bluuebunny/crossref_metadata_2025 huggingface dataset:
The Linear Complementarity Problem
Authors: Eaves B. Curtis
Published: November 2008

This study centers on the task of efficiently finding a solution of the linear complementarity problem: Ix − My = q, x ≥ 0, y ≥ 0, x ⊥ y. The main results are: (1) It is shown that Lemke's algorithm will solve (or show no solution exists) the problem for M ∈ L where L is a class of matrices, which properly includes (i) certain copositive matrices, (ii) certain matrices with nonnegative principal minors, (iii) matrices for bimatrix games. (2) If M ∈ L, if the system Ix − My = q, x ≥ 0, y ≥ 0 is feasible and nondegenerate, then the corresponding linear complementarity problem has an odd number of solutions. If M ∈ L and q > 0 then the solution is unique. (3) If for some M and every q ≥ 0 the problem has a unique solution then M ∈ L and the problem has a solution for every q. (4) If M has nonnegative principal minors and if the linear complementarity with M and q has a nondegenerate complementary solution then the solution is unique. (5) If yTMy + yTq is bounded below on y ≥ 0 then the linear complementarity problem with M and q has a solution and Lemke's algorithm can be used to find such a solution. If, in addition, the problem is nondegenerate, then it has an odd number of solutions. (6) 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. (7) If a quadratic program has an optimum and satisfies a nondegeneracy condition then there are an odd number of stationary points.
Selective Control of Independent Activities: Linear Programming of Markovian Decisions
Authors: Hinomoto Hirohide
Published: November 2008

This study is related to optimum control strategies used by a manager supervising a group of independent activities whose performances deteriorate with time. At the end of a day, the manager evaluates information regarding the performance levels of the activities during that day and decides which activity to attend to, since he can control only one at a time. The deterioration of performance and the improvement of the deteriorated performance by a control action from one level to other levels are given by stationary transition probabilities. Optimal strategies for this control are obtained by the linear programming method proposed by Manne [Manne, A. S., Linear programming and sequential decisions. Management Science Vol. 6 No. 1 (April 1960), pp. 259–267.].
Programme Selection in Research and Development
Authors: Lockett A. Geoffrey , Gear Anthony E.
Published: November 2008

Mathematical programming as an aid to R & D project portfolio selection has been suggested by many authors, but few practical applications have been reported. This paper discusses some, of the difficulties, associated with the application of the proposed models, and describes procedures for handling these problems. Problem areas considered are:

Allowance for future opportunities in multi-period models,

Generation of alternative risk-return solutions,

Inclusion of projects not completed during the planning period,

Comparison of linear and integer programming outputs.

In the main, both the problems and methods of solution are clarified by means of numerical examples, and details of a practical case study are given.
A Nonlinear Approximation Method for Solving a Generalized Rectangular Distance Weber Problem
Authors: Wesolowsky G. O. , Love R. F.
Published: November 2008

This paper provides a method for approximating optimal location in a multi-facility Weber problem where rectangular distances apply. Optimality is achieved when the sum of weighted distances is minimized. Two upper bounds on the error incurred by using the approximation are developed. The formulation can be used in convex programming to solve some nonlinearly constrained problems.
A Modified Simulation of Cyert, Feigenbaum, and March's Duopoly Model
Authors: Tuckman Howard P. , Holmblad L. Peter
Published: November 2008

This paper utilizes a duopoly model to simulate the effects of various management rules of thumb and of changing economic conditions on the market share and profit-goals of the firm. Part I presents and discusses a behavioral model, Part II gives the initial market conditions and the parameters for the alternative simulations, and the remaining sections discuss the effects of the parameter changes.

Several findings are of interest to management scientists. If a firm incorrectly estimates market demand its market and profit share will decrease. Estimates of the market demand curve slope which are far away from the true slope have a lesser proportional effect on the firm's share of the market than estimates close to the “true” slope. If costs rise rapidly due to internal slack, the price of a product will rise, market output will fall, and the two firms will have lower profit goals. Moreover, policies which encourage both short- and long-run expansion result in a larger share of the market for the newer firm. The paper ends with recommendations for further development of the model.
A Recursive Optimization and Simulation Approach to Analysis with an Application to Transportation Systems
Authors: Nolan Richard L. , Sovereign Michael G.
Published: November 2008

Modeling large systems with either an optimization or a simulation method has several disadvantages. Simulation is usually expensive if adequate detail and experimental designs are employed. Complete detail in optimization models may press the bounds of computability. A recursive approach integrating both types of models is presented.

The recursive approach involves, an allocation of resources by optimization models at an aggregate level. At this level computation is not difficult and broad alternatives can be easily explored. Simulation models can then be designed to address detailed questions of productivity of resources, discreteness, and complex relationships. The simulation can use the particular schedules generated by the optimization so that experimental designs can be limited in size. The revised productivities can then be input to the optimization model for a more refined optimal solution. The recursive approach has been applied to the strