bluuebunny/crossref_metadata_2025 huggingface dataset:
Letter to the Editor—A Test for Suboptimal Actions in Markovian Decision Problems
Authors: MacQueen J.
Published: November 2008

In a Markovian decision problem, choice of an action determines an immediate return and the probability of moving to the next state. It is desired to maximize the expected total of discounted future returns. If upper and lower bounds on the optimal expected return are available, a simple test is described that may show that certain actions are suboptimal, permanently eliminating them from further consideration. This test may be incorporated into the dynamic programming routine for solving the decision problem. This was tried on Howard's automobile replacement problem, using the upper and lower bounds described in “A Modified Dynamic Programming Method” (J. Math. Anal. and Appl. 14, April, 1966). The amount of computation required by the dynamic programming routine was reduced, conservatively, by 75 per cent.
Letter to the Editor—An Optimal Stopping Rule
Authors: Randolph Paul
Published: November 2008

Suppose the random variables X1, X2, …, all from the same population, are observed sequentially. After the nth observation, the experimenter can stop and receive the net payoff of c1 [max(x1, x2, …, xn)] − nc2, where c1 is the unit value of the maximum and c2 is the sampling cost. In this paper a rule is given to determine if the experimenter should stop in the nth observation or if he should continue until the (n + 1)st observation, at which time he is faced with this decision all over again.
Letter to the Editor—Comments on a Paper by A. Novaes and E. Frankel, “A Queuing Model for Unitized Cargo Generation”
Authors: Brown J. F.
Published: November 2008

Some discrepancies in an earlier paper describing a bulk service queuing situation with customer balking or reneging are pointed out. Necessary modifications to make the model more valid are incorporated in a reformulation and an approach for developing the state-time probabilities of the system is suggested.
Truck Queues at Country Grain Elevators
Authors: Bouland Heber D.
Published: November 2008

During grain harvest, especially wheat harvest in the Central Great Plains, truck queuing at country grain elevators is a problem. Truck waiting times were studied for three types of receiving systems, using information from limited field studies and simulation using electronic computers. Several methods of evaluating truck waiting costs were investigated. From the information on waiting times and costs, the optimal capacities of receiving systems for different ranges of truck receipts were determined. Several methods of improving truck receiving at country elevators were discovered.
The Use of Models in Marketing Timing Decisions
Authors: Hess Sidney W.
Published: November 2008

Two cases illustrate the utility of simple models to aid pricing of obsolescent products. Both models yield surprisingly simple, easily implemented decision rules. They demonstrate that “back of the envelope” modeling can still help management decision making.
On the Uses of Industrial Dynamic Models
Authors: Wismer David A.
Published: November 2008

This paper introduces a philosophy of industrial dynamics based on obtaining results in as quick and economical a fashion as possible. This economy is achieved by stating explicitly the objectives expected and tailoring the model toward the achievement of those objectives. Three specific and widely differing uses of a dynamic model are proposed. These are called analysis, feasibility, and control, and are demonstrated in terms of the dynamic model of earnings for a cement company.
Learning by Doing—An Adaptive Approach to Multiperiod Decisions
Authors: Ying Charles C.
Published: November 2008

A decision-maker is required to make a decision in each period over a sequence of periods. His decision in any period will affect: (1) the immediate consequence resulting from his decision in that period, and (2) the new information based on which decisions in future periods will be made. An adaptive approach to the above multiperiod decision process is suggested here, in which a decision-maker acts while learning from his experience so as to maximize the expected accumulative utility payoff from the entire decision process. It is demonstrated that the value of information, in this situation, depends not only on (1) the uncertainty of environment, (2) the nature of information, (3) the utility payoff function, but also on (4) the expected rate of learning.
“Optimal” Policy in a Maintenance Cost Problem
Authors: Elandt-Johnson Regina C.
Published: November 2008

This paper is concerned with estimating the “optimal” policy when the (unknown) cost function C(x) is nonlinear with a single minimum, and can be approximated in the neighborhood of the minimum by a polynomial regression. The value x0, at which C(x) attains minimum, is approximated by ◯0 obtained from the regression function, and the expected value of the difference between the actual cost, Ŷ0 = C(◯0), and the true minimum cost, Y0 = C(x0), is evaluated. The Central Limit Theorem and Taylor series expansion of the multivariable function is applied in this procedure.
The Sequential Unconstrained Minimization Technique (SUMT) Without Parameters
Authors: Fiacco Anthony V. , McCormick Garth P.
Published: November 2008

An unconstrained minimization technique for solving nonlinear programming problems that involves no parameter selection is presented. The algorithm generates a sequence of interior feasible points with decreasing objective function values that converge to the optimum.
Queues with Hyper-Poisson Input and Exponential Service Time Distribution with State Dependent Arrival and Service Rates
Authors: Gupta S. K.
Published: November 2008

