bluuebunny/crossref_metadata_2025 huggingface dataset:
A General Model for Investment Policy
Authors: Reisman Arnold , Buffa Elwood S.
Published: November 2008

This article presents a mathematical model describing the most general case in equipment investment policy. A systematic study of all other cases in the order of decreasing complexity follows. The general model reduces to their present worth all disbursements and receipts involved in the possession and operation of a succession of equipment having varying initial costs, life spans, salvage values, income and cost functions. With one recent exception (1), it is a more general model than those seen by the authors. All possible special cases of the general model are presented in a systematic fashion. Finally, previous models and working decision rules are fit into the framework of this model as special cases.
Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing
Authors: Shubik Martin
Published: November 2008

A goal of good management should be to design a reward system for those who take risks in making decisions in such a manner that the rewards to the individual correlate positively with the worth of the decision to the organization (taking into account the attitude of the top management to variance as well as to expected gain). In many organizations cost accounting supplies much of the information used for control at several levels. In this paper we examine some of the control problems that arise if joint costs are assigned by various cost accounting and some internal pricing conventions.
A Note on Parametric Linear Programming
Authors: Simons Edgar
Published: November 2008

This note considers linear programming problems in which the components of the cost vector are linear functions of a set of parameters. The main result is a proof that the set of parameters which yield cost functions that have optimal solutions is a convex polyhedron.
The Use of Linear Programming and Mathematical Models in Under-Ground Oil Production
Authors: Aronofsky J. S. , Williams A. C.
Published: November 2008

This paper describes how linear programming models can be used to solve crude-oil producing problems for the purpose of economic planning of coordinated operations. Although the methods of linear programming have been used extensively in the oil industry, very little work has been reported to date in extending these methods to the area of underground oil production. Two separate models are presented. The first model schedules production and assumes either a completely developed field, or, in the case of only partially developed fields, it assumes a given drilling schedule. The second model schedules drilling-rig operations when it is assumed that the production from a given well follows a specified production-decline curve. Consideration also is given to a means for optimizing the investors rate of return which appears as a nonlinear parameter in the objective function.
Generalizations of the Optimal Final Inventory Model
Authors: Hadley G.
Published: November 2008

The purpose of this note is to generalize the optimal final inventory model presented previously [Hadley, G., T. M. Whitin. 1961. An optimal final inventory model. Management Sci. 7(2) 179–183]. Two generalizations are made. First, the mean demand is allowed to vary with time so that dynamic situations may be studied. Secondly, the date of obsolescence is no longer required to be fixed but is instead allowed to be described by a probability distribution.
A Family of Dynamic Inventory Models
Authors: Hadley G. , Whitin T. M.
Published: November 2008

A family of inventory models in which demand is allowed to change with time is studied. One general model is presented which includes every member of the “family” as a special case. The general model assumes that demand is a random variable. The mean rate of demand may vary over time but demands in different time periods are assumed independent. It is assumed that there is a date of obsolescence for the item with no demands occurring after this date. The time of obsolescence may be either known or alternatively a finite number of obsolescence dates and their probable occurrence may be specified.

Procurement lead times are allowed to be random variables, subject to certain restrictions which are discussed. Procurements are allowed only at a finite number of predetermined times which may be specified in any way desired. Demands occurring when the system is out of stock are assumed to be backordered. The procurement quantities are determined by solving a dynamic programming problem which minimizes the sum of the expected costs of procurement, carrying inventory, stockouts, and losses from obsolescence. The dynamic programming problem is within the range of feasibility computationally, because only tables involving a single parameter are required.

A number of special cases of the general model are studied and it is shown that most dynamic models which have appeared in the literature are special cases of the general model.
Computation for the Redistribution Model with Set-Up Charge
Authors: Allen S. G.
Published: November 2008

A systematic computation procedure is given for determining redistribution of stock among several user activities when set-up charges are involved. The procedure is divided into two phases, the first of which determines whether any redistributions should be made at all. Then the second phase determines the total amount to be shipped or received at each activity.
A Model for Industrial Learning Costs
Authors: Kilbridge Maurice
Published: November 2008

This paper presents a framework for the analysis of operator learning cost with special reference to assembly groups. Learning has the limited meaning of skill acquisition as measured by increased productivity. Learning cost is formulated as a function of the length of task to be learned, other variables being fixed. Three components of learning cost are distinguished and analyzed separately. The total learning cost model is the sum of the three component models.
A Note on the Optimality of (S, s) Policies in Inventory Theory
Authors: Zabel Edward
Published: November 2008

In this paper a proof of Herbert Scarf's on the optimality of (S, s) policies in inventory theory is extended to cases where differentiability of cost functions may not be available. In addition to an ordering cost composed of a unit cost plus a reorder cost all that is needed in the proof is that the expected holding and shortage cost function be convex.
Optimal Service Policies and Finite Time Horizons
Authors: Carr C. R. , Howe C. W.
Published: November 2008

This paper characterizes optimal service policies in terms of the frequency and timing of services which are intended to maintain a stock of assets. The model is non-stochastic. The results are obtained by a two-stage step-wise minimization procedure wherein dynamic programming is first used to characterize sub-optimal policies and then the calculus of finite differences is utilized to select the optimal policy. The effect of the time horizon on the optimal policy is emphasized throughout and, in two specific interpretations of the model, the classical results of the economic lot-size and equipment replacement policy are shown to be limits of more general policies.
On Sequential Decisions and Markov Chains
Authors: Derman Cyrus
Published: November 2008

Several problems in the optimal control of dynamic systems are considered. When observed, a system is classifiable into one of a finite number of states and controlled by making one of a finite number of decisions. The sequence of observed states is a stochastic process dependent upon the sequence of decisions, in that the decisions determine the probability laws that operate on the system. Costs are associated with the sequence of states and decisions. It is shown that, for the problems considered, the optimal rules for controlling the system belong to a subclass of all possible rules and, within this subclass, the optimal rules can be derived by solving linear programming problems.
Inspection—Maintenance—Replacement Schedules Under Markovian Deterioration
Authors: Klein Morton
Published: November 2008

A problem of finding optimal policies for the management of systems whose deterioration can be expressed as a Markov chain is considered. Using methods due to Manne and Derman for sequential decision problems involving average cost per unit time criteria, it is shown that the problem can be formulated in linear programming terms.
Replacement of Randomly Deteriorating Equipment
Authors: Eisen M. , Leibowitz M.
Published: November 2008

The replacement of a machine which deteriorates at a random rate is considered. We measure this deterioration in terms of a cost per unit time—i.e., a cost-density γ(t) where t is the age of the machine. Given the probability distribution of γ(t) and the replacement cost R(c, t) when γ(t) = c, we discuss optimal replacement using two different procedures:

(1) replacement at a fixed age

(2) replacement when the cost-density reaches a given value

Expressions are derived for the resulting costs incurred in using either procedure over a long period of time. Method (2) is in general preferable.
A Simplified Model for Portfolio Analysis
Authors: Sharpe William F.
Published: November 2008

This paper describes the advantages of using a particular model of the relationships among securities for practical applications of the Markowitz portfolio analysis technique. A computer program has been developed to take full advantage of the model: 2,000 securities can be analyzed at an extremely low cost—as little as 2% of that associated with standard quadratic programming codes. Moreover, preliminary evidence suggests that the relatively few parameters used by the model can lead to very nearly the same results obtained with much larger sets of relationships among securities. The possibility of low-cost analysis, coupled with a likelihood that a relatively small amount of information need be sacrificed make the model an attractive candidate for initial practical applications of the Markowitz technique.
A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities
Authors: Armour Gordon C. , Buffa Elwood S.
Published: November 2008

This paper presents a new methodology for determining suboptimum relative location patterns for physical facilities. It presents a computer program governed by an algorithm which determines how relative location patterns should be altered to obtain sequentially the most improved pattern with each change, commands their alteration, evaluates the results of alterations, and identifies the sub-optimum relative location patterns.3 The computer output yields a block diagramatic layout of the facility areas, and the areas need not be equal.4 A manufacturing plant layout example is used because the methodology is well illustrated by reference to some kind of example, and this one is commonly known. The methodology itself, however, is general in nature and not restricted to such applications.
Consistency and Optimality in Managerial Decision Making
Authors: Bowman E. H.
Published: November 2008

This paper reports some research, ideas, and theory about managerial decision making. The first research projects dealt with are aggregate production and employment scheduling. From this is developed the idea that management's own (past) decisions can be incorporated into a system of improving their present decisions. Decision rules are developed, with the coefficients in the rules derived from management's past decisions (rather than from a cost or value model). Half a dozen test cases are used to illustrate and test these ideas (theory). Some rationale about decision making in organizations and criteria surfaces is supplied to help interpret the major ideas presented.
The Dissemination and Use of Recorded Scientific Information
Authors: Martin Miles W. , Ackoff Russell L.
Published: November 2008

Two separate field studies of chemists and physicists were made which were concerned with how scientists spend their time, especially the amount and kind of communication in which they engage. Approximately 2,200 chemists and physicists were observed.

