bluuebunny/crossref_metadata_2025 huggingface dataset:
Note—On Madigan's Approach to the Deterministic Multi-Product Production and Inventory Problem
Authors: Baker Kenneth R.
Published: November 2008

The deterministic multi-product single-machine production and inventory problem is one of the simplest models in which production and inventory factors interact. There is at present no algorithm available which solves the problem optimally, and several different types of approaches have been presented in the literature. Madigan's heuristic method [Madigan, J. G. 1968. Scheduling a multi-product single machine system for an infinite planning period. Management Sci. 14(11, July) 713–719.] avoided some of the drawbacks characteristic of other methods, but there are some errors and limitations in his original presentation, to which this note is addressed.
A Production Scheduling Model by Bivalent Linear Programming
Authors: Haehling von Lanzenauer Christoph
Published: November 2008

The paper focuses on multi-stage production systems. If such a system is of the more general type than a production line and many products have to be manufactured according to different technological sequence restrictions then two problems arise: (1) scheduling and (2) sequencing. The formulation of that problem requires the simultaneous consideration of the scheduling and sequencing aspect. The paper integrates these two functions into one single model using zero-one programming.
A Generalized Model of Administrative Decisions: An Experimental Test
Authors: Dickson Gary W.
Published: November 2008

A model intended to predict decisions made from among alternatives having fixed characteristics is hypothesized and the experimental procedure used to test the model and the results of testing the model are presented. The model, which is based upon decision segmentation and disutility minimization, was tested in the framework of vendor selection decisions. The results indicate that the model was able to predict the vendor selections of the purchasing agent-subjects with a high degree of accuracy.
Smoothing Start-Up and Shut-Down Costs: Concave Case
Authors: Sobel Matthew J.
Published: November 2008

We consider nonstationary deterministic production smoothing problems with coats for starting and halting production. Inventory holding costs and production costs are assumed to be concave. The algorithms developed for optimal policies exploit known features of the economic lot size problem.
The Effectiveness of the Cognitive-Style Constraint in Implementing Operations Research Proposals
Authors: Huysmans Jan H. B. M.
Published: November 2008

This paper describes a laboratory experiment designed to test the impact of cognitive style differences between operations researcher and manager on the managerial implementation of operations research recommendations. Three hypotheses are presented and the results of their testing in the experiment are discussed.
Compensation of School District Personnel
Authors: Bruno James E.
Published: November 2008

Recently considerable attention has been focused on the inadequacy of presently used methods of compensating school district personnel. The increasing incidence of teacher strikes in many school districts has established the need for an effective alternative to the inherent rigidity of the commonly used fixed step salary schedule. The purpose of this study is to propose one such alternative that is based upon mathematical programming techniques. In this study a salary evaluation model was derived then applied to a school district. Salary schedules were derived which (1) were consistent with both the imposed hierarchical and budgetary constraints, (2) considered ten factors in the salary evaluation, and (3) reflected established school district priorities and objectives. This latter feature was accomplished by solving the model with various objective functions.
Behavioral Externalities in Decentralized Organizations
Authors: Ruefli Timothy W.
Published: November 2008

A number of analytic formulations of resource allocation activities in decentralized organizations have considered the effects of economic or technological externalities but most treatments have neglected concomitant organizational or behavioral effects. This paper introduces the concept of a behavioral externality and relates it to the decision-making process in decentralized organizations. Alternative analytic formulations of behavioral externalities are examined, and a numerical example is presented.
A Suggested Behavioral Approach to Cost-Benefit Analysis
Authors: Spier Leo
Published: November 2008

Whenever problems arise from differences of opinion, there probably exists a lack of understanding of the behavioral situations that contributed to the problems. In his interaction with others, man passes from a level of ignorance to one of awareness and seldom reaches a level of understanding. Without that understanding, however, there is no common premise for resolving problems either with regard to methods or results. Today's executive faces issues that deal not only with the familiar technical business decisions but, more significantly, with related labor, social and environmental responsibilities, and political implications both at home and abroad. Consequently, he must be equipped with the essential tools for analysis of complex behavioral interactions as a requisite to effective application of quantitative techniques.

The objective here is to develop a systems approach to behavior by building a common analytical premise. This is done (1) by showing consistency between internal need and environmental resources as determinants of behavior, (2) by establishing values as explanations of these initiating forces, and (3) by then letting these values serve as standards of conduct for man's individual and group personality patterns as end-products of behavior. The basic hypothesis is that a triadic paradigm of unique combinations of need-resource qualities generates corresponding actions and interactions among individuals which are observable in the personalities defined by psychoanalysts. The relationship permits a theoretical classification of behavior patterns for identification, prediction, and resolution of problems within the specific contexts of need and environment that govern man's actions. Through this approach, the manager gains a systematic tool for behavioral analysis on an integrated basis, somewhat like the economic concept of pure competition serving as a reference parameter against which reality becomes a measurable entity. Many salient features had to be condensed in this paper, permitting only a symbolic application of the behavioral theory to cost-benefit analysis of the war in Vietnam. However, present working papers using nonmetric multi-dimensional scaling, factor analyses, and clustering techniques already indicate the applicability of such a behavioral framework.
Towards a System of Systems Concepts
Authors: Ackoff Russell L.
Published: November 2008

The concepts and terms commonly used to talk about systems have not themselves been organized into a system. An attempt to do so is made here. System and the most important types of system are defined so that differences and similarities are made explicit. Particular attention is given to that type of system of most interest to management scientists: organizations. The relationship between a system and its parts is considered and a proposition is put forward that all systems are either variety-increasing or variety-decreasing relative to the behavior of its parts.
A Study of Lexicographic Expected Utility
Authors: Fishburn Peter C.
Published: November 2008

A relation <L on a set of real vectors a, b, … is a lexicographic order when a <Lb if and only if a ≠ b and for every j such that bj < aj there is an i < j such that ai < bi. A simple and direct derivation is given for a multidimensional utility function whose lexicographically-ordered expected utility vectors preserve an individual's preference order on a set of probability measures. All but one of Hausner's axioms yield an equivalence on the set of preference intervals, and the resulting bet of equivalence classes is shown to account for the hierarchy in the lexicographic structure. A lexicographic utility representation is noted for the finite-dimensional case. When Hausner's other axiom is added, his theorem for lexicographic linear utility is obtained. This theorem is applied to sets of simple and discrete probability measures.
On Quadratic Programming
Authors: Eaves B. Curtis
Published: November 2008

A procedure based on Lemke's algorithm is developed which either computes stationary points for general quadratic programs or else shows that the program has no optimum. If a general quadratic program has an optimum and satisfies a non-degeneracy condition then it is demonstrated that there are an odd number of stationary points.
An Algorithm for Separable Nonconvex Programming Problems II: Nonconvex Constraints
Authors: Soland Richard M.
Published: November 2008

We extend a previous algorithm in order to solve mathematical programming problems of the form: Find x = (x1, …, xn) to minimize ∑φi0(xi) subject to x ∈ G, l ≦ x ≦ L and ∑φij(xi) ≦ 0, j = 1, …, m. Each φij is assumed to be lower semicontinuous, possibly nonconvex, and G is assumed to be closed. The algorithm is of the branch and bound type and solves a sequence of problems in each of which the objective function is convex. In case G is convex each problem in the sequence is a convex programming problem. The problems correspond to successive partitions of the set C = { x ∣ l ≦ x ≦ L}. Two different rules for refining the partitions are considered; these lead to convergence of the algorithm under different requirements on the problem functions. An example is given, and computational considerations are discussed.
A Language for Organization Design: Part II
Authors: Ansoff H. I. , Brandenburg R. G.
Published: November 2008

This paper develops a language for designing the structure of a purposive organization so as to maximize organizational performance potential for achieving given objectives. Four categories of performance attributes are specified, each contributing to the particular objectives an organization pursues in seeking maximum return from the resources it employs: steady-state efficiency, operating responsiveness, strategic responsiveness, structural responsiveness.

A fifth category, decision and information quality criteria, further contributes to organizational success. These five types of criteria, combined with tests of economic and human resource feasibility, are used to select and tailor one of several basic organizational forms to meet the particular needs of a firm.

Basic organizational forms, observable in business practice, analyzed with respect to the above performance attributes, include: centralized functional form, decentralized divisional form, project management form, innovative form.

Several variations on these forms, which have been used in business, are listed along with conditions for the applicability of each, reflecting the need for individual firms to adapt basic structures to suit their distinctive requirements.

Major steps in the logic of the overall design process are specified.
On the Nature of the Cost-Benefit Schedule
Authors: Jones Carl R.
Published: November 2008

In this paper the nature of a set of coat-benefit studied alternatives is studied. An integrated set of submodels is assumed to provide the foundation for a cost-benefit schedule. The model is formulated as an efficiency problem using the technique of vector maximization. Efficient points are characterized by a set of decision rules. A local cost-benefit function is developed. Comparative statics (sensitivity analysis) results show that there exist efficiency substitution and benefit effects. These effects are the basis for rigorous definitions of efficiency substitutes and complements.
An Implicit Enumeration Algorithm for the Machine Sequencing Problem
Authors: Florian M. , Trepant P. , McMahon G.
Published: November 2008

An implicit enumeration algorithm is developed for the machine sequencing problem. The method is based on the graph-theoretical representation of the problem. The convergence of the algorithm is demonstrated, and its efficiency is evaluated by experiments carried out with a code written for the CDC 6400 computer.
An Algorithm for Optimal Project Scheduling under Multiple Resource Constraints
Authors: Davis Edward W. , Heidorn George E.
Published: November 2008

An algorithm is described which permits the computation of optimal (minimum-duration) solutions for the resource-constrained project network scheduling problem under conditions of multiple resource requirements per job (activity). The approach is a form of bounded enumeration and employs techniques originally developed for the solution of the assembly line balancing problem. Initial computational results are given, along with an example of the type problems solved. Among the advantages of the procedure are that resource requirements can vary over job duration, and various assumptions concerning job continuity are allowable, with no extra computational effort.
Remarks on Graduate Education in the Management Sciences
Authors: Cooper William W.
Published: November 2008

Remarks on graduate education in management sciences reflecting opinions at the Carnegie-Mellon University.
Some Ideas on Education in the Management Sciences
Authors: Ackoff Russell L.
Published: November 2008

The brevity of this statement hardly permits a position to be presented fully let alone defended adequately. Hence what follows are a set of assertions whose baldness gives them a dogmatic tone that they are not intended to have. Enough of apologies. There is no more space to spare. This discussion is divided into what I consider to be the four essential parts of an educational program in the Management Sciences: Foundations, Fundamentals, Frontiers, and Facility.
Some Comments on Graduate Education in the Management Sciences
Authors: Lieberman Gerald J.
Published: November 2008

The educational goal of a graduate program in the management sciences should be to adequately prepare a student for a lifetime pursuit of any phase of management science he chooses. More specifically, the program should be designed for a student who desires a management science education to meet his career goal in either a university, business or government position. However, any educational program must distinguish between the objectives of a doctoral student and a terminal master's student. A program leading to a Ph.D. degree should be directed to those primarily interested in a teaching and research career in University, or a research career in business or government Training at the master's level should emphasize applications of the techniques associated with management science. Such technically trained personnel are often used to develop advanced planning methods and/or operating policies within a company.
What's OR-MS?
Authors: Littauer Sebastian B.
Published: November 2008

I believe that college departments' programs fall into two essential categories. The more common and less interesting type is that of the directed program, that is to say, the one which has been set either by the head of the department or by past tradition. As teachers are added to the staff the program goes on without any real searching thought. The other type of program is one that is genuinely thought out by the persons responsible and reflects the methods, ideas, capacities and caprices of various members of the faculty, although sometimes one vigorous member of the group essentially puts his stamp on the program. We will call this type the “freely evolved” program and this is the kind we will talk about.
Some Comments on Graduate Education in the Management Sciences
Authors: Starr Martin K.
Published: November 2008

There are sundry purposes to be served by graduate education in the management sciences. These purposes include the development of professional abilities in model-building and mathematical model-transformation; and managerial implementation skills in model-use. These abilities require different mixtures of behavioral and quantitative sensitivities. Degrees of specialization and generalization are evidently in conflict both for teaching time and by the natural inclinations of various personality types (both students and teachers). It is unclear how (if at all) it is possible to achieve the purposes of specialization and generalization at the same time. Also, we know very little about how to combine behavioral and quantitative considerations.
Organizational Communications Systems and the Decision Process
Authors: Ference Thomas P.
Published: November 2008

The emergence and solution of organizational problems are examined from the framework of the communications system. A general model is developed based on the information-processing activities of the individual members of a communications network. The model describes the problem-solving process as a sequence of five stages: problem recognition, identification procedures, information acquisition and integration, definition of constraint set, and comparison and adaptation. The relations among the critical variables of the model are then specified in a series of propositions. The main purpose of the model, as exemplified in the propositions, is to provide a testable framework for the empirical analysis of the decision process in organizations.
A Simulation of Labor Efficiency and Centralized Assignment in a Production Model
Authors: Nelson Rosser T.
Published: November 2008