The queuing system considered in this paper is characterized by (i) hyper-Poisson input with k branches with mean arrival rates depending upon the state of the system; (ii) first-come, first-served queue discipline; (iii) exponential service time distribution with mean service rate depending upon the state of the system; and (iv) finite waiting space. The functions defining the dependence of the mean arrival and service rates upon the state of the system are assumed to be arbitrary. Assuming steady-state conditions to obtain, a recurrence relation connecting the various probabilities introduced is found. By specifying a few particular forms of the state functions, graphs depicting two queue characteristics, viz., (i) probability of no delay, and (ii) mean number of units in the system are drawn. One of the particular cases has been interpreted as “a queuing problem with reneging” and another as “a multiple server queuing problem.”
Bayes Markovian Decision Models for a Multiperiod Reject Allowance Problem
Authors: White Leon S.
Published: November 2008

Two versions of a multiperiod reject allowance problem are formulated as Markovian decision models. In the first, total output capacity is considered fixed; in the second, a maximum production rate is postulated. In both models it is assumed that output may be inspected at intermediate points within the production time span as well as at the conclusion of production. Also in both models the production process is characterized as a Bernoulli process with unknown parameter p, the probability of producing a defective. It is shown that optimal sublot size decision rules may be computed via linear programming methods.
Discrete Programming by the Filter Method
Authors: Balas Egon
Published: November 2008

In this paper (section 1) a two-phase procedure, the filter method or accelerated additive algorithm, is proposed for solving linear programs with zero-one variables. In Phase I an auxiliary problem is constructed that, in Phase II, is used to “filter” the solutions to which the tests of the additive algorithm are to be applied. The filter method is then extended (section 2) by J. F. Benders’ partitioning procedure to the mixed-integer zero-one case, as well as to general integer and mixed-integer programs. Finally, a specialized version of this method is used (section 3) to tackle a general machine-sequencing model, formulated as the problem of finding a minimaximal path in a disjunctive graph.
Letter to the Editor—Counts Delayed but Not Lost—A Note on a Paper of Haight
Authors: Anderson J. A. , Bithell J. F.
Published: November 2008

This paper generalizes, by the use of compound distributions, a result of Haight (Haight, F. A. 1966. A Poisson generalization based on counts that are delayed but not lost. Opns. Res. 14 943–945.) on counts that are delayed but not lost. An application of Markov chains indicates a simple method of numerical evaluation of the distributions involved. Finally a continuous time analogue is studied.
Letter to the Editor—Some Remarks Concerning the Departure Process of a Queue with Poisson Arrivals and no Balking
Authors: Shanbhag D. N.
Published: November 2008

This note gives a technique to obtain for a queue with Poisson arrivals and no balking, the joint distribution of the number of departures during (0, t⌋ and the queue length at t from the marginal distribution of the queue length at t. As an illustration the joint distribution for the queuing system M/G/1 is given.
Exact Solution of a Simple Cutting Problem
Authors: Barnett S. , Kynch G. J.
Published: November 2008

Recently Gilmore and Gomory have discussed in detail cutting stock problems in two and more dimensions. However the generality of their approach seems to obscure the existence of exact solutions to very simple situations given in this paper. We discuss here the problem of optimal dissection of a large rectangular plane area into smaller rectangles having unit width and integral length so as to obtain the least waste. When the strips are of only one or two sizes the problem is solved completely. It is shown that when the strips are of two different lengths then, if the area being dissected is large enough and the two lengths are relatively prime numbers, strips can be cut so as to leave no remainder. Possible future extensions are suggested.
Functional Selection for the Stochastic Assignment Model
Authors: Weil Roman L.
Published: November 2008

The choice of a function to be optimized is unambiguous in the ordinary assignment model. In the stochastic assignment model there is no clear choice of functional. Six different criteria for the stochastic assignment model are discussed and one is suggested as best.
An Imbedded Chain Approach to a Queue with Moving Average Input
Authors: Pearce C.
Published: November 2008

A generalization of the GI/M/1 queue is considered in which the interarrival times do not constitute an identically and independently distributed sequence but are correlated. The transient behavior of the queue length is treated, both in continuous time and on an imbedded chain. The busy period is also considered.
Letter to the Editor—An Analysis of Economic System Subdivision—A Rule for Just Partition
Authors: Treadwell Richard J.
Published: November 2008

A simple analysis of the factors giving the most economic subdivision of a complex system into units for the purpose of manufacture and test is derived from assumed relations between fabrication and test costs, complexity, and the probability that individual elements are faulty. Expressions are derived for relative system cost, minimum system cost, optimum unit size, and optimum unit yield. The last is shown to be independent of fault probability. The results of the analysis are interpreted and possible applications are considered.
The Stationary Solution of a Multiserver Queuing Model with Discouragement
Authors: Reynolds John F.
Published: November 2008

Several authors, including Morse, Ancker and Gafarian, and Cox and Smith have studied single-server queuing models in which the arrival rate is a decreasing function of queue length. This paper analyzes a multi-server generalization of the model given by Cox and Smith. A generating function is derived for the equilibrium distribution of queue length, and from it are derived expressions for the probability of finding all servers busy on arrival, and for the mean number of customers in the system and waiting for service to begin. Also, an expression is obtained for the proportional loss in custom caused by discouragement. Finally, the distribution of waiting time is obtained using characteristic functions and the mean waiting time is calculated. The variations of these quantities with traffic intensity and number of servers are illustrated graphically.
Applying Cost-Effectiveness Concepts to the Community Health System
Authors: Packer A. H.
Published: November 2008

This paper investigates ways in which concepts of model building and cost-effectiveness can be applied to the health planning process. The problem is described and methodological implications drawn that recommend large-scale digital-computer simulation techniques. A study of effectiveness measures suggests that the system's basic purpose is to reduce the likelihood that individuals will be in a state of ill health. The proposed measure of ineffectiveness is defined as the expectation of the weighted sum of the population's expected duration of stay in each of m disability states. The applicability of this and other measures to specific health problems is also discussed. The paper deals with the problem of estimating costs. Distinctions are made among the various kinds of costs and among the various bearers of the costs.
The Allocation of Computer Time in Comparing Simulation Experiments
Authors: Fishman George S.
Published: November 2008

This paper investigates the problem of efficiently allocating computer time between two simulation experiments when the objective is to make a statistical comparison of means. For a given level of accuracy our results show that significantly less computer time is required when the sample sizes are determined according to a certain rule than when the sample sizes are equal. A graphical analysis suggests that small errors in estimating the population parameters of the allocation rule do not significantly affect the efficient allocation of time. The influence that the degree of autocorrelation has on the time allocation is also investigated; results show that small differences in the autocorrelation functions are important when each process is highly autocorrelated. Positively correlated samples for the two experiments are examined and incorporated into the efficient allocation rule. It is shown that their use leads to a saving in computer time. A two-stage procedure is described wherein initial estimates of the population parameters are computed which permit the experimenter to estimate how many more observations to collect on each experiment. The procedure is simple and straightforward to implement and should be of practical value. When the computer time requirements turn out to be prohibitive, we suggest using negatively correlated replications on each experiment. This may be accomplished by using antithetic variates. The two-stage procedure also applies in this case.
A Method for Approximate Solutions to Stochastic Dynamic Programming Problems Using Expectations
Authors: Norman J. M. , White D. J.
Published: November 2008

This note describes and illustrates a computational technique to obtain approximate solutions to stochastic dynamic programming problems. The technique is to replace probability distributions by their corresponding expectations, and to use the values of the states in the corresponding deterministic system under its optimal policy to determine an approximate policy in the stochastic system through a single application of Howard's policy improvement operation. Two examples are given.
Programming Problems with Convex Fractional Functions
Authors: Bector C. R.
Published: November 2008

The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of this result and a few applications to mathematical programming are also considered.
Optimum Redundancy for Maximum System Reliability by the Method of Convex and Integer Programming
Authors: Mizukami Koichi
Published: November 2008

This paper demonstrates the applicability of convex and integer programming to the problem of determining optimum redundancy. A design method to maximize system reliability subject to several constraints on total cost, weight, volume, etc., is described and numerical examples are given to illustrate the procedure for the case of parallel redundancy.
Letter to the Editor—The Multidimensional Assignment Problem
Authors: Pierskalla William P.
Published: November 2008

The multidimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be thought of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch-and-bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem.
Letter to the Editor—Quasilinearization and Inverse Problems for Lanchester Equations of Conflict
Authors: Bueil J. D. , Kagiwada H. H. , Kalaba R. E.
Published: November 2008

This letter applies quasilinearization and digital computation to the solution of certain problems concerning the Lanchester equations of combat. The study shows how the enemy's strength and replenishment rate may be estimated on the basis of information on friendly units. The problem is phrased as a nonlinear, multipoint, boundary-value problem, and quasilinearization is used for the numerical solution. The results of some numerical experiments performed with the aid of an IBM 7044 computer are presented, and the problem of errors in the observations is examined.
Letter to the Editor—A Note on the Generalized Lagrange Multiplier Solution to an Integer Programming Problem
Authors: Nemhauser George L. , Ullmann Zev
Published: November 2008

The problem of applying Generalized Lagrange Multipliers (GLM) to 0-1 integer programming problems is investigated. It is shown that GLM can produce optimal solutions if and only if these solutions are extreme points of the convex set of linear equations. The presentation is based on a capital allocation problem recently discussed by Kaplan. Kaplan's procedure for finding optimal solutions that are not extreme points is discussed in terms of linear programming.
Solution of a General, Nonadaptive, Many-vs-Many Duel Model
Authors: Helmbold Robert L.
Published: November 2008

The solution of a general attrition model for two-sided battles between heterogeneous forces is obtained under the assumption that (1) interaction between the two sides takes place by an exchange of volleys, (2) each participating unit follows a prescribed attack pattern rather than adapting its behavior to the situation, and (3) target survival is stochastically independent of the actions of other fire units.
Optimization of Resource Allocation in Project Planning
Authors: Petrović Radivoj
Published: November 2008

This paper deals with a problem of optimization of resource allocation in a project plan. It is assumed that the technological ordering of activities in a project is defined by the project graph. The predecessor-successor relations of activities are mapped into a set of transformations, where the state variables are the amounts of work required to complete the activities. The resources allocated to each activity are considered as decision variables. They are constrained when resources are limited. This enables one to consider the project execution as a discrete multistage decision process with the associated objective function. The optimization of this process is viewed as a dynamic programming problem. It is shown that the high dimensionality of the functional equations that appear can be overcome by means of (a) subproject programming, (b) two-level concept of management control evaluation, and (c) by approximation in policy space.
The Conditions for Dominance Between Alternatives which are Independent Multiplicative Random Variables
Authors: Cohen Dan
Published: November 2008

The conditions for dominance between alternatives that are independent multiplicative random variables have been worked out. For any two alternatives 1 and 2, 1 dominantes 2 if H(Y1) ≧ E(Y2), where Y is the yield, H(Y1) is the harmonic mean 1/E(1/Y1), and E(Y2) is the expectation. This dominance is strengthened when the contribution of other alternatives is increased.
Jointly Optimal Inventory and Maintenance Policies for Stochastically Failing Equipment
Authors: Falkner Charles H.
Published: November 2008

A dynamic programming problem is formulated to find the inventory, x, of a spare component and a sequence of maintenance intervals r= (r1,…,rx + 1) that minimize the expected cost of operating an equipment for a finite planning horizon, T. It is assumed that the component fails according to a life distribution function, F(⋯), with an increasing hazard function and that it is cheaper to replace components prior to failure. An operating cost function is found to be strictly convex in the time remaining to the end of the period and that at any time there is a finite nonincreasing sequence of economical maintenance policies, each a continuous nondecreasing function of the time remaining. A procedure is given for calculating the optimal initial inventory and reorders when the procurement cost function is K + c ⋯ x.
A Priority System with Setup Times
Authors: Mevert Peter
Published: November 2008

A single server system is considered with 2 classes of customers. Customers of class 1 have preemptive priority over customers of class 2 but the order of service within each class is first-come, first-served. Whenever service is changed from one class to the other an orientation or change-over time is incurred. Arrivals are Poisson, service and orientation times are independent and arbitrarily distributed. Laplace Transforms and expected values of the steady state-waiting time distributions are obtained for each class.
Letter to the Editor—A Criterion for the Economic Application of Imperfect Inspections
Authors: Morey Richard C.
Published: November 2008

A decision rule is developed, based on the associated penalty costs and the likelihood of successfully detecting an existing failure, to determine whether or not an inspection policy is economically of value. Necessary and sufficient conditions are developed if the failure distribution is known explicitly, whereas a sufficient condition is given if it is known only that the mechanism experiences “wearout.”
A New Foundation for a Simplified Primal Integer Programming Algorithm
Authors: Glover Fred
Published: November 2008

Following the approach underlying the Pseudo Primal-Dual Integer Programming Algorithm, a new foundation for a simplified primal integer programming algorithm is given. In addition, new choice rules are prescribed which guarantee finite convergence, and a criterion of optimality is introduced that permits the algorithm to terminate before dual feasibility is achieved.
Blocking and Delays in M(n)/M/c Bulk Queuing Systems
Authors: Kabak Irwin W.
Published: November 2008

The current literature on the subject of queuing systems has included the analytical study of systems with bulk arrivals. Heretofore, all analyses have been concerned with single server systems only. This paper presents results for queuing systems with bulk arrivals; the particular systems are characterized by Poisson arrival epochs with n arrivals at each epoch, exponential service times and c servers. The probability of blocking for both loss and delay systems are investigated. In addition, the average delay, the variance of the delay, and the delay distribution for first-come-first-served delay systems are presented. Special cases are indicated and numerical aspects of the computation are discussed.
Bounds for Some Generalizations of the GI/G/1 Queue
Authors: Marshall K. T.
Published: November 2008