The studies were also concerned with finding out what journals scientists read, what parts of journals, the purposes for which they are read, and the variance of costs of disseminating information through journals, as well as the effect which characteristics of employing organizations have on the way a scientist spends his time.

Outstanding features of the research design and those results which are most likely to be of general scientific interest are presented in this article.
The X of X
Authors: Churchman C. West
Published: November 2008

A featured presentation at the Ninth Annual International Meeting of The Institute of Management Sciences, jointly with the Econometric Society, at Ann Arbor, Michigan, September 11, 1962.

“A unified science of management.” Is it a matter of faith or of enterprise? A unified science of management conceals the self-reflective paradox. Science is an organized activity. Hence it operates according to some managerial principles. A unified science of management implies a management of science: a science of science, a self-reflective science.
Optimal Replacement Policies for a Ballistic Missile
Authors: Jorgenson D. W. , McCall J. J.
Published: November 2008

This paper applies, to ballistic missile systems, replacement policies for equipment subject to stochastic failures in which the actual state of the system—good or failed—is not known with certainty. Although it applies these policies only to the missile itself, optimal maintenance policies for the system as a whole are conceptually similar. The criterion employed for comparison of alternative maintenance policies is to minimize the total cost per expected piece of equipment good per period of time. Maximization of system reliability is a special case of this criterion which ignores the financial costs of maintenance actions.

The range of maintenance policies examined may be subdivided in two ways. First, it may be assumed that the distribution of times to failure for parts not subject to inspection is known. Secondly, it may be assumed that the distribution is known but that one or more parameters characterizing the distribution are unknown. The central feature of these latter policies is that the interval between replacements is adapted to new information as it accumulates.

A second subdivision encompasses those maintenance policies in which the time to replacement for the non-monitored part depends on the state of the remaining parts of the system, and those in which only the failure rate of the uninspected part and the cost of maintenance actions are taken into account in determining the replacement interval. The first class of policies is called “opportunistic,” since optimal policies are designed to take advantage of opportunities arising through failures of the remaining parts. Opportunistic policies have a structure which may be described by a critical number N and a set of such critical numbers n1,n2, …, each corresponding to one of the parts under inspection. The optimal policy may be described as follows: For 0 ≦ x ≦ ni, the non-monitored part is not replaced if the i-th monitored part fails; for ni ≦ x ≦ N, the non-monitored part and the i-th monitored part are replaced whenever the i-th monitored part fails.

For illustrative purposes, optimal policies of each type are computed for a hypothetical ballistic missile system. They are then compared with each other and with a rule of thumb frequently proposed for replacement policy: Replace at the mean time to failure.
On the Symmetry Approach to the Committee Decision Problem
Authors: Theil H.
Published: November 2008

The order of discussion is as follows. In Section 2 the basic ideas (which are already “classical”) are briefly restated and the problem is formulated. In Section 3 some proposals are made for the weights of the linear combination of individual preference functions. Section 4 illustrates the committee decision problem by a very simple example of measures of central tendency, the solution of which suggests a method for solving the general problem. Section 5 is the heart of the article; it introduces the symmetry condition. The last section deals with the case when symmetry cannot be realized.
Minimum-Cost Cattle Feed Under Probabilistic Protein Constraints
Authors: van de Panne C. , Popp W.
Published: November 2008

The optimal composition of cattle feed, which can be formulated as a linear programming problem in the case of certainty, is considered when compositions of inputs vary. In the corresponding linear programming formulation the coefficients of the constraints are not constant but can be considered as stochastic. Reformulating the constraints as chance constraints, a nonlinear programming problem results. For an illustrative example this problem is solved using one of Zoutendijk's methods of feasible directions.
Optimal Replacement and Maintenance Under Markovian Deterioration with Probability Bounds on Failure
Authors: Derman Cyrus
Published: November 2008

A system is observed periodically and classified into one of a finite number of states. On the basis of the observations certain maintenance or replacement decisions are made. Transitions probabilities from state to state are determined by the decisions. The problem considered is that of finding the decision rule which maximizes the expected length of time between replacements subject to the side conditions that the probabilities of replacement through certain undesirable states are bounded by prescribed numbers.
Assembly Line Balancing with a Precedence Matrix
Authors: Hoffmann Thomas R.
Published: November 2008