This paper reports a set of simulation experiments with a service system model in which labor interchange is possible between service centers. It explores design and control aspects of labor and machine limited systems. A simple model with two service centers and two laborers is employed to explore the relationships among three experimental variables. The variables are the efficiency of labor interchange, the degree of centralized control exercised in labor assignment, and the queue discipline. Both series and job-shop type job routings are studied.
The Variable Reduction Method for Nonlinear Programming
Authors: McCormick Garth P.
Published: November 2008

A first-order method for solving the problem: minimize f(x) subject to Ax − b ≧ 0 is presented. The method contains ideas based on variable reduction with anti-zig-zagging and acceleration devices based on the Variable Metric Method. Proof of convergence to a Kuhn-Tucker Point, and statement of the rate of convergence when the strict second order sufficiency conditions hold are given.
A Note on Optimal Maintenance Policy and Sale Date of a Machine
Authors: Arora S. R. , Lele P. T.
Published: November 2008

In the paper “Optimal Maintenance Policy and Sale Date of a Machine,” Dr. G. L. Thompson [Thompson, G. L. 1968. Optimal maintenance policies and sale date of a machine. Management Sci. 14(9, May) 543–550.] provided a model to interrelate economic life and maintenance policy, using Pontryagin's maximum principle. His results are very interesting, but these can be made more representative of the real life by a simple modification of the deterioration function d(t).
Stochastic Capacity Models
Authors: Giglio Richard J.
Published: November 2008

Capacity of a facility is defined as its maximum rate of production. Although capacity can be changed by paying the appropriate capital costs, it is often impossible or undesirable to expand or contract capacity to meet exactly a time-varying demand. This paper presents work designed to help determine the optimal amount and timing of capacity expansions for situations where demand or facility life are stochastic. A series of models is developed to handle time stationary and nonstationary demand functions and approximations are presented allowing the use of modified deterministic models to solve stochastic problems.
A Selection Problem of Shared Fixed Costs and Network Flows
Authors: Rhys J. M. W.
Published: November 2008

An apparently combinatorial problem is defined, and a method given for solution by reduction to a network flow problem. The basic problem defined is that of assessing the desirability of incurring a number of fixed costs, when the benefits to be obtained cannot be related to individual cost-incurring items (facilities) but only to combinations.
Decision-Making in a Fuzzy Environment
Authors: Bellman R. E. , Zadeh L. A.
Published: November 2008

By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined.

An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0 ,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples.

Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value.

The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
Analysis of a Decision Making Investigation
Authors: Mackenzie Kenneth D. , Barron F. Hutton
Published: November 2008

Those management and social scientists dealing with organizational behavior are severely limited by the need for more operational theory and by the paucity of experimental data on important events and phenomena. The many practical and conceptual reasons why experiments in the classical sense cannot be conducted lead us to consider a less rigorous form of inquiry called an investigation. A possible heuristic procedure for analyzing data from investigations is proposed. The heuristic has the property that rather than selecting favorable events to support a theory, it codes and incorporates observed events systematically into a testing of theory. This procedure is applied to data from the Churchman-Ratoosh laboratory investigations of implementation processes. Our results are consistent with the assumption of a constant source diffusion of innovation process. Data for the diffusion process and attendant structural change are presented in terms of models. The application of the heuristic also suggests questions for further diffusion and implementation experiments.
Validation of Simulation Results
Authors: Van Horn Richard L.
Published: November 2008

Simulation models are designed and used with a goal of learning about a process. Validation is the act of increasing to an acceptable level the confidence that an inference about a simulated process is correct for the actual process. There is no such thing as “the test”. The experimenter selects a set of tests from the many possible—a standard decision problem of balancing the cost of testing against the cost of an incorrect inference. This paper outlines possible validation actions and suggests considerations that enter into their choice. Three major classes of actions are finding models with face validity, testing assumptions and testing input-output transformations. Actions range from such highly technical approaches as spectral analysis to behaviorally oriented ones such as the “Turing” test. Validation often becomes more tractable if simulation is viewed as one of several modes of investigation. Complementary research activities—related experiments, empirical analysis, analytic models, or prototypes—are widely used in the physical sciences to increase validity and appear equally appropriate for the management sciences. Some of the ideas and problems of validation are illustrated briefly in an example that involves all-machine simulation, man-machine simulation, related psychological experiments and a field test.
Equivalent Integer Programs and Canonical Problems
Authors: Bradley Gordon H.
Published: November 2008

A theory of equivalent integer programs is developed that shows that every all-integer integer programming problem is equivalent to infinitely many other integer programming problems. The equivalence is such that the solution to any one problem in the equivalence class determines the solution to every other problem in the class. Procedures to construct certain canonical problems in each equivalence class are described. The relationship of this theory to computational algorithms is discussed.
A Simple CPM Time-Cost Tradeoff Algorithm
Authors: Siemens Nicolai
Published: November 2008

This article describes an algorithm for efficiently shortening the duration of a project when the expected project duration exceeds a predetermined limit. The problem consists of determining which activities to expedite and by what amount. The objective is to minimize the cost of the project.

This algorithm is considerably less complex than the analytic methods currently available. Because of its inherent simplicity, the algorithm is ideally suited for hand computation and also is suitable for computer solution. Solutions derived by the algorithm were compared with linear programming results. These comparisons revealed that the algorithm solutions are either (a) equally good or (b) nearly the same as the solutions obtained by more complex analytic methods which require a computer.

With this method the CPM time-cost tradeoff problem is solved without access to a computer, thereby making this planning tool available to managers who otherwise would find implementation impractical.
An Alternative to Uniform Expenditure Reductions in Multiple Resource State Finance Programs
Authors: Bruno James E.
Published: November 2008

The purpose of this study was to demonstrate an alternative procedure for reducing state expenditures in ongoing state programs without resulting in the major description commonly associated with uniform or across-the-board state budget cuts. Using, for purposes of illustration only, a problem involving the reduction in state expenditures for a school finance program, a linear programming model was derived—then applied. The purpose or objective of the model was to determine the required state resource allocation strategy which would minimize the state's financial commitment (however it may be defined by educators and legislators) without seriously affecting the financial support for educational expenditures at the school district level. In the state finance program studied, the total state expenditure could have been reduced by over one million dollars with no reduction in the state guaranteed minimum level of expenditure (referred to as the foundation level) per ADA (student in average daily attendance). Peripheral benefits such as a large amount of property tax relief, more state aid to districts with a poor tax base, and a decrease in the dollar spread in per pupil expenditures between districts were also achieved. The results of the study indicate possibilities for utilizing linear programming or similar methods for other state resource allocation problems involving revenues from federal, state or local sources.
A Marginal Cost Model for the Hiring-Overtime Decision
Authors: Lundgren Earl F. , Schneider V.
Published: November 2008

In the case where a given demand increase over a finite time span is known and exceeds current production capacities, a marginal cost analysis can provide decision criteria for work-force adjustments. Using the marginal costs of hiring new workers and for various periods of overtime as a basis, decisions can be made to hire new workers, to work overtime, or to do both. The marginal cost analysis for hiring new workers includes the application of learning curve data to their increasing productivity rate over the time span. The approach minimizes costs, assuming it is not necessary to buy new equipment or add supervisors. The greatest applicability for the model may be found in certain job shop situations.
On the Optimality of Generalized (s, S) Policies
Authors: Porteus Evan L.
Published: November 2008

A standard inventory model is examined with a concave increasing ordering cost function rather than simply a linear one with a setup cost. A generalized (s, S) policy is shown to be optimal in the n-period problem. A generalization of k-convex and quasi-convex functions to quasi-k-convex functions is required in the process. The probability densities of demand must be one-sided Pólya densities.
A Stochastic Model for Adaptive Behavior in a Dynamic Situation
Authors: Jones J. Morgan
Published: November 2008

A stochastic model of adaptive behavior in a dynamic situation is proposed, and its properties developed. The model is developed from a hypothetical construct of behavior, and, in the limit, becomes a nonstationary probability diffusion process. Although the model has wide potential applicability, it is discussed in the marketing context for which the model was first proposed. In addition to properties of the model, important aspects of the model as it applies to marketing will be discussed.
Inventory Models with Forecasting and Dependent Demand
Authors: Brown George F. , Lloyd Richmond M. , Corcoran Timothy M.
Published: November 2008

In general, the single-product inventory model in which demands in successive periods are not independent is difficult to treat. This paper defines a large class of such problems, when there is a positive lead time for delivery, which can be treated by the classical formulation with a single state variable. All results which hold for inventory models with a constant delivery lag can be shown to hold also for this model. An application is made to a system in which demands are generated by part failure and in which a portion of these failures are repaired after a given (constant or probabilistic) time.
The New-Trier Stochastic Model of Brand Choice
Authors: Aaker David A.
Published: November 2008

This paper presents a description and an empirical evaluation of a new stochastic model of brand choice, the new-trier model, developed to model the purchasing process following the first purchase of an unfamiliar (to the purchaser) brand. Empirical analysis and model refinement yields several interesting insights into consumer decision processes. Several managerial applications of the model are considered.
Three Pricing Policies for a Multi-Product Multi-National Company
Authors: Rutenberg David P.
Published: November 2008

A price leader must formulate list prices every time he introduces a new product line (fairly frequently in a technologically developing industry). This is not easy. When the company is multi-national, pricing policy becomes further complicated by the issues of centralization versus autonomy of the national subsidiaries, and three pricing schemes are encountered in practice.

Scheme 1. The price of an item is the same around the world, except that the customers absorb freight plus import duty. Very simple price coordination and auditing results from this policy.

Scheme 2. National prices for the line equal an optimally determined national weighting factor multiplied by a set of benchmark prices.

Scheme 3. The subsidiaries can take advantage of local competitive climates with no fixed requirement that prices be coordinated across the nations.

For each pricing scheme the overall profit equals the model profit minus administrative costs. The three schemes are sequenced in order of their model profits, which is also their likely administrative cost sequence. We shall compute their comparative model profitabilities so as to have bonds against which to gauge administrative costs. A base case is presupposed. Adjustments to prices and to marketing budgets induce changes in the quantity sold, and hence in the production cost. The profit function is approximated as quadratic in the control variables of price and marketing budget, so that optimal adjustments can be calculated by little more than inverting a partitioned matrix.
Efficient Distribution of Resources Through Three Levels of Government
Authors: Cassidy R. G. , Kirby M. J. L. , Raike W. M.
Published: November 2008

This paper presents a model for determining how a central government can most efficiently allocate resources among other levels of government. The model explicitly includes the fact that lower levels of government can make independent decisions once they have been given resources by the central government. A key feature of the model is the mathematical formulation of the central government's objective of distributing resources efficiently, while at the same time being as fair as possible to all those receiving allocations. An algorithm for solving the model is presented along with a numerical example.
Linear Programming Models for Production-Advertising Decisions
Authors: Thomas Joseph
Published: November 2008

This paper studies the problem of simultaneously smoothing production and inventory and setting advertising levels. The models given are linear programming models, assuming a deterministic demand-advertising-price relationship. The formulations include both one period and multiperiod models. Advertising has a decreasing effect within each period with a saturation level of advertising included and advertising also has a decreasing effect through time, allowing a build up of a stock of goodwill. A decomposition approach is given which is very efficient computationally due to the simplicity of the subproblems. Other computational aids are discussed; the pricing problem is examined briefly; and a numerical example is given to indicate the possible effect of considering production and advertising (and pricing) decisions together.
Decomposable Regression Models in the Analysis of Market Potentials
Authors: Bass Frank M.
Published: November 2008

A regression method for estimating geographic market potentials is developed. Aggregation issues are explored, and a macro model is derived in which it is not necessary to assume that the relationships among variables are the same within the micro subsystems. An estimating procedure is presented and empirically illustrated in which the estimates satisfy additivity and nonnegativity constraints.
Optimal Maintenance and Sale Age for a Machine Subject to Failure
Authors: Kamien Morton I. , Schwartz Nancy L.
Published: November 2008

A problem of optimal machine maintenance policy is studied. The value of the machine's output is independent of age, but the natural probability of machine failure increases with age. Preventive maintenance can be applied to reduce the probability of machine failure (but a failed machine can only be junked). The machine may be sold at any time providing it is still effective. The problem is to select an optimal preventive maintenance policy for the period of ownership and a planned sale date at which the machine will be sold providing it has not yet failed.

The optimal policy calls for a continuous nonincreasing maintenance rate, although not necessarily a decreasing rate of maintenance expenditure. The necessary condition for machine age at sale is critical in the determination of optimal maintenance policy. The necessary conditions for an optimal maintenance policy are shown to be sufficient as well. The novelty of the approach lies in the explicit distinction between the machine's “natural” failure rate and the actual failure rate resulting from selection of preventive maintenance policy.
Proximal Decision Analysis
Authors: Howard Ronald A.
Published: November 2008

This paper presents simplified techniques for analyzing the effect of uncertainty in large decision problems.

Starting with the development of approximate expressions for the moments of a value lottery, we show that the probabilistic assessments of jointly related random variables necessary for these approximations are quite reasonable in number. The concepts of risk aversion, certain equivalent, and exponential utility function then permit writing useful approximations for the certain equivalent of the value lottery.