Expressions are derived for the expected number and expected wait in queue for the following generalizations of the GI/G/1 queue: (1) arrivals in batches of random size, (2) service in batches of fixed size, (3) queues with added delay for the first customer in a busy period. These expressions contain the mean and variance of the idle time distribution. Results on the idle period moments, which were derived by the author in a previous paper, are used to obtain bounds for the expected wait and expected number in queue under two different assumptions on A(t), the interarrival time distribution. As an example of (3) we mention the queue where the server, once he becomes idle, does not restart until m customers have arrived (called the GIm/G/1 queue). Such a queue arises when one considers a class of optimization problems in single server queues.
Letter to the Editor—Bruce's Spider and Renewal Theory
Authors: Downton F.
Published: November 2008

The theory of an alternating renewal process with absorption at the renewal points is examined. The problem is discussed in the context of the behavior of Bruce's spider that attempted to climb a smooth wall but repeatedly slipped back and had to start again; but it provides a model for many other processes, of which two typical examples are given. Results are obtained under fairly general distributional assumptions for the distribution of the time to absorption and for the probabilities, conditional upon no absorption having taken place, of the process being in one phase or the other of the alternating process.
Letter to the Editor—Remarks on Finite Queuing Tables
Authors: Votaw D. F. , Peck L. G.
Published: November 2008

Formulas are given for a quantity, D, tabled in Peck and Hazelwood's Finite Queuing Tables (1958, Wiley). D is the equilibrium probability of delay of an arriving customer in a finite queuing system. Formulas involving D are given for the cumulative distribution of the system's state.
A Loading Problem in Process Type Production
Authors: Elmaghraby Salah E.
Published: November 2008

Given a set {di} of continuous rates of demand for n products, the associated costs, unit processing times, and set-up times, and given N different types of processors (with possibly more than one processor per type), it is desired to determine the single-stage production pattern under the constraint that only EMQ's are manufactured. An LP is formulated to which we apply the decomposition principle and generate a nonlinear programming problem in integer variables as a subproblem to be generated at each iteration. This subproblem is solved by dynamic programming approach.
Group Theoretic Algorithms for the Integer Programming Problem II: Extension to a General Algorithm
Authors: Shapiro Jeremy F.
Published: November 2008

The main result of this paper is a group theoretic algorithm (GTIP2) for the integer programming problem. This algorithm is an extension of an algorithm from an earlier paper (part I). The algorithm in part I solves a group optimization problem derived from a given integer programming problem. The optimal solution to the group problem thereby obtained is an optimal solution to the integer programming problem if it is feasible. Unfortunately, an optimal solution to the group problem may yield an infeasible integer solution. The algorithm GTIP2 of this paper is an extension of the method of part I when it fails. In particular, GTIP2 employs a search procedure to find an optimal solution to the integer programming problem. The extent of the search is bounded by procedures derived from a variety of relevant group problems that are solved by the algorithm of part I. There is a discussion of the class of problems for which GTIP2 is primarily intended and the relation of GTIP2 to other algorithms is indicated. A numerical example and some partial computational results are included.
A Discrete-Time Queuing Analysis of Conveyor-Serviced Production Stations
Authors: Beightler Charles S. , Crisp Robert M.
Published: November 2008

This paper analyzes production stations that operate in conjunction with conveyors. Two types of production stations are considered: (1) loading stations that load processed material to the conveyor, and (2) unloading stations that remove material from the conveyor. An operating policy, the sequential range policy, is proposed as a method for operating the production stations. An analysis of the sequential range policy is given. The system is considered as a discrete-time queuing process with a stationary Bernoulli arrival rate. In-process storage is treated as a Markov process discrete in time and discrete in space. The expected number of units in storage and the expected delay per unit produced are derived. Certain economic problems are considered.
Management Research in State and Local Governments
Authors: Holmer Freeman
Published: November 2008

The forces of change—and the rate of change—pose a special challenge for government (since governments tend to support the status quo). The expanding roles of government, the political pressures on government, and the multiplicity of governments create a difficult managerial climate, particularly for the effective application of managerial research. The response to these difficulties is found in part in the work of the associations of governments, but there are a large number of these. What seems to be needed is a focal point—perhaps a corporation or association (created by and responsible to the major governmental associations)—to undertake or arrange for the accomplishment of governmental research and development in accord with a pattern of rational priorities.
A Service System with Unfilled Requests Repeated
Authors: Keilson J. , Cozzolino J. , Young H.
Published: November 2008

The object of this paper is to analyze a model of a queuing system in which customers cannot be in continuous contact with the server, but must call in to request service: If the server is free, then the next request to arrive is served immediately; if the server is occupied, however, the unsatisfied customer must break contact and later re-initiate his request. Thus, repeat requests for service from the pool of unsatisfied customers are superimposed on the normal stream of arrivals of first attempts. This system is characteristic of situations in which there is a single operator or source of information that must be called and busy signals are not held. This paper calculates several characteristic quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first requests and repeat requests.
Chance-Constrained Equivalents of Some Stochastic Programming Problems
Authors: Symonds Gifford H.
Published: November 2008