Assembly line balancing consists of assigning work elements, which are subject to sequencing restrictions, along an assembly line in an optimal manner. The procedure presented in this paper leads to optimal line balances by operation on a matrix of zeros and ones called a “Precedence Matrix.” A nine element problem is used to illustrate the method in detail and comparisons with other procedures are made. Several balances obtained by applying the FORTRAN program appended to the paper to actual and sample problems are also shown.
Some Experiments in Planning and Operating
Authors: Bass Bernard M. , Leavitt Harold J.
Published: November 2008

Three experiments are reported relating types of planning activities to performance and attitudes. In general, the findings are consistent with earlier studies showing strong, positive relationship between participation in planning on the one hand and morale and productivity on the other. In all three experiments, performance and attitudes were better when subjects were using plans developed by themselves than plans developed by others.
The Quadratic Assignment Problem
Authors: Lawler Eugene L.
Published: November 2008

This paper presents a formulation of the quadratic assignment problem, of which the Koopmans-Beckmann formulation is a special case. Various applications for the formulation are discussed. The equivalence of the problem to a linear assignment problem with certain additional constraints is demonstrated. A method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions. Further generalizations to cubic, quartic, N-adic problems are considered.
Convex Programming by Tangential Approximation
Authors: Hartley H. O. , Hocking R. R.
Published: November 2008

This paper describes an algorithm for the solution of the convex programming problem using the simplex method. The algorithm is computationally very simple, requiring the solution of a single linear programming problem which can be accomplished with only slight modification of existing computer codes for the revised simplex method.
A Heuristic Program for Locating Warehouses
Authors: Kuehn Alfred A. , Hamburger Michael J.
Published: November 2008

The linear programing algorithms available for optimizing the routing of shipments in multi-plant, multi-destination systems cannot, in the current state of knowledge, be applied directly to the more general problem of determining the number and location of regional warehouses in large-scale distribution networks.

This paper outlines a heuristic computer program for locating warehouses and compares it with recently published efforts at solving the problem either by means of simulation or as a variant of linear programing. The heuristic approach outlined in this paper appears to offer significant advantages in the solution of this class of problems in that it (1) provides considerable flexibility in the specification (modeling) of the problem to be solved, (2) can be used to study large-scale problems, that is, complexes with several hundred potential warehouse sites and several thousand shipment destinations, and (3) is economical of computer time. The results obtained in applying the program to small scale problems have been equal to or better than those provided by the alternative methods considered.
Communications to the Editor—A Note on Utility and Attitudes to Risk
Authors: Borch Karl
Published: November 2008

Most theories of economic decision-making under uncertainty recognize that the value assigned to an uncertain prospect may differ from its “actuarial value,” or that the utility of an expectation may differ from the expectation of the utility. One way of formalizing this idea is to assume that the utility of a prospect is given by a function f(E, V), where E = the mathematical expectation of the gain, V = the variance of the gain. Various considerations about existence and possible shape of such function f(E, V) are presented.
The Operations Research Society of America
Authors: Morse Philip M.
Published: November 2008

Editorial about the founding of the Journal of the Operations Research Society of America.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Experiences in Commercial Operations Research
Authors: Levinson Horace C.
Published: November 2008

The operations-research practitioner who studies problems of industrial or business operations may be either external or internal to his customer's organization; i.e., either he may be working under contract to the company (as an individual or as a member of an independent firm), or he may actually be an employee of the company. Most of my own experience has been in the latter situation, my research being directed to the analysis of operations of the company with which I was associated. I shall therefore take that point of view here.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
A Generalized Network Approach to the Planning and Scheduling of a Research Project
Authors: Eisner Howard
Published: November 2008

This paper describes a configurational and mathematical tool that may be used in the planning and scheduling of a research program. The configuration, termed a decision box (db) network, is a generalization of the PERT network and allows alternative procedures for accomplishing research tasks to be considered. The probability of following each alternative is estimated, leading to a ranking, in terms of probability of occurrence, of the possible outcomes of the research program. The entropy of the process is calculated using classical information theory concepts Standard PERT techniques for time estimating and scheduling, superimposed upon the db network structure, complete the description of this research management tool.
Mathematical Model for Operational Readiness
Authors: Coleman John J. , Abrams I. Jack
Published: November 2008

