axiom leads to an additive utility representation for the elements in X. The potential usefulness of the theory in connection with incomplete product sets is demonstrated with priority orderings and assignments.
Letter to the Editor—On the Necessary Conditions for the Existence of the Solution of the Multi-Index Transportation Problem
Authors: Morávek J. , Vlach M.
Published: November 2008

A note about a special type of a three-index transportation problem.
Letter to the Editor—Optimum Locations on Graphs with Correlated Normal Demands
Authors: Frank H.
Published: November 2008

The traffic demands at the stations of a traffic network are assumed to be random variables with a joint normal distribution. The location of optimum points on the linear graph model of the network is discussed. Techniques to locate these points are given.
Letter to the Editor—On the “Logarithmic Law” of Attrition and its Application to Tank Combat
Authors: Peterson R. H.
Published: November 2008

In a recent article appearing in this Journal, H. K. Weiss indicates that, in extremely large scale engagements during the Civil War attrition tended to follow the logarithmic law and refers to the use of this law by the author in a study of tank combat. In this study it was found that in the 1-vs-n tank engagements in North West Europe during World War II the first kill of an engagement did seem to follow the logarithmic law, but that the second kill came closer to following the square law. Data on subsequent kills became too sparse to be statistically meaningful.
Letter to the Editor—Improper Solutions of the Vector Maximum Problem
Authors: Klinger Allen
Published: November 2008

Many problems in operations research, engineering, and economics require that several objectives be maximized simultaneously. It is well known that ‘maximizing’ the vector whose components are these objectives can yield more solutions than maximizing one linear combination of the objectives. Kuhn and Tucker (Kuhn, H. W., A. W. Tucker. 1951. Nonlinear programming. Proc. Second Berkeley Symp. on Math. Stat. and Prob. University of California Press, Berkeley, Calif. 1951.) discuss the vector maximum problem and derive necessary and sufficient conditions for a vector x0 to be a proper solution. However, their basic paper presents only a definition of ‘proper’ and a particular vector maximum problem for which an ‘improper’ solution has an undesirable property. The purpose of this note is to show that all ‘improper’ solutions have this undesirable property, thus justifying the calculation of only the ‘proper’ solutions.
Simulation and Adaptive Forecasting as Applied to Inventory Control
Authors: Packer A. H.
Published: November 2008

This paper describes a case study of selected inventory accounts maintained by a large manufacturer of rocket engines. It was hypothesized that a significant improvement in average inventory levels, number of purchase orders, and number of stockouts could be obtained by augmenting existing methods of inventory management with certain OR based techniques. These techniques included exponential smoothing of demand forecasts and statistical determination of optimum safety stock levels. Computerized simulation was used to determine: (1) the most effective parameter (α) values for use in the exponential smoothing formulas, (2) an estimate of the potential dollar savings obtainable if the proposed methods were implemented, and (3) a means by which these methods could be implemented. A simulation model was developed for two particular inventory accounts, its correspondence with the real world was tested, and the alpha values and anticipated dollar values were determined. Additionally, a set of curves were developed for use by inventory management to assist in determining an optimized policy for varying values of purchase order cost, inventory carrying rate, and cost of stockouts.
Optimal Control of a Continuous-Time Markov Chain with Periodic Transition Probabilities
Authors: Martin-Löf Anders
Published: November 2008

Controlled stationary Markov chains with a finite number of states and possible actions and continuous time have been studied by many authors. It is well known that a control maximizing the expected reward in a finite time interval can be obtained from the equation of dynamic programming, and that there exists a stationary control giving maximal (discounted or average) reward in an infinite time interval. In this paper controlled Markov chains whose transition probabilities are periodic in time are considered. It is shown that there exists a periodic control giving maximal expected future reward, and that it can be approximatively calculated by making a discretization in time. An example of a system that can be described by such a process is a service system or an inventory whose input is, e.g., a Poisson process with an intensity that varies seasonally.
Direct Search Algorithms for Zero-One and Mixed-Integer Programming
Authors: Lemke Carlton E. , Spielberg Kurt
Published: November 2008

A method of solution for the mixed integer-programming problem is proposed. It is based on an exhaustive search of the integer variables, coupled with an efficient use of the product form of the basis matrix inverse, for the linear programming calculations. In this connection a detailed algorithm for the (0 − 1) problem is developed and experimental results are discussed.
A Simple Proof of: L = λW
Authors: Jewell William S.
Published: November 2008

