bluuebunny/crossref_metadata_2025 huggingface dataset:
Duality in Discrete Programming: II. The Quadratic Case
Authors: Balas Egon
Published: November 2008

This paper extends the results of “Duality in Discrete Programming” [1] to the case of quadratic objective functions. The paper is, however, self-contained. A pair of symmetric dual quadratic programs is generalized by constraining some of the variables to belong to arbitrary sets of real numbers. Quadratic all-integer and mixed-integer programs are special cases of these problems. The resulting primal problem is shown, subject to a qualification, to have an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. The dual of a mixed-integer quadratic program can be formulated as a minimax problem whose quadratic objective function is linear in the integer-constrained variables, and whose linear constraint set does not contain the latter. Based on this approach an algorithm is developed for solving integer and mixed-integer quadratic programs.
A Branch-and-Bound Algorithm for Multi-Level Fixed-Charge Problems
Authors: Jones Arnold P. , Soland Richard M.
Published: November 2008

Multi-level fixed-charge problems are mathematical optimization problems in which the separable portion of the objective function is the sum of piecewise continuous functions of a single variable. This paper describes a branch-and-bound algorithm that will find a global solution to this type of problem. The algorithm has the feature that a good feasible solution is generated at the start. Moreover, at each step of the algorithm an additional feasible solution may be generated for comparison with the best solution found previously.
Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach
Authors: Pritsker A. Alan B. , Waiters Lawrence J. , Wolfe Philip M.
Published: November 2008

A zero-one (0-1) linear programming formulation of multiproject and job-shop scheduling problems is presented that is more general and computationally tractable than other known formulations. It can accommodate a wide range of real-world situations including multiple resource constraints, due dates, job splitting, resource, substitutability, and concurrency and nonconcurrency of job performance requirements. Three possible objective functions are discussed; minimizing total throughput time for all projects: minimizing the time by which all projects are completed (i.e., minimizing makespan); and minimizing total lateness or lateness penalty for all projects.
Analysis of Factors Affecting Least-Cost Size of Plant
Authors: Babb E. M. , Yu T. H.
Published: November 2008

A general model used to analyze the effects of assembly and distribution factors and economies of scale in processing on least-cost size of plant and on cost components is described. This model is applied to empirical data from fluid milk plants and country elevators. In both cases, it appears that total per unit cost (combined assembly, processing and distribution cost) is a continuously falling function of plant size, at least to the limit of observed plant sizes. In the two cases studied, the larger plants observed appeared to have from 20 to 30 percent lower cost than plants of average size. The results of these two applications indicate the basis for much of the current consolidation of plants.
Multi-Item Production Planning—An Extension of the HMMS Rules
Authors: Bergstrom Gary L. , Smith Barnard E.
Published: November 2008

The Linear Decision Rules (LDR) proposed by Holt, Modigliani, Muth, and Simon for the production planning problem determine an optimum plan in terms of an aggregate production rate and work force level. The criteria of the LDR assume we wish to make decisions so as to minimize costs over a specified time horizon, given estimates of future aggregate demand. This paper extends the LDR to a multi-item formulation (MDR) which solves directly for the optimum sales, production, and inventory levels for individual items in future periods.

To remove the restriction of specified demand, revenue curves are estimated for each item in each time period. The MDR model then seeks a solution to maximize profit for the firm over the time horizon by an application in a firm producing a line of electric motors. The results of the MDR are compared to management's proposed plan and some important differences are detected.
An Exploratory Analysis of Individual Information Processing
Authors: Cravens David W.
Published: November 2008

Information-processing is an integral part of decision-making; yet the state of knowledge concerning the individual problem solver in his role as an information-processor is limited. This paper presents a conceptual framework for examining individual, task-oriented information-processing as a multi-stage process. Relationships between variables in the model are investigated at a research site which provides a number of the advantages of both a laboratory and a field environment. The “information element” is used as the basic unit of analysis. Data are examined via the multivariate statistical technique of canonical analysis. The implications of the study are also discussed.
Elements of Large Scale Mathematical Programming Part II: Synthesis of Algorithms and Bibliography
Authors: Geoffrion Arthur M.
Published: November 2008

The problem manipulations and solution strategies of Part I of this paper are now further illustrated by combining them in various ways to yield several known algorithms. The main object is not an exposition of these algorithms, although this is certainly important; rather, we wish to focus on the principal patterns in which manipulations and strategies can be assembled. These patterns constitute the real common denominators in the literature on large-scale programming. See Table 2 in Part I.
An Analysis of Private and Public Sector Location Models
Authors: Revelle Charles , Marks David , Liebman Jon C.
Published: November 2008