Deterministic sensitivity analyses are described first for the case when the decision variables are fixed and then for the case when they can be changed to compensate for variations in state variables. The approximate effect and value of clairvoyance (revelation of ultimate values of uncertain variables) is derived from the original probabilistic assessment and the results of the deterministic sensitivity analysis. We next determine the approximate value of wizardry (changing uncertain variables into decision variables). The amount by which decision variables must be adjusted to account for risk aversion is established from earlier results.

The final portion of the paper discusses a simple economic example that illustrates the application of the development.
Flows in Arborescences
Authors: Glover Fred
Published: November 2008

This paper gives efficient methods for solving four specially structured network problems that arise in connection with certain integer programming methods developed by Cook and Cooper, Hillier, and Glover. Such problems have also independently been studied in inventory theory by Ignall and Veinott, who have developed extensive qualitative (nonalgorithmic) implications of their structures. In the integer programming context, special subclasses of these network problems are generated and solved as part of a strategy for solving more general integer linear programs. By providing particularly efficient methods for accommodating somewhat broader network structures, our results enable the development of related integer programming solution strategies that generate more complex subproblems.

We show that the first of the four network problems can be solved by a procedure that assigns each variable a value exactly once, without subsequent revision. Properties of optimal solutions for the remaining problems are developed that enable the algorithm for the first to be extended to the second and then, by suitable transformation of variables, to the third and last problems as well. Moreover, while the last three problems involve an additional linear constraint that nullifies the “integer extreme point property,” we show that optimal integer solutions to these problems can nevertheless easily be obtained from the optimal continuous solutions.
A Note on Marginal Allocation in Multiple-Server Service Systems
Authors: Rolfe Alan J.
Published: November 2008

In this note we consider the allocation of servers to a multiple facility service system. Each facility consists of a number of parallel channels and the arrival processes are Poisson. When service times are constant we prove that marginal allocation is an optimal and easily implemented solution technique and suggest that it is also optimal for exponential service times.
Communications to the Editor—Some Comments Concerning Revelle, Marks and Liebman's Article on Facility Location
Authors: Robers Philip D.
Published: November 2008

The recent survey paper entitled “An Analysis of Private and Public Sector Location Models,” by ReVelle, Marks, and Liebman. [Management Science, Vol. 16, No. 11 (July 1970), pp. 692–707] should be of considerable interest to operations research practitioners. To my knowledge it represents the first synthesis of the many results which have been published in the interesting area of facility location. Unfortunately, I am afraid that the article is somewhat misleading in some regards, and may tend to confuse some readers who are not familiar with the literature in this area.
Estimating Sample Size in Computing Simulation Experiments
Authors: Fishman George S.
Published: November 2008

A method is described for estimating and collecting the sample size needed to estimate the mean of a process (with a specified level of statistical precision) in a simulation experiment. Steps are also discussed for incorporating the determination and collection of the sample size into a computer library routine that can be called by the ongoing simulation program.

We present the underlying probability model that enables us to denote the variance of the sample mean as a function of the autoregressive representation of the process under study and describe the estimation and testing of the parameters of the autoregressive representation in a way that can easily be “built into” a computer program.

Several reliability criteria are discussed for use in determining sample size. Since these criteria assume that the variance of the sample mean is known, an adjustment is necessary to account for the substitution of an estimate for this variance. It is suggested that Student's distribution be used as the sampling distribution, with “equivalent degrees of freedom” determined by analogy with a sequence of independent observations.

A bias adjustment is described that can be applied to the beginning of the collected data to reduce the influence of initial conditions on events in the experiment. Four examples are presented using these techniques, and comparisons are made with known theoretical solutions.

One unfortunate shortcoming of the proposed procedure is that its performance is directly linked to the initially chosen sample size. Our results show that as this sample size increases, the procedure gives results which agree more closely with predicted results.
Economic Order Quantities and Multiple Set-Up Costs
Authors: Lippman Steven A.
Published: November 2008