A simple proof of the fundamental queuing formula L = λW is given that is based on renewal theory. The basic assumptions that are needed are: (1) the event system is empty is recurrent, and (2) the arrival and waiting-time mechanisms are reset by the next arrival after this event occurs.
Some Points in the Methodology of Urban Population Distributions
Authors: Wilkins C. A.
Published: November 2008

For some operational problems concerned with urban populations, the actual location of population within each city is not of primary importance. For such problems, it may be best to proceed in terms of the function A(D) defined as being the city area over which the population density ≧ D. Knowledge of this function enables a suitable symmetric representation of a city of fairly arbitrary form to be determined, and Weiss' problem of maximizing the population in a given total area chosen from the regions of a sequence of cities to be tackled in reasonably general terms. General equations are given for this problem. Simple cities of nonstandard form may satisfy a generalization of Sherratt's form, to which a number of Sherratt's results are easily extended. When distance from the (unique) city center is important—such as in a single-bomb centrally-directed nuclear attack—Clark's type of representation is appropriate. Equations for the expected number of casualties in such an attack are given for Sherratt's (asymmetric) and Clark's type of city.
Dynamic Programming Algorithms for the Integer Programming Problem—I: The Integer Programming Problem Viewed as a Knapsack Type Problem
Authors: Shapiro Jeremy F.
Published: November 2008

Gomory has transformed the integer programming problem into a related group optimization problem which can be more easily solved. An optimal solution to the group problem is optimal for the integer programming problem from which it is derived if the solution is feasible. An algorithm (IP Algorithm I) for solving the group optimization problem is developed, and sufficient conditions on its use are given. The usefulness of IP Algorithm I is extended by amending it to find alternative optima. In a subsequent paper, this algorithm is extended to an algorithm that can solve any integer programming problem.
Metric: A Multi-Echelon Technique for Recoverable Item Control
Authors: Sherbrooke Craig C.
Published: November 2008

Metric is a mathematical model of a base-depot supply system in which item demand is compound Poisson with a mean value estimated by a Bayesian procedure. When a unit fails at base level there is a probability r that it can be repaired at the base according to an arbitrary probability distribution of repair time, and a probability 1 − r that it must be returned to the depot for repair according to some other arbitrary distribution. In the latter case the base levies a resupply request on depot. No lateral resupply between bases is considered in the model. For high-cost, low-demand items the appropriate policy is (s − 1, s), which means that items are not batched for repair or resupply requests. This problem has a simple analytic solution that is a function of the mean repair times rather than the repair time distributions. A practical and efficient computer program has been designed to show the cost-effectiveness tradeoff for a large group of recoverable items. In addition to minimizing expected backorders for any system investment, the program can evaluate any distribution of stock and it can compute the optimal redistribution of stock. No arbitrary estimates of backorder cost or holding cost are required.
Chance-Constrained Games with Partially Controllable Strategies
Authors: Charnes A. , Kirby M. , Raike W.
Published: November 2008

This paper is the second of a series directed at the investigation of relations of chance-constrained programming to problems in game theory. The model introduced and analyzed herein is a two-person game model with zero-sum payoff matrix in which the strategies selected by the players do not in themselves determine the payoffs, but in which random perturbations with known distributions modify the strategy of each player before actual implementation of the strategies. A major hypothesis is that, while the strategy perturbations may be random vectors with known distributions, the selection of strategies (or more accurately strategy policies) is to be made before any observations of the random variables are made so that the strategies chosen are to be “zero-order” decision functions of the random perturbations, in the customary terminology of chance-constrained programming. The strategy selected by each player is to be chosen to extremize that payoff which the player can be assured with at least some (a priori specified) probability. A key result shows that the deterministic equivalents for these problems yield a deterministic two-person game that is not zero-sum.
Letter to the Editor—Multichannel Queuing System with Bulk Service
Authors: Ghare P. M.
Published: November 2008

A multichannel queuing system with unlimited Poisson input and exponential service is considered under a bulk-service discipline. Earlier results by Arora for the two-channel case have been generalized to c (c ≥ 2) channels by using standard generating functions and Laplace transform methods. The transient state probabilities are obtained as Laplace transform and the steady probabilities are obtained as their limits.
Letter to the Editor—Common Terminal Multicommodity Flow
Authors: Rothfarb W. , Shein N. P. , Frisch I. T.
Published: November 2008