To ensure a high degree of operational readiness of a complicated device or system, either continuous monitoring or periodic testing of the components that are subject to failure must be undertaken. These procedures may in themselves, however, subject the device or system to further stresses that may lead to failures. Furthermore, the efficiency of such tests in detecting failures, their rate of making false alarms and thus subjecting the system to unnecessary repairs also determine the long-run proportion of time during which the system is ready for use when demanded. This paper develops an operational-readiness model, in terms of military-type equipment, which includes uncertain test results and failures caused by testing.
Some Weapon System Survival Probability Models—I. Fixed Time Between Firings
Authors: Schoderbek Joseph J.
Published: November 2008

The various survival probability models considered in this series of two papers can be reduced to basically two types depending on whether the time between firings is fixed or random. In Part I several deterministic models for estimating weapon system survival probability are considered. These are introduced by way of problems of increasing complexity, the first being concerned with the simple problem of determining the probability that a weapon system engaged in a duel with another will survive a specified length of time. The time between firings is assumed to be the same for both sides and the friendly force is assumed to have fired first. In the second problem, the former assumption is removed. Problem 3 introduces the concept of evacuation and illustrates the effect evacuation capability has on probability of survival. Problem 4 is a natural extension of Problem 3 and uses results from the previously derived models. In the very last model the deterministric nature of which side fires first is removed. All told, the models serve to highlight the effects of kill probability, vulnerability, guidance errors, kill radius, mobility, and rate of fire on the probability of survival.
Some Weapon System Survival Probability Models—II. Random Time Between Firings
Authors: Schoderbek Joseph J.
Published: November 2008

Part II of this study centers about mathematical models in which the number of times a weapon system fires during a time interval of length t is assumed to be random and given by a Poisson distribution with parameter λt where λ is the average rate of fire. The single-shot kill probabilities are permitted to be time dependent—an increasing kill probability reflecting the effect of improved target location, a decreasing kill probability indicating possible movement of the target. Still other interpretations are possible. In another model the friendly force is permitted to evacuate, its position after evacuation being a random variable. In this model the distance that the friendly force moves in time t is assumed to be given by a Rayleigh distribution with parameter λt, which is a function of time. The possible tradeoff between increased numbers of weapon systems and greater surveillance capability is indicated. Lifetime distributions and other quantities of interest are obtained for both the friendly and the enemy force.
A Theory of Reconnaissance: I
Authors: Danskin John M.
Published: November 2008

A study is made of the optimum distribution of aerial reconnaissance effort against land targets in the presence of decoys. The model considered is one in which the reconnoitering forces allocate effort among various regions, their objective being the location of the targets, assuming that the side being reconnoitered is passive. The information function of the theory of communication is chosen as the measure of effectiveness. It is proved that under certain reasonable assumptions the information function is increasing and convex-concave. Thus the problem is reduced to a familiar one in operations research, the maximization of the sum of several convex-concave functions subject to linear side conditions.
Periodic Structure in the Brownian Motion of Stock Prices
Authors: Osborne M. F. M.
Published: November 2008

The internal structure of stock prices is examined by comparison with simple random walks of basic step 1/8, in which the individual price changes ΔP are the step length, and the volume measures the rate at which the steps are taken. It is found that there is definite evidence of periodic in time structure corresponding to intervals of a day, week, quarter, and year, these being simply the cycles of human attention span. The evidence is not in the periodicity of the price sequences P(t), rather in the distribution of the first and second differences of P(t), especially the second moment of ΔP (or variance), and in the rate at which the steps are taken. It is also shown that there is a periodic “space structure” in the price coordinate P, corresponding to the Brownian motion in the presence of equally spaced sites of preferred occupancy and reflection barriers, at the whole numbers. There is also marked evidence of “clustered” activity, the data being analyzed by methods appropriate to cosmic ray bursts, or star counts on astronomical photographs. In general, the picture of price motion as simple random walks is supported qualitatively, quantitatively there are some substantial departures from this simple picture.
Letter to the Editor—The PERT Model for the Distribution of an Activity Time
Authors: Clark Charles E.
Published: November 2008

An earlier paper describes the PERT analysis of a network of activities (Malcolm, D. G., J. H. Roseboom, C. E. Clark, W. Fazar. 1959. Application of a technique for research and development program evaluation. Opns Res. 7 646–669.), its analytic details, not written by a mathematician, are confusing to many analysts who continually request elucidation. This note is intended to answer the question most frequently asked, namely, whence the statements in that paper concerning the distribution of an activity time?
Letter to the Editor—Optimum Preventive Maintenance Policies when Immediate Detection of Failure is Uncertain
Authors: Noonan G. C. , Fain C. G.
Published: November 2008