We consider the problem of scheduling the production of a single product at each instant during a time horizon of length T (≦ ∞) so as to minimize the average cost per unit time; backlogging of demand and disposal of stock are not allowed. Two types of costs are incurred; the holding cost per unit time is assumed to be proportional to the inventory level while the ordering cost is that associated with the multiple set-up cost function (see (3) and Figure 1). By studying a special case (K = 0 in (3)) in §2, the analysis of the problem practically becomes that of the standard economic lot size model so that we can rigorously derive some not too widely known results about the lot size model while exploring our model. In particular, we obtain planning horizon theorems and characterize the form of an optimal production schedule for T < ∞ and T = ∞. In §3 the special assumption is removed and similar, but slightly weaker, theorems are established. For example, an optimal production schedule may have several orders of two different sizes in contrast to the special case where every order is the same size. In addition, simple algorithms for finding optimal policies for both T < ∞ and T = ∞ are given.
Some Bounds for Discounted Sequential Decision Processes
Authors: Porteus Evan L.
Published: November 2008

New bounds are obtained on the optimal return function for what are called discounted sequential decision processes. Such processes are equivalent to ones satisfying the contraction and monotonicity properties (Denardo [Denardo, E. V., 1967. Contraction mappings in the theory underlying dynamic programming. SIAM Review. Vol. 9, pp. 165–177.]). The bounds are useful primarily in the infinite horizon case. Certain subprocesses are exploited, based on the simple notion of taking only those states which are relevant into consideration. Some existing algorithms and some of their obvious extensions are listed. The possibility of identifying nonoptimal decisions, as in MacQueen [MacQueen, J. B., 1966. A Modified dynamic programming method for markovian decision problems. Journal of Mathematical Analysis and Applications. Vol. 14, pp. 38–43.], is included.
Extensions of the Group Theoretic Approach in Integer Programming
Authors: Wolsey Laurence A.
Published: November 2008

By relaxing the nonnegativity constraints on a set of basic variables, an integer programming problem can be reduced to a shortest route problem over a finite Abelian group. Here it is shown how given a similar relaxation on any set of variables, a structurally simpler problem is obtained, which can be regarded as a shortest route problem over an Abelian (but not necessarily finite) group. In particular if the non-negativity constraints are relaxed on all but one of a set of basic variables, a knapsack (or very close to knapsack) problem is obtained, which either gives the solution of the integer problem, or when solved by dynamic programming provides bounds at least as strong as those provided by the above group problem.

The difficulty that arises when the order of groups encountered is very large is also considered in the same framework, and by further relaxation it is shown how the groups can be reduced to manageable size, which can be used to provide simple bounds for the above group problem. Finally applications of these results are suggested with reference to various existing integer programming algorithms.
On Elmaghraby's “The Theory of Networks and Management Science”
Authors: Yen Jin Y.
Published: November 2008

In [Elmaghraby, S. E. 1970. The theory of networks and management science. Management Sci. 17(1, September) 1–34.], Elmaghraby presents several network problems. However, many points made in this paper regarding shortest path network problems may be misleading. The purpose of this letter is, on one hand, to examine these points, and, on other hand, to present some additional information on some of the problems being discussed in the original paper for the reader's reference.
Rejoinder
Authors: Elmaghraby Salah E.
Published: November 2008

Author's rejoinder to comments [Yen, J. Y. 1971. On elmaghraby's “the theory of networks and management science.” Management Sci. 18(1, September) 84–86.] about his paper.
Estimating Dynamic Effects of Market Communications Expenditures
Authors: Montgomery David B. , Silk Alvin J.
Published: November 2008

This paper is concerned with the problem of measuring market response to a “communications mix”—the various means which a firm employs to transmit sales messages to potential buyers. Distributed lag models are applied to time series data for an ethical drug to estimate the short-run, intermediate, and long-run effects on market share of expenditures made for journal advertising, direct mail advertising, and samples and literature. Important differences were found among the communications variables with respect to the magnitude and over-time pattern of effect each had on market share. Significantly, the results indicate that the average historic allocation of resources to alternative communication vehicles has been in inverse relation to measured market response. A variety of econometric checks on the models lends credibility to the results. The managerial implications of the findings are discussed.
A Scoring Methodology for Assessing the Suitability of Management Science Models
Authors: Souder William E.
Published: November 2008

In this study, five major criteria (realism, flexibility, capability, ease of use, and cost) for evaluating the suitability of management science models for R&D project selection are established, through personal interviews with R&D administrators and management scientists. A suitability rating system, based on these criteria, is used by the author to rate twenty-six management science models for their suitability of use in R&D project selection decision making. Profitablility index and scoring types of models were found to have generally higher ease of use and lower cost performances than the other types. The linear and nonlinear models had generally higher flexibility, while the linear, nonlinear and zero-one models had generally higher realism than the other model types.