This paper shows that chance-constrained equivalents exist for several stochastic programming problems that are concerned with selecting a decision vector which will optimize the expectation of a random loss function, sometimes subject to deterministic constraints. The equivalent chance-constrained problems are concerned with selecting a decision vector that will optimize a deterministic function subject to one or more probability constraints of the form pr[yi≧ ξi] ≧ α i, i ∈ I, and sometimes also subject to deterministic constraints. Equivalence is shown for stochastic programming problems with either linear or nonlinear random loss functions, including many stochastic scheduling and inventory problems. Such stochastic programming problems may be converted to equivalent chance-constrained problems that can be solved in their certainty equivalent form, for example, by the Horizon Method of Stochastic Scheduling.
A Simple Class of Parametric Linear Programming Problems
Authors: Barnett S.
Published: November 2008

To find changes in coefficients that can occur without affecting the choice of optimal feasible basic variables is a well known problem in linear programming sensitivity theory. This paper shows that there is a very simple solution to this problem when the m × m matrix A of optimal basis vectors is varied parametrically, provided the matrix B of variations is chosen so that the inverse of A + λ B is linear in λ. It gives a general expression for such matrices B, which allows a considerable degree of arbitrariness; in particular, there exist B's, that can have rank as high as m/2. Extensions to include variations in the nonbasic part of the coefficient matrix and in the objective function coefficients are briefly described.
Letter to the Editor—Fractional Container-Loads and Topological Groups
Authors: Goldman A. J.
Published: November 2008

The problem treated is that of finding those probability distributions of fractional “tails” on the input volumes to a unitization facility during successive time periods that yield a time-invariant distribution of backlog levels. It is shown that this reduces to the determination (which is carried out) of all closed subgroups of the circle group.
Letter to the Editor—Parameter Estimation in a Markov Dependent Firing Distribution
Authors: Rustagi J. S. , Srivastava R. C.
Published: November 2008

In the study of tank weapon systems, the probability distribution of the number of trials required to obtain a preassigned number of successes in a Markov chain with two states arises naturally. This paper studies this distribution, tabulates it for a few values of the parameters, and then discusses the problems of estimating the parameters and of applications to tank-weapon systems.
Letter to the Editor—A Note on the Waiting-Time Distribution for the M/G/1 Queue with Last-Come-First-Served Discipline
Authors: Keilson Julian
Published: November 2008

The waiting-time distribution for an M/G/1 queue with last-come-first-served discipline has a simple structure that may be found from an argument based on the Takács server backlog process. This structure provides real-time information in a convenient form.
Letter to the Editor—A Note on Two Coverage Problems for Multiple Shots
Authors: Breaux Harold J.
Published: November 2008

The solutions to several coverage problems for multiple shots are obtained by Weiss in the form of finite series. This note shows that the series solution to one of these problems reduce to the incomplete Beta function, for which tables are available, and obtains a new series solution, more amenable to computation, for a second problem.
Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs
Authors: Sobel Matthew J.
Published: November 2008

This paper examines pure stationary policies for starting and stopping service in a single-server queue with respect to the state space consisting of queue length and whether or not the service facility is operating. Almost any such policy is shown to be equivalent to one that depends on two parameters. For a wide class of cost functions, the “almost any” is shown to be without loss of optimality in the sense of average cost per unit time over an infinite horizon. The results are largely distribution-free and are obtained with random-walk arguments. They apply also to certain repair problems and to production smoothing problems in which demand is a renewal process and goods are made sequentially.
Errata
Authors: Pincus Martin
Published: November 2008

Corrections to the letter to the editor “A Closed Form Solution of Certain Programming Problems” by Martin Pincus (Opns. Res. 16, 690–694, 1968).
A Probabilistic Model for Obsolescence
Authors: Morse Philip M. , Elston Caroline
Published: November 2008

A Markovian model is presented of a class of items with use-rate that is randomly distributed and with mean use or popularity that diminishes exponentially with time. Tables are given of the functions involved. As an example, it is shown that the yearly circulation of books in a library corresponds to the model, thus enabling circulation characteristics of various book classes to be predicted probabilistically.
Event Classification
Authors: Nash Robert T.
Published: November 2008