Recent models of location are drawn together and compared as to structure, criteria, and constraints. Private sector models are distinguished as those in which the total cost of transport and facilities is isolated as the objective to be minimized. The solution techniques of six such models are discussed. Public sector models are characterized by a criterion function involving a surrogate for social utility and by a constraint on investment in facilities or on the number of facilities. Five models with this format are discussed and compared. The two types of problem, location in the private sector and location in the public sector, are seen to have the same conceptual foundation, but formats which differ of necessity due to our inability to relate social utility to dollar value.
Dissection Methods for Solutions in Chance Constrained Programming Problems Under Discrete Distributions
Authors: Raike William M.
Published: November 2008

Under the assumption of discrete distributions for the random variables involved, deterministic equivalent problems are derived for a general class of chance constrained (but not necessarily linear) programming problems. These permit the explicit solution of such problems for all or most types of optimal stochastic decision rules which are of interest, including optimal multistage rules and not restricted to the class of linear rules. The formulation given encompasses certain cases of stochastic programming with recourse, and the deterministic equivalents derived for these reduce to well-known versions available in the literature.
An Approximation of the Cost Function for Multi-Echelon Inventory Model
Authors: Hochstaedter Dieter
Published: November 2008

For an inventory model with a central warehouse that supplies two satellite warehouses an approximation of the cost function by upper and lower bounds is presented under the assumption that the satellites follow (s, S) policies that are optimal for the satellites alone. The difference between these upper and lower bounds for each period is less than a fixed number. In the infinite horizon model with a discount rate less than one this difference is less than a constant that depends on the mean of the demands, the holding, and the penalty costs. The results are shown for two satellites, they can easily be generalized to k satellites.
Précis—Sufficiency Conditions for Constrained Optima
Authors: Huang C. C. , Erickson L. G. , Wellek R. M.
Published: November 2008

The sufficiency conditions for constrained optimization problems are derived through an alternate approach and result in a simpler form than one latest work [Schechter, R. S., G. S. G. Beveridge. 1966. Sufficiency conditions in constrained variations. Indus. Eng. Chemistry Fundamentals 5 571–573.]. The relations can be used with equality and/or inequality constraints. The sufficiency conditions of Phipps [Phipps, C. G. 1952. Maxima and minima under restraint. Amer. Math. Monthly 59 230–235.] which have been quoted for years in the literature were corrected in this work.
Free For All
Authors: Fromm Erich
Published: November 2008

—Editorial by Erich Fromm, National University of Mexico
An Introduction to Some Papers on Urban Planning, Information, Goals and Implementation
Authors: Cooper W. W.
Published: November 2008

The papers which follow have been assembled from two sources: the ones by Dr. Branch and by Professors Eastman and Kortanek were submissions to Management Science; the others formed one part of a program organized by Ezra Glaser for the American Association for the Advancement of Science's 1969 meetings in Boston. As vice president for AAAS' statistics section, Mr. Glaser had organized an all-day session on “Statistics, Governments and the Analysis of Social Problems.”
Delusions and Diffusions of City Planning in the United States
Authors: Branch Melville C.
Published: November 2008

A number of concepts and conditions in current city planning are questioned: the grand master plan delusion; planning after the fact; intermittent master planning; the illusion of complete study; avoiding the critical problems; trying to do everything; sematic confusion; conflicts of role and organization; unrealistic derivation of goals and objectives; failure of city planning in the general public interest; deficiencies of planning personnel; inadequacies of theory and research; underestimating fundamental difficulties of the city planning endeavor.
A New Approach: To an Urban Information Process
Authors: Eastman Charles , Johnson Norman J. , Kortanek Kenneth
Published: November 2008

This paper outlines a proposed method for gaining continuous information about the activities, attitudes, and concerns of citizens within an urban community. The method provides quick feedback on actions and changes made within the community. It monitors longitudinally, the effects of actions and changes on the population.

The approach is derived from marketing panel surveys. It utilizes neighborhood personnel. The organizational aspects of such an enterprise are emphasized, a basic objective being to guarantee the availability of better information to citizen groups as well as public officials. Possible uses of the data collected from such a reporting system are outlined, along with possible modeling efforts and methods of community distribution and utilization. The ultimate goal is the wielding of an effective interface between competing decision-making centers as these wrestle with the major problem of confronting the urban community—uncertainty.
Measuring Progress Towards Social Goals: Some Possibilities at National and Local Levels
Authors: Terleckyj Nestor E.
Published: November 2008

The need for progress in measuring social change is evident. Without measurement it is improbable that desirable goals can be reached. Yet, in contrast to a few exceptionally advanced fields, most areas of social concern and public policy suffer from lack of even the most elementary information, leaving the field wide open for guessing, emotion, low-grade politics, and waste, while the problems remain. Considerable progress is feasible, however. The existing information can be organized and provided regularly, and serious work can be initiated to develop information now missing altogether, improve existing information, and develop workable ways for communicating data.

This paper, drawn from the experience of an on-going project, deals with the measurement of social goals. Indicators can be identified which reflect reasonably well critical aspects of some of the most important objectives not only of individuals and families but also of local, state, and federal governments. About 20 such indicators were selected including life-expectancy at birth and the number of persons with chronic disabilities as the indicators reflecting the health goals, the rate of violent crimes as the measure of public safety, the number of persons in poverty and in near-poverty as indicative of concerns with equity, etc. Most of this information had to be pieced together. The existing statistical systems are not geared to provide it. Big gape exist. For many concerns, e.g., quality of the physical environment, where the concepts for measurement can be specified the data do not exist. In still other fields, e.g., “leisure” or discretionary time, even the conceptual work remains to be done. Very useful local information systems describing many important aspects of social change can be put together with the information now in existence without much trouble. More complete reporting systems, and systems aimed at assessment of possibilities for future changes require much additional basic and development work.
The Impact of Cybernetic Information Technology on Management Value Systems
Authors: Ericson Richard F.
Published: November 2008

The first three sections of the paper are background discussions of relevant types of value questions. First, we consider the historical evolution of managerial value conflict, as they are rooted in a fundamental value polarisation reflected in U. S. society. Then we relate management values to environmental values, especially in the corporate context. Finally, we review contemporary analyses of the bases of general value systems, and consider their relationship to current research in management value systems.

The fourth section is concerned with the other prong of our general analysis: After reviewing several examples of cybernetic system models, we consider their relevance for management systems in terms of the apparent future organizational impacts of the so-called “information technology.”

Section five brings us to the heart of our discussion: an estimation of the likely impacts of better understanding of organisational cybernetics upon management value systems. A paradigm of ecosystem (ecological system) influence upon organizational policy formation is presented, together with a schematic organizational ecosystem decision matrix for management.

In the final section of the paper, we relate corporate values to the emerging organizational ecosphere, emphasizing that cybernetic information technology creates new possibilities effectively to implement appropriate redefinitions of traditional management values.
An Unequal-Period Model for Cash Management Decisions
Authors: Orgler Yair E.
Published: November 2008

A lack of synchronization between cash inflows and outflows presents the problem of investing positive net flows and financing negative net flows. In addition to the basic investment-financing issue there are other interrelated problems such as the payment schedule and the minimal cash balance that directly affect cash management decisions. Previous attempts to solve these problems have imposed constraints that limit their application. The purpose of this study is to develop an applicable method for solving the cash management problem by deriving a linear programming model that is divided into unequal periods. The unequal time division maintains the day-to-day aspect of the problem while reducing the number of periods and variables to a manageable size. Decision variables are divided into four groups: the payment schedule, securities transactions, short-term financing, and the cash balance. The model determines the optimal values of these variables subject to institutional constraints and within a framework of managerial risk preferences that are expressed as subjective constraints and subsequently evaluated by the dual model. Although a certainty assumption is made, inputs are analysed by sensitivity analysis and the dual model, while the effects of uncertainty are further reduced by the unequal time structure of the model. Tests of the model indicate that it is both profitable and generally applicable by most business firms.
Information Processing and Programmed Decision Systems
Authors: Kriebel Charles H.
Published: November 2008

The capacity to evaluate decisions and information within a unified analytical model of the firm is at best a complex task. Even if, for the sake of simplicity, we ignore the effects of human behavior within organizations, most research on information processing design and evaluation has sought simulation in lieu of an explicit mathematical model.

The purpose of this discussion is to suggest some practical extensions of the decision theory model for the design of management information processing systems and to illustrate these ideas through the detailed analysis of an aggregate planning problem.
On Optimum Stochastic Allocation
Authors: Klinger Allen
Published: November 2008

Analytic results involving the optimum return and strategy functions of an inventory allocation problem are presented. The problem requires that a number of randomly functioning units be apportioned among randomly many points to maximize the probability that at least one unit functions at each point. The maximum probability function has been shown often, but not always, to be a monotonic non-increasing function of the number of units. When it is monotonic nonincreasing, it is proven here that the ratio improvement of maximum probability is a decreasing function of the number of units. When the ratio is only nonincreasing, it is proven1 here that the strategy is a monotonic nonincreasing function of the number of units. The theoretical results relate to the management use of increment and ratio measures of effectiveness and to properties of the optimum allocation strategy.
Optimal Production, Investment, Advertising, and Price Controls for the Dynamic Monopoly Firm
Authors: Thompson Russell G. , Proctor Michael S.
Published: November 2008

In this paper, a dynamic continuous time model, encompassing operations, investments, output prices, informative advertising, and brand advertising, is formulated as an optimal control problem in an activity analysis context. In the model, the objective of the firm is to maximise, subject to various constraints, the discounted value of accumulated savings over the finite decision-making interval plus the discounted value of capacity at the end of the interval. The state variables are capacity, goodwill of type 1 reflecting informative advertising, goodwill of type 2 reflecting brand advertising, net debt, and the output price. The controls are the scale of operation, the purchase of new capacity, informative advertising, brand advertising, and the rate of change of the output price. Final capacity, goodwill of types 1 and 2, net debt, and price are control parameters. There are several inequality constraints.

Using results in control theory, the optimal controls are completely characterized. These results are interpreted using the properties of the Value Equation. In addition, the control problem is transformed into an approximate programming problem.
A Queueing Process with Some Discrimination
Authors: Scott Meckinley
Published: November 2008

This paper deals with the analysis of a queueing process involving two classes of customers where the arrival mechanism of each class is subject to a particular control doctrine based on the queue length. Expressions are obtained for the equilibrium distribution of the queue length, the expected queue length and other characteristics which measure the effectiveness of the control doctrine.
Computational Analysis of Scoring Models for R and D Project Selection
Authors: Moore John R. , Baker Norman R.
Published: November 2008

Several authors have proposed using scoring models for prescriptive analysis of the R and D project selection decision problem. This research indicates that these models do not meet with important practical requirements. For example, many authors recommend a multiplicative index, over an additive index, in order to generate a wide range of project scores. The additive index is shown to have important advantages over the multiplicative index. The most serious shortcoming in the models, however, is the relatively arbitrary fashion in which the models have been constructed and the failure of the model builders to recognize the impact of certain structural considerations on resulting project scores. Comparative analyses relating project rankings produced by scoring models to rankings produced by a profitability index and by a linear programming model demonstrate that the performance of a scoring model is highly sensitive to decisions made during the development of the model. Considerations such as (1) the underlying distributions of project data, (2) time preferences, (3) the number of ranking intervals or categories, and (4) the width of the intervals, all have important implications for final project scores and associated rankings.
A Fractile Approach to Linear Programming Under Risk
Authors: Sengupta J. K. , Portillo-Campbell J. H.
Published: November 2008

The implications of a fractile approach to linear programming under risk through maximizing a given fractile of the distribution of profits under linear programming restrictions are examined here both theoretically, computationally and empirically.
Symmetric Mathematical Programs
Authors: Greenberg Harvey J. , Pierskalla William P.
Published: November 2008

Mathematical programs with S-convex and with symmetric objective and feasibility regions are investigated. Optimal solutions and algorithms are presented for both continuous and discrete optimization problems.
A Decomposition Method for Interval Linear Programming
Authors: Ben-Israel Adi , Robers Philip D.
Published: November 2008

An interval linear program is [Formula: see text] where the matrix A, vectors b−, b+, and c are given. If A has full row rank, the optimal solutions of (IP) can be written explicitly (A. Ben-Israel and A. Charnes: “An explicit solution of a special class of linear programming problems,” Operations Research 16 (1968), 1166–1175). This result is used in conjunction with the Danteig-Wolfe decomposition principle to develop a finite iterative technique for solving the general (IP). Since any bounded linear program may be cast in form (IP) the technique may also be considered as an alternative method for linear programming.
Real-Time Information Systems: A Comparative Economic Analysis
Authors: Zani William M.
Published: November 2008

There are several generally accepted suppositions concerning the cost and benefits of real-time information systems. These suppositions expect that real-time systems can generate sufficient benefits to offset the higher costs of processing relative to traditional batch processing systems. The objective of this study was to examine in actual operating environments the generally accepted notions of costs and benefits of real-time systems that were supplied by a computer utility. These suppositions were examined by analyzing the empirical data of six matched firms. The cost and benefits of the information systems of three companies which used a computer utility real-time system were compared to the costs and benefits of three similar companies which used private batch processing systems. The findings of the research were the reverse of expectations. The data analysis strongly suggested that the real-time information did not produce any significant information benefits, but that the real-time data processing costs were less than the comparative batch data processing costs. The primary reason the results differed from expectations is that the real-time information was not fruitfully used. The findings of the study suggest that real-time information system benefits are not gained automatically, but can be achieved only if the systems are meaningfully integrated into the management process.
Effect of Three Voting Rules on Resource Allocation Decisions
Authors: Birnberg Jacob G. , Pondy Louis R. , Davis C. Lee
Published: November 2008

This paper is concerned with the effect of the voting rule adopted by a capital budgeting committee on the allocation of resources among divisions. The results of a laboratory experiment indicate that different voting rules have different characteristics measured in terms of the size of the total budget allocation made and the inter division variability. In addition, an attempt is made to ascertain the techniques followed within the groups to reach a decision. None of the four models offered provides an adequate explanation of the observed behavior. However, a mixed model consisting of two of the approaches does provide a reasonable explanation for the observed behavior.
Models of Fact: Examples from Marketing
Authors: Ehrenberg A. S. C.
Published: November 2008

The first step in model-building is to note some simple observable patterns and to establish their degree of empirical generalisation. The second step is to integrate different empirical relationships of this kind. This is where the more complex mathematical models come in.

Two examples of model-building in marketing are discussed and the empirical approach is contrasted with the prevalent tendency either to try to develop mathematical models without any prior empirical knowledge (“sonking”), or to search for statistical significance as an end in itself. The basic question in model-building remains as follows:

Take away the mathematical language and what generalised factual knowledge of the process in question still remains? If the answer is none, the mathematical symbol for that is very simple.
Generalization of Dilworth's Theorem on Minimal Chain Decomposition
Authors: Raghavachari M. , Mote V. L.
Published: November 2008

The decomposition of a finite partially ordered set of elements as a union of chains was considered by Dilworth [2]. Dantzig and Hoffman [1] formulated this problem as a linear programming problem and obtained Dilworth's theorem from duality theory. For some practical applications and for a method to obtain a minimal decomposition see Ford and Fulkerson [3]. In this paper we generalize this problem to the case when the set is not necessarily partially ordered and obtain a method of finding a minimal chain decomposition of the set.
Optimal Political Districting by Implicit Enumeration Techniques
Authors: Garfinkel R. S. , Nemhauser G. L.
Published: November 2008

An algorithm is given which finds all optimal solutions, for a given set of criteria, to political redistricting problems. Using “population units” as indivisible elements, the first phase generates all feasible districts, where feasibility indicates contiguity, compactness and limited population deviation. The second phase finds that set of M feasible districts which “covers” each population unit exactly once, and minimizes the maximum deviation of any district population from the mean district population. Computational results indicate that states with 40 counties or fewer can be solved in less than 10 minutes on an IBM 7094. However, our attempt to solve a 55 county state was unsuccessful.
A Simulation Model for Harvest Operations under Stochastic Conditions
Authors: Sorensen Eric E. , Gilheany James F.
Published: November 2008

The scheduled allocation of resources for large-scale harvesting operations is vulnerable to delays caused by variables of a stochastic nature such as rainfall and equipment breakdown. A computer simulation model was developed to test the merits of different harvesting strategies and decision rules on a sugar cane plantation. The model takes into account weather, hauling, equipment logistics, and equipment breakdowns. For a given man-machine harvest strategy and harvest schedule, it will simulate assigning harvest units (men and equipment) to fields, harvesting the cane, hauling the cane to mills, and milling. Submodels, based on a statistical analysis of historical data, generate values of simulated daily rain in each field, equipment breakdown, and repair times. Harvesting delays occur when the simulated rain reaches critical values. The hauling and milling capacity in the model depends to a great extent on both current and previous rainfall and is updated when required for new field conditions brought about by rain. The model keeps account of each cane-hauler round trip (some 50,000 trips a year) from field to mill, causes the haulers to queue when the loader or unloader is busy, and sends them to a repair shop when damaged. Simulated work hours and labor practices are also included in the model. For example, a submodel calls for overtime when progress indicates that the harvest may extend into the rainy season. The model gives periodic reports on the simulated production and information on capacity requirements for many of the tasks within the harvest operation.
Communication to the Editor—Is the “Diet Problem” Identical to the “Menu Planning Problem”?
Authors: Eckstein Eleanor
Published: November 2008