The purpose of this note is to develop the preventive maintenance schedule that will optimize system performance when immediate detection or repair of failures cannot be assured. Under these conditions it will be shown that, even for exponential failure rates, optimum preventive maintenance schedules exist.
New Methods in Mathematical Programming—Some Simplex-Like Nonlinear Programming Procedures
Authors: Wolfe Philip
Published: November 2008

This paper surveys certain recent procedures for the computational solution of convex nonlinear programming problems, related to one another through being based on the simplex method of linear programming. The first procedure, the simplex method for quadratic programming, is a terminating algorithm for the extremization of a quadratic function under linear constraints. The next two procedures employ efficient techniques for the development of a grid on which nonlinear objectives and constraints can be represented by linear functions, the separable programming method is applicable to problems involving separable functions, and the decomposition method to those in which a simpler subproblem can readily be solved. Finally, the cutting-plane method employs an efficient sequential means of approximating to the nonlinear functions involved through first-order Taylor's series approximations.
New Methods in Mathematical Programming—The Solid Transportation Problem
Authors: Haley K. B.
Published: November 2008

This paper describes the solution of a multi-index transportation problem where there are three indices. The method of solution is an extension of the modi-method.
New Methods in Mathematical Programming—Methods of Solution of Linear Programs Under Uncertainty
Authors: Madansky A.
Published: November 2008

The three most usual methods of reducing the effects of uncertainty in the technology matrix, requirement vector, or cost vector of a linear programming problem are the expected-value solution, the “fat” solution, and the “slack” solution. These methods are explained in some detail, and the relation between these various methods is pointed out.
New Methods in Mathematical Programming—On Varying All the Parameters in a Linear-Programming Problem and Sequential Solution of a Linear-Programming Problem
Authors: Courtillot Marcel
Published: November 2008

The purpose of this paper is to analyze the resulting effect on an optimal solution of arbitrary variation of any coefficient of a linear program. A method for sequential solution of a linear program is also given “in fine.”
A Dual Labelling Method for the Hitchcock Problem
Authors: Briggs F. E. A.
Published: November 2008

An alternative labelling method is given for the Hitchcock problem. The method changes the dual variables in a manner which differs from that given by Ford and Fulkerson. A comparison is given with the Ford-Fulkerson method in an application to a 10 × 10 problem.
A Review of Analytical Systems of Line Balancing
Authors: Kilbridge Maurice D. , Wester Leon
Published: November 2008

Although progressive assembly has been practiced for fifty years in American industry, most of the basic problems associated with the system have, through the years, received little analytical attention. Among these is the line-balancing problem. It is of great practical importance, and yet, until very recently, industry has been satisfied to use trial-and-error techniques for line balancing that are time consuming and generally yield poor results. In the last few years this problem has come into vogue resulting in a rash of analytical papers on the subject. Some of these present systems of line balancing that are proving to be useful. This paper summarizes and discusses these systems, shows their applicability to different kinds of assembly lines, and points up the unsolved problems remaining in this area.
The Loading Problem
Authors: Pandit S. N. Narahari
Published: November 2008

Two techniques, of lexicographic search and of bracketing bounds, are developed in the context of the loading or knapsack problem. Starting from an initial feasible selection, the first technique proceeds to an “intelligent enumeration” of all the exchanges possible and leads to a better selection, when one exists. The second technique sets upper bounds to feasible values (of the objective function) and allows us to take decisions about the selection of articles by employing a criterion involving conditional bounds. The techniques are easy to apply and allow of direct extension to the case of multiple criteria.
On the Relation Between the Traveling-Salesman and the Longest-Path Problems
Authors: Hardgrave William W. , Nemhauser George L.
Published: November 2008

The main result of this paper is that the traveling-salesman problem is a special case of the longest-path problem. Two formulations of the traveling-salesman problem are considered, the version in which the salesman visits each city exactly once and the more general formulation in which each city may be visited more than once. Both cases are reduced to the problem of finding the longest path between two nodes in a finite, connected graph. The remainder of the paper is then devoted to possible algorithms for the longest-path problem, since none presently exist.
Letter to the Editor—Bibliography on Project Planning and Control by Network Analysis: 1959–1961
Authors: Bigelow Clifford George
Published: November 2008

Network analysis—also known as PERT (program evaluation and review technique), PEP (program evaluation procedure), CPM (critical-path method), CPS (critical path scheduling), and arrow diagramming—for the planning and control of research and industrial projects and programs has been the subject of many published articles. The following bibliography lists the major titles, classified as to (1) basic principles, (2) industrial applications, and (3) military applications, that have appeared in over forty publications from 1959 through 1961.
The Measurement of Acceleration Noise—A Traffic Parameter
Authors: Jones Trevor R. , Potts Renfrey B.
Published: November 2008

The dispersion of the acceleration noise distribution of an automobile is measured from the velocity-time trace on a tachograph chart. The method is convenient and rapid and has enabled a large experimental program to be carried out. The acceleration dispersion has been compared for different highways, different drivers, and different traffic conditions, and the results obtained suggest that the dispersion is a useful traffic parameter.
Stochastic Models for the Duration and Magnitude of a “Deadly Quarrel”
Authors: Weiss Herbert K.
Published: November 2008

Once a war has been initiated, its continuation or termination may be considered to be determined by two transition probabilities—one describing the probability that in a small interval of time an additional death occurs, and the other describing the probability that in the same small interval of time the war is terminated. Given forms for these transition probabilities, one may obtain distribution functions for the duration and magnitude of a war, given that it has begun. The inverse problem of determining the form of the transition probabilities, given the distribution of war durations and magnitudes, is more difficult. However, functions are developed in this paper that will generate distributions corresponding to those presented in the tabulation of 315 wars prepared by L. F. Richardson. The expressions for the transition probabilities are derived based on the assumption that they depend at each instant only as the cumulative number of deaths to that point and the time over which the deaths have been incurred. Some of the implications of the expressions and the possibility of their use to categorize classes of wars are discussed.
Letter to the Editor—Implementation of Problems in O. R.
Authors: Stillson Paul
Published: November 2008

In any description of an operations-research application there is usually some mention of solution implementation. Virtually all practitioners agree on this phase of an operations-research study and the necessity for its consideration. Despite this concurrence, the references that are made to the practical usage of the model and solution are very vague and general and imply that implementation follows in the normal course of the operations to which the study has been applied. In many cases, there is only the phrase “the study was successfully implemented” as if this were a simple and natural consequence of the effort. What problems were encountered in the implementation of the study? What was required on the part of the company to ensure the success of the operations-research study? What effect did these implementation problems have on the “optimum” solution? These questions have a direct bearing on the acceptance and potential of the operations-research activity in business and industry, and there is an urgent need for more extensive documentation of experiences in this area.
The Best Estimate of Reliability in the Exponential Case
Authors: Pugh Edward L.
Published: November 2008

The commonly used estimate of reliability in the exponential case, i.e., the maximum likelihood estimate, is shown to exert a strong negative effect on reliability calculations because of its bias. A minimum variance unbiased estimate is then derived using a theorem of Blackwell and Rao.
Queuing with Breakdowns
Authors: Thiruvengadam K.
Published: November 2008

A single-server queuing process in which the service facility is subject to breakdowns, is considered in this paper as a “preemptive resume priority” queuing process. The restrictions imposed on arrival process of breakdowns give rise to several breakdown models with different operational parameters. The time-dependent and the steady-state queue-length generating functions of two breakdown models are given in this paper, when the service time process and repair time process are general distributions. The results of White and Christie and Heathcote are obtained as particular cases.
Accommodation of Second-Class Traffic
Authors: Gaver Donald P.
Published: November 2008

Situations exist in which a facility performs a primary function but is available, during otherwise idle periods between primary jobs, to service secondary tasks as well. Such is the case at side-street intersections with a main highway, aspects of this particular problem have been considered by many authors, recently by Weiss and Maradudin and Oliver in this journal. In this paper the durations of the secondary tasks are taken to be random variables, independently sampled for each “second-class” task, and held fixed until an adequate gap (idle period) appears. The model thus differs from that of Weiss and Maradudin in that it reflects between-task variability. For this model we investigate the long-run rate of task completion, the time for completion of a task that is “first in line,” and the waiting time of a task that arrives to find a queue of tasks ahead of him at the facility.
Some Queuing Problems with Balking and Reneging. I
Authors: Ancker C. J. , Gafarian A. V.
Published: November 2008

Balking (refusing to join the queue) and reneging (leaving the queue after entering) are considered. The model assumes (1) Customers arrive from a single infinite source in a Poisson stream (2) Arriving customers balk with probability n/N where n is the number in system and N is the maximum number allowed in the system (3) Joining customers renege if service does not begin by a certain time, which is a random variable with negative exponential distribution (4) A single-service facility operates on a first-come, first-served basis with negative exponential service time distribution. For the steady state, the following are obtained the state probabilities, mean number in queue and system, the probability of R or more in system, the probabilities of balking, waiting, reneging, and acquiring service, the customer loss rate, the distribution and mean value of time in queue for customers who acquire service, and the corresponding results for those who renege. All of these results are also obtained for a pure balking system (no reneging) by setting the reneging parameter equal to zero. This case may be interpreted as the simple machine interference problem for which some of our results appear to be new.
Analysis of Bunching in Rural Two-Lane Traffic
Authors: Miller Alan J.
Published: November 2008

A model is proposed for the formation of bunches in rural two-lane traffic. An overtaking rate is defined and estimated from data. The relation between these overtaking rates and various other factors is investigated. It is shown that with the data available, the model provides an exceptionally good fit. Formulas are then derived for the rate of delay to vehicles on rural roads caused by restricted overtaking. The model is not recommended for the analysis of urban traffic. For urban traffic, it is suggested that variance/mean ratios provide a useful measure of bunching.
A Simplified Procedure for Quadratic Programming
Authors: Shetty C. M.
Published: November 2008

The problem discussed in this paper deals with maximization (minimization) under linear restrictions, of a quadratic function of the form (1/2XtUX + VX) where U is negative (positive) semi definite. The optimum solution to this problem can be obtained by solving a certain enlarged system of equations representing the Kuhn-Tucker conditions. In this paper we will show that an equivalent system of equations of smaller dimensionality can be derived directly from any basic solution to the quadratic programming problem. We will also show that a variant of Wolfe's procedure for quadratic programming, which essentially uses the simplex method, can be used to solve this equivalent problem using a n × (2n + 1) tableau giving the optimum solution in a finite number of iterations. The procedure can be programmed on a computer with minor modifications to the code for linear programming.
On Assembly Line Balancing
Authors: Klein Morton
Published: November 2008

This paper gives a simple method for finding an optimal assignment of operations to work stations when the order of operations is specified. It is shown that the problem with a specific ordering can be formulated as an assignment problem or as a shortest-route problem for which an inspection-type solution is available. The more general problem, when it is possible to enumerate all feasible orderings of operations, can then be handled by repeating the required calculations for all such orderings.
Letter to the Editor—The Output of an M/G/∞ Queuing System is Poisson
Authors: Mirasol Noel M.
Published: November 2008

Burke [Burke, P. J. 1956. The output of a queuing system. Opns. Res. 4 699–704.] has shown that, in steady state, a queuing system with a Poisson input and independent (negative) exponential service times has an output that is also a Poisson process with a rate equal to the input rate, regardless of the number of channels. He has also shown that the interdeparture interval is independent of the state of the system at the end of the interval.

We will show that if a queuing system has a Poisson input and an infinite number of channels, the output is also Poisson, regardless of the distribution of service times, provided that these times are independent.
Location-Allocation Problems
Authors: Cooper Leon
Published: November 2008

The calculational aspects of solving certain classes of location-allocation problems are presented. Both exact extremal equations and a heuristic method are presented for solving these problems. Directions for further investigation are also indicated because of the need for methods to shorten the total amount of calculation involved.
The Multi-Index Problem
Authors: Haley K. B.
Published: November 2008

The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities.
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
Authors: Everett Hugh
Published: November 2008

The usefulness of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions. They can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set. While the use of the Lagrange multipliers does not guarantee that a solution will necessarily be found for all problems, it is “fail-safe” in the sense that any solution found by their use is a true solution. Since the method is so simple compared to other available methods it is often worth trying first, and succeeds in a surprising fraction of cases. They are particularly well suited to the solution of problems of allocating limited resources among a set of independent activities.
Theory of Combat: The Probability of Winning
Authors: Brown Richard H.
Published: November 2008

As two forces engage in combat without replacements, the numbers of survivors on the two forces will diminish. The force first reaching zero loses, the other wins Let P(x, y) be the probability that the first force wins if there are x members for it and y members for the second force, and let A(x, y) be the probability that the next casualty is on the second force. It is shown that P(x, y) = A(x, y)P(x, y − 1) + [1 − A(x, y)]P(x − 1, y). From this equation and the conditions that P(x, 0) = 1 and P(0, y) = 0, P(x, y) can be given in terms of A. Lanchester's Linear Law governs the case that A(x, y) is a constant, p, and his Square Law governs the case that A(x, y) = rx(rx + y), where r is the ratio of the relative effectiveness of a member of the first force to that for a member of the second force. The exact solution of the problem of finding P(x, y) is given for both the linear law and the square law. The exact solution is cumbersome, however, and useful approximations to the exact solutions are also given in terms of the normal probability integral.