Choosing a suitable set of signals for measurement in classification procedures is poorly understood. Since classification is generally associated with a decision process, this paper shows how the entire question is most sensibly formulated as a two-stage statistical decision process. The first decision involves the detection of some suitable inferential signal, while the second is the selection of a suitable course of action or a control policy. The paper discusses techniques for choosing a set of signals for measurement, subject to certain constraints that are imposed upon this selection process, and demonstrates that the classification procedure must be considered in conjunction with the associated decision or control process, if the most appropriate inferential signals are to be selected. In this formulation, pure classification occurs if the possible actions are chosen in a particular manner. The selection of the best signal or signals for measurement may be influenced significantly by the time-dependent nature of the statistical risk.
Letter to the Editor—A Method for Obtaining the Optimal Dual Solution to a Linear Program Using the Dantzig-Wolfe Decomposition
Authors: Walker Warren E.
Published: November 2008

It is well known that the dual variables of a linear program may be obtained easily if the simplex method is vised to solve the problem. This note shows how to obtain these dual variables if the problem is solved by using the Dantzig-Wolfe decomposition principle.
Information Analysis Without States of the World
Authors: Fishburn Peter C.
Published: November 2008

A set of acts is specified. The decision maker can perform an experiment to learn more about his environment before he selects an act. Potential outcomes of each experiment are assumed to be known. Models are provided for determining optimal decision rules and an optimal experiment regardless of whether detailed consequences or states of the world have been formulated.
A Priority Rule Based on the Ranking of the Service Times for the M/G/1 Queue
Authors: Nair S. Sreekantan , Neuts Marcel F.
Published: November 2008

This paper studies the virtual waiting time for the M/G/1 queue under this priority rule: within each generation, customers are served in the order of shortest (or longest) service times. It also considers the limiting behavior of the virtual waiting time, and compares the asymptotic means with those of the first-come, first-served discipline.
A Duel Involving False Targets
Authors: Sweat Calvin W.
Published: November 2008

A duel is initated by an attacker at some time t in [−T, 0]. The defender possesses weapons at −T and encounters “false” targets that occur at time t with probability density λ(t) and are classified as “real” with probability cfa. At the time of attack, the probabilities that the attacker is detected and classified as real are D and caa (D, caa, cfa are constant). If the defender responds with one of his k weapons at the time of attack, he survives with probability pk, and, if he does not respond, he survives with probability qk; qk < pk, pk ≦ pk+1, qk ≦ qk+1 for k = 0, 1, 2, …. The payoff is the defender's survival probability. Both players are informed of the current time, the defender's weapon level, λ, D, caa, Cfa, pk and qk (k = 0, 1, 2, …). The attacker selects a time of attack to minimize the payoff. He may change the attack time as the defender expends weapons against false targets. The defender responds to classifications so as to maximize the payoff. This paper derives an iterative system of first-order differential equations whose unique solution V1(t), V2(t), …, Vk(t), … at time t is the value of the game when the defender has 1, 2, …, k, … weapons, respectively, at time t. It expresses the optimal strategies in terms of the values, and determines the limit of Vk(t) as k → ∞ with k / ∫t0λ(s) ds held constant.
Minimization of Fatalities in a Nuclear Attack Model
Authors: Owen Guillermo
Published: November 2008

This paper considers a two-sided war game in which one side (the defender) must first deploy its defenses, consisting of both a passive defense (shelters), and an active defense (anti-missile missiles); the other side (the attacker) then decides how to aim its missiles. The defender is constrained by budget limitations, while the attacker is constrained by the number of missiles available. The payoff is in term of fatalities. The paper uses a convex duality theorem to change the min-max problem to a pure minimization problem, and obtains a solution that obeys the no-soft-spot rule. An example shows the effects of attack and budget sizes, as well as of the costs of ABM defense.
Letter to the Editor—Some Comments on the Traveling Salesman Problem
Authors: Isaac Akkanad M. , Turban Efraim
Published: November 2008

The purpose of this note is to complement Bellmore and Nemhauser's recent (1968) survey of the traveling salesman problem.
Letter to the Editor—Finding Minimal Cost-Time Ratio Circuits
Authors: Fox Bennett
Published: November 2008

In the treatment of routing problems, other authors have used column generators to introduce, into the basis of the master problem, the solution that corresponds to a cycle in a graph with minimal cost-to-time ratio. This subproblem is of independent interest and corresponds to deterministic Markov renewal programming; this note presents an efficient method for its solution, intuitive basis for which is a search for a way to route flow so that the cost-time trade-off is optimal. This flow-circulation problem is solved parametrically by the out-of-kilter algorithm.
Letter to the Editor—Binomial Distribution Sample-Size Nomogram
Authors: Matlin S.
Published: November 2008

This note gives a nomogram that provides a rapid approximation to the required sample size to be taken from a binomial distribution for a desired precision and confidence.
Shortest Paths in Probabilistic Graphs
Authors: Frank H.
Published: November 2008