Although the “diet problem” for animals and humans is similar in basic formulation, psychological parameters relating to monotony and production factors complicate the model for the human diet. The “diet problem” differs from the “menu planning problem” in (1) simplicity of the problem, (2) complete definition of the relevant parameters, and (3) availability of accurate, complete, and reliable data. For these reasons the designation “diet probem” should be restricted to linear programming methods applied in animal feed blending; textbook examples should use feedstuffs for illustration. The term “menu planning problem” should refer to methods for planning menus for the human diet, including the related psychological parameters and production factors, but should not include projects in data collection or the peripheral problems of menu control.
Minimax Optimization of Unimodal Functions by Variable Block Search
Authors: Beamer John H. , Wilde D. J.
Published: November 2008

A minimax search plan is developed for locating the maximum of a one dimensional unimodal function using a sequence of blocks of simultaneous function evaluations. Any number of evaluations can be made in each block, generalizing a previously developed constant block plan based on the Avriel numbers [1, 5]. A new set of numbers is produced, containing the Avriel numbers as a subset and filling the large gaps between consecutive Avriel numbers. This enables the selection of a search strategy more closely meeting the desired reduction ratio, reducing the number of experiments required by as much as 50% compared to constant block search. The proposed search strategy is optimal in the sense that for a required final interval of uncertainty, known to contain the point where the function obtains its maximum, and for given values for the number of experiments in each block, it has the largest possible starting interval. A plan for determining the optimal number of experiments per block is given. A discrete variable version of the search plan is also described.
Game Theoretic Analysis of a Problem of Government of People
Authors: Chidambaram T. S.
Published: November 2008

The general problem of control of a set of individuals to achieve the objective of a controller is common to many areas such as business and government. This paper attempts a mathematical formulation and analysis of such problems. It is assumed that each individual is a rational being acting in his own self-interest. The interests of different individuals are, in general, conflicting, thus leading to a competitive situation which can be analyzed using Game Theory notions. An important aim of mathematical analysis of such a situation will be to study the effectiveness of various kinds of power that a controller might have over the individuals. Most of the results in this paper are concerning a class of “coordination problems” where the controller's objective is to maximize the total utility to the whole group of individuals and where competition arises due to constraints on strategies. The analysis indicates that in such cases the simple power to accept or reject strategies which violate the constraints may be sufficient to realize the controller's goals.
Jointly Optimal Deterministic Inventory and Replacement Policies
Authors: Falkner Charles H.
Published: November 2008

A deterministic, continuous time, nonstationary inventory and replacement system model is formulated to find the number of orders, the order quantities, the times at which orders should be placed, and the replacement intervals which minimize the cost of operating, maintaining, and replacing a piece of equipment over a finite time horizon. Conditions are given for when the optimal policy is to buy equipments only when the last inventoried item is ready for replacement. A dynamic programming algorithm is presented for solving this problem. The structure of optimal policies is examined for the stationary case. Finally a computational procedure is given for solving the stationary, infinite horizon case.
Note—The Distribution Problem with Upper and Lower Bounds on the Node Requirements
Authors: Charnes A. , Klingman Darwin
Published: November 2008

This paper considers a distribution model with upper and lower bounds on the number of units shipped from an origin or to a destination. Our problem differs from the classical distribution model in which the node shipping amounts are, by contrast, specified exactly. This generalization of the classical distribution problem not only makes the model more versatile from a theoretical standpoint but also makes the model more usable from an applications viewpoint.
The Theory of Networks and Management Science. Part I
Authors: Elmaghraby Salah E.
Published: November 2008

An expository treatment of three network models most often encountered in Management Science applications: (i) The Shortest Path Problems, (ii) Flow Networks, and (iii) Activity Networks.

In the first problem are discussed the shortest path between two specified nodes; the shortest distance matrix; as well as the special case of directed acyclic networks. In the second problem, a brief exposition of the “labeling procedure” leads into multiterminal networks and the general minimal cost circulation problem and a discussion of the “out-of-kilter” method. In the third problem, the “classical” models of CPM and PERT are reviewed, together with a discussion of generalized activity networks and the viewing of GERT as a signal flow graph of a semi-Markov process. Illustrations of the application of each model are also given. The first two models appear in the September issue; and the third model in the October issue of Management Science.
A Process Analysis Model of the U.S. Steel Industry
Authors: Tsao C. S. , Day R. H.
Published: November 2008

In this paper a process analysis model of production in the U.S. Steel Industry is developed and tested. A technology matrix, which represents recent industry input-output structure, is estimated using engineering and metallurgical information. This matrix together with detailed cost, sales and resource capacity data is then used in a linear programming model of short-run resource allocation for the industry as a whole. Linear programming solutions are obtained and compared with available industry statistics for each year in the period 1955–1968. Theil's U statistic is computed to indicate how well the model performs. We conclude that it performs “fairly well” and that it should prove useful in various economic applications.
Problem Solving with Ordinal Measurement
Authors: Bartee Edwin M.
Published: November 2008

Modern socio-political-economic problems often represent situations in which the traditional numerical problem models fall far short of being adequate for determining formal solutions. The basic reason for this inadequacy is the fact that the objective functions in such problems contain abstract criteria. It, therefore, is difficult, if not impossible, to determine how much one alternative in the problem is preferred to another alternative. When such information is not available in a problem, a numerical model will serve to fabricate this information and, therefore, reduce the degree of isomorphism between the problem and the problem model.