An algorithm is presented to determine a multicommodity flow pattern which maximizes the objective function ∑ i=ni=1 αifi for graphs having n sources and a common terminal, where fi is the amount of flow of the ith commodity and αi is a given set of nonnegative constants.
Reliability of a Parallel Redundant Complex System
Authors: Kulshrestha D. K.
Published: November 2008

An attempt has been made to study the analytical behavior of a complex system with redundancy in parallel by the method of Discrete Transforms. This paper reveals the use of Discrete Transforms in solving the reliability problems. Laplace Transforms of various pointwise availabilities of the system have been calculated. Behavior of the system under steady state has also been studied.
A Renewal Theoretic Approach to the Estimation of Future Demand for Replacement Parts
Authors: Soland Richard M.
Published: November 2008

This expository paper presents a renewal theoretic approach to the determination of the probability distribution of the demand for replacement parts in a specified future time interval. Ordinary, modified, and equilibrium renewal processes are discussed as models for physical processes in which parts are replaced as they fail. Some results from renewal theory are stated and then used to estimate the demand for replacement parts under a number of different conditions. Practical difficulties, and ways to circumvent them, are then discussed. The paper concludes with an illustrative example.
Allocation of Transportation Units to Alternative Trips—A Column Generation Scheme with Out-of-Kilter Subproblems
Authors: Rao M. R. , Zionts S.
Published: November 2008

The problem of allocating transportation units to alternative trips can be solved by linear programming. However, the linear programming formulation has three shortcomings: (1) the optimal solution obtained does not have an integer number of trips; (2) the optimal solution may have sets of disconnected cycles; and (3) problems of considerable size will be intractable because of the vast number of variables and constraints. In some applications, it has been found that shortcomings 1 and 2 are not serious, but the third one—the size of the problem—presents considerable difficulty. This paper describes an approach—a column generation scheme with out-of-kilter subproblems—that reduces the size of the problem considerably. An algorithm for the method is given, and it is proved that the algorithm solves the problem in a finite number of steps. Computational experience thus far with this method has been limited, but encouraging.
A Decomposition Algorithm for Shortest Paths in a Network
Authors: Hu T. C.
Published: November 2008

Given an n-node network with lengths associated with arcs: the problem is to find the shortest paths between every pair of nodes in the network. If the network has less than n(n − 1) arcs, then it is possible to treat parts of the network at a time and then get the shortest paths between every pair of nodes. This decomposition algorithm saves the amount of computation as well as the storage requirement of a computer.
Sensitivity of Decisions to Probability Estimation Errors: A Reexamination
Authors: Fishburn Peter C. , Murphy Allan H. , Isaacs Herbert H.
Published: November 2008

In the subjective expected utility model for decision making under uncertainty the decision maker often has difficulty assigning to the states probabilities with which he is completely satisfied. Six approaches that might be used to help the decision maker resolve his uncertainty about the values of his state probabilities are outlined. One approach tells the decision maker how much he must perturb his initial probability estimate in order to change his maximum expected utility alternative from the alternative originally best under the initial estimate. This approach is examined in greater detail and an iterative algorithm for solving the minimum-perturbation problem is presented.
The Measurement of Combat Effectiveness
Authors: Hayward Philip
Published: November 2008

This paper proposes that a satisfactory quantitative measure of the combat effectiveness of a military force is its probability of success in combat. The probability of success depends not only on the capabilities of the specified force but also on the nature of the enemy, the combat environment, and the mission. Since it is impractical to measure combat effectiveness experimentally, i.e., in actual combat, military judgment must be called on to specify the relation between the probability of success and the parameters of force capability, environment, and mission.
Dual-Resource Constrained Series Service Systems
Authors: Nelson Rosser T.
Published: November 2008

A Poisson arrival, exponential service queuing system consisting of two service stages in series is the subject of this study. The distinguishing characteristic is that the system has only one laborer. The labor and machine limited system is compared to its ordinary machine limited counterpart by means of a comparison of simulation results and theoretical results. Implications of the experiments are discussed with respect to various facets of system design and control, including labor assignment procedures, size of labor force, and control of arrival and (or) service rates. Average labor utilization is proposed as a measure of system utilization for labor- and machine-limited queuing systems. From this emanates the concept of “blocking” of labor and concomitant problems that complicate any nonexperimental determination of average labor utilization in terms of system parameters. The possibility of equivalence relations between labor and machine-limited queuing models and reduced machine-limited queuing models is also explored. Although the experimental systems yield one example of such a relation, they also provide evidence to support a conjecture that no general equivalence exists.