This paper considers the problem of finding shortest-path probability distributions in graphs whose branches are weighted with random lengths, examines the consequences of various assumptions concerning the nature of the available statistical information, and gives an exact method for computing the probability distribution, as well as methods based on hypothesis testing and statistical estimation. It presents Monte Carlo results and, based on these results, it develops an efficient method of hypothesis testing. Finally, it discusses briefly the pairwise comparison of paths.
Perturbation Theory and Undiscounted Markov Renewal Programming
Authors: Schweitzer Paul J.
Published: November 2008

A recently-developed perturbation formalism for finite Markov chains is used here to analyze the policy iteration algorithm for undiscounted, single-chain Markov renewal programming. The relative values are shown to be essentially partial derivatives of the gain rate with respect to the transition probabilities, and they rank the states by indicating desirable changes in the probabilistic structure. This both implies the optimality of nonrandomized policies and suggests a gradient technique for optimizing the gain rate with respect to a parameter. The policy iteration algorithm is shown to be a steepest-ascent technique in policy space: the successor to a given policy is chosen in a direction that maximizes the directional derivative of the gain rate. The occurrence during policy improvement of the gain and relative values of the original policy is explained by their essentially determining the gradient of the gain rate.
Letter to the Editor—Computational Results of an Integer Programming Algorithm
Authors: Krolak Patrick D.
Published: November 2008

This note reports on a method for solving the general integer linear programming problem that is called the Bounded Variable Algorithm. It first describes the basic algorithm and then makes a comparison of limited scope between the Bounded Variable Algorithm and other published algorithms on a set of common problems.
Letter to the Editor—The Dependence of Sojourn Times in Tandem M/M/S Queues
Authors: Burke P. J.
Published: November 2008

It has been shown in previous work that a sufficient condition for the sojourn times of a customer in a sequence of stationary M/M/s queues in series to be mutually independent random variables is that all queues except the first and last have single servers. An example is considered which shows that, in general, the single-server condition is also necessary.
Errata
Authors: Smith R. D. , Dudek R. A.
Published: November 2008

Errata to authors' article “A General Algorithm for Solution of the n-Job, M-Machine Sequencing Problem of the Flow Shop,” Opns. Res. 15, 71–82 (1968).
Experimental Design and Simulation in Unloading Ships by Helicopter
Authors: McQuie Robert
Published: November 2008

Should military cargo be unloaded from ships by lighter or by helicopter? To evaluate various unloading vehicles, a simulation was constructed around a linear programming algorithm. It represented helicopters, lighters, trucks, and the maintenance, stevedoring, and supply units required on shore to support them. The type of helicopter performing best in the simulation was sensitive to the estimate of its productivity. A field test to determine this figure was planned, and data from the simulation was used to determine what mathematical characteristics the test design should have. As finally developed, the test selected was a three-quarter replication of an unblocked, fractional-factorial design employing an analysis of covariance. The design had to make provision for sudden changes arising during the course of test execution, as it was to be carried out in Vietnam.
One-Dimensional Space Allocation: An Ordering Algorithm
Authors: Simmons Donald M.
Published: November 2008

The space-allocation problem arises when an architect tries to arrange rooms of fixed area but unspecified shape on a floor plan in such a way as to minimize a given linear combination of the distances between all pairs of rooms. In one dimension, this is the problem of ordering line segments along a simple axis or rooms along one side of a corridor. This paper devises an efficient branch-and-bound algorithm for finding the optimal ordering, and shows that the algorithm can solve one special type of facilities-to-locations assignment problem. Space allocation in two dimensions is also discussed briefly.
System Availability and Some Design Implications
Authors: Kabak Irwin W.
Published: November 2008

This paper analyses in detail a system with an exponential reliability function and a constant repair time. It first presents the availability and its variance for a given number of cycles, a finite length of time, and a steady state. Then, it shows how the variance of the availability can be used to support an economic evaluation of start-up operations, presents some design criteria based on a total system cost model that includes a function of the availability (a down-time that is the complement of availability), gives optimal values of the mean time to failure and the mean repair time, and exhibits methods for a sensitivity analysis of these optimal values and of the total system. The paper concludes with a numerical example.
The Set-Partitioning Problem: Set Covering with Equality Constraints
Authors: Garfinkel R. S. , Nemhauser G. L.
Published: November 2008

This paper gives an enumerative algorithm for the set-partitioning problem, that is, the set-covering problem with equality constraints, and presents computational results for real and randomly generated problems. The fact that many problems can be solved more rapidly than the corresponding linear programs demonstrates the efficiency of the algorithm; for example, a randomly generated problem with 1,400 variables and 100 constraints was solved in 15 minutes.
On Finding the Maximal Gain for Markov Decision Processes
Authors: Odoni Amedeo R.
Published: November 2008

The method of successive approximations for solving problems on single-chain Markovian decision processes has been investigated by White and Schweitzer. This paper shows that White's scheme not only converges, but also can be modified so that monotonic upper and lower bounds on the maximal gain can be obtained.