A linear program that uses a relations set as its objective function can maintain isomorphism. In such models, the single optimal solution may not be determinable. However, if the set of feasible solutions is ordered, the optimal solution can be determined. The same ordered approach also has some useful applications to games.
A Communication Model of Dialectical Inquiring Systems—A Strategy for Strategic Planning
Authors: Mitroff Ian I.
Published: November 2008

Using Bayesian probability theory and Ackoff's Behayorial Theory of Communication, a mathematical model of the Hegelian Dialectical Inquirer is developed. The model strongly argues against the widely held and naive distinction between “fact” and “theory.” The model strongly argues for a new way of treating statistical data, in a sense, for a “new” theory of statistics. A fundamental principle of the Hegelian Inquirer is formalized, i.e., that one only stands to understand any issue by witnessing the strongest possible kind of debate take place on that issue. The model suggested is one that is seen as especially suited to issues involved in Strategic Planning.
Optimal Management of a Research and Development Project
Authors: Lucas Robert E.
Published: November 2008

This paper offers a series of models designed to aid in the evaluation and control of an individual research and development project. The project under consideration is assumed to involve costs incurred over a period [0, T] and a return earned at T (or discounted to T) when the project is completed. In two of the models discussed below, the completion time T is regarded as known; in two others, T is taken to be a random variable with a known distribution. In two models, the costs per unit of time of operating the project are assumed to be fixed; in the other two, costs are variable, with increased expenditure resulting in a decreased completion time. Each of the four possible combinations of assumptions is treated in a separate section. The last section contains a summary and discussion of results.
A Statistical Theory for Pert in Which Completion Times of Activities are Inter-Dependent
Authors: Ringer Larry J.
Published: November 2008

This paper presents a method for taking into account dependency among certain activities in PERT networks. The method presented can be used with the reduction algorithm presented by Hartley and Wortham [Hartley, H. O., Wortham, A. W., A statistical theory for PERT critical path analysis. Management Science, Vol. 12 No. 10 (June 1966), pp. B-469–B-481.]. The addition of dependency among the completion times for certain types of activities should be a valuable aid in sensitivity analyses of PERT networks.
Equipment Replacement Under Uncertainty
Authors: Meyer Robert A.
Published: November 2008

This paper will present a model of equipment replacement in a stochastic environment utilizing a number of the component characteristics of an operations research orientation while being designed to emphasize the role of a stochastic representation of technological change and/or maintenance costs and the implications these have for the decision about replacement of equipment. The “replacement” referred to here is replacement of a machine in its entirety rather than the usual periodic-review-replacement-of-individual-pieces analysis to which the term “replacement” frequently refers in operations research literature. The paper outlines the approaches to equipment replacement in the literature of economics and the well-known Terborgh model and then introduces a stochastic model for studying certain aspects of equipment replacement together with the form of its analytic solution. A comparison of the cost implications of the Terborgh and stochastic model is presented for a specific example utilizing motor vehicle data. In addition, a general analytic comparison of the two replacement rules is provided.
Optimal Sale of a Commodity Stockpile (Errata)
Authors: Kupperman Robert H. , Smith Harvey A.
Published: November 2008

We wish to thank Henry Peskin for pointing out misprints in line 18, p. 756 of the above titled paper, which appeared in the July 1970 issue of Management Science.
Optimal Bluffing Strategies in Poker
Authors: Friedman Lawrence
Published: November 2008

Bluffing in poker is examined as a problem in game theory. A very common situation occurs where the “kitty” contains K, player B has the apparent high hand, and player A has an apparent probability, P, of having a better hand than B, and considers a bluff. Under these conditions it can be shown that A should raise 1 unit with probability (1/(1 + K))(P/(1 − P)) · B, in turn, should call A's potential bluff with probability K/(1 + K). This says that in pot limit poker, if the potential bluffer has the appearance of having the winning hand with probability 0.25, he should bluff 1/2 · 1/3 = 1/6 of the time. The optimal strategy is to call a potential bluffing hand half the time.
Utility Theory Applied to Multivariable System Effectiveness Evaluation
Authors: Turban Efraim , Metersky Morton L.
Published: November 2008

In this paper, utility and decision theories are applied to determine the effectiveness of a complex system with several measures of performance. A significant number of individuals, both systems analysts and operational personnel in the NADC and related organizations, were asked to rank the measures of performance according to their importance and to assign utility indices to each. Churchman and Ackoff's method for checking the consistency of the ranking has been modified and applied to the study. The evaluations of the individual judges were then adjusted, and the estimates of all judges were combined to form an overall utility index (measure of performance). The “Coefficient of Concordance” test was employed to measure the degree of agreement among the judges. The weighted overall measure of performance is used to evaluate proposed courses of action and to establish stopping rules for a simulation study.
Preface to Some Papers on Educational Issues in the Management Sciences and Operations Research
Authors: Churchman C. West
Published: November 2008

In an era where many curricula are being examined for their relevance, it seems appropriate to explore the fundamental purpose of the graduate programs in management science. A letter was sent to a sample of educators asking for their statement that would be published in Management Science.
The Product-Mix Problem under Stochastic Seasonal Demand
Authors: Hodges S. D. , Moore P. G.
Published: November 2008

The product-mix problem of production planning is to determine the best quantity of each product to manufacture, over a complete range of products competing for a number of limited resources. This paper examines the problem when uncertainty of demand is a major factor, making any differences between the penalties of over- and under-production important. In these circumstances the basic linear programming technique is insufficient, and a model has been developed as a multi-item newsboy problem in which a number of linear resource constraints affect the decision variables.

The formulation is one of linear programming under uncertainty. A marginal analysis approach is used to obtain a detailed insight into the structure of the solution and to develop an effective computational procedure. Very little additional data is required, beyond that needed for a conventional linear program.
Information Systems in Management Science: Management Information System—What It Is and Why?
Authors: Stern Harry
Published: November 2008

The topic, “A Management Information System—What It is and Why” was suggested by work that I did recently in preparation for the German symposium, “MIS—A Challenge to Scientific Research.” In reviewing my own ideas about management information, I keep coming back to one primary thought, that the only value that information has to management is to allow better decisions to be made.
Comments on Graduate Education in the Management Sciences
Authors: Hare Van Court
Published: November 2008

Comments on graduate education in management sciences reflecting opinions at the University of Massachusetts.
Management Science Education: Nature and Nurture
Authors: Howard Ronald A.
Published: November 2008

I have earlier commented on the need for practicality in management science education. Here I would like to emphasize the form of the educational program and the personal characteristics of those who complete it successfully.

The crucial problem in education would seem to be the development of individuals who have the intellectual curiosity and competence of our best research students and yet retain the pragmatism, perception, and judgment of our best practitioners. I believe that one answer to this problem is a Ph.D. level professional program that combines a unified view of theory with the opportunity to test the theory in practice. I believe further that the key to integration is the utilization of a new language for decision processes founded on decision theory and systems analysis—the language of decision analysis.
Management Science Education
Authors: Thrall Robert M.
Published: November 2008

In this brief comment on education and management science I will focus my attention on what the universities should provide, recognizing (1) that this is only one part of a management scientist's education and (2) that not all management scientists fit into a single mold.

In general the universities seem to be doing excellently in teaching the basic mathematical skills. They have developed courses covering all phases of mathematical programming, statistics, and stochastic processes. They are doing increasingly well in offering computer science courses relevant to management science (e.g. simulation, file manipulation). By contrast, truly relevant courses in the behavioral sciences seem to be much less well developed as are courses centered on the philosophy and practice of management science and operations research.
Operations Research as a Profession
Authors: Churchman C. West
Published: November 2008

This paper is concerned with the profession of operations research and specifically with the preparation for the profession. On a fairly general plain, the paper expresses a concern about the future of a profession which ought to be in the lead in the growing societal anxiety over poverty, pollution and privacy, but in fact plays virtually no significant role in these matters.

In his autobiography, Memories, Dreams, Reflections, C. G. Jung argues for a fascinating way of telling the story of one's life. There are, he says, two stories. One story is the rational, a story of a man's struggles, frustrations and joys in seeking his life's goals. The other is the “irrational,” the primitive often unexpressed mythic elements of his life. At some risk of perverting the richness of Jung's suggestion, I'd like to tell two stories of a profession, operations research, but in the end I'll not be sure which is the rational.

The reason for telling these two stories is to obtain a critical overview of the profession of operations research, primarily to assess its educational base, not just in colleges and universities, but in the overall program of learning: in meetings, journals and informal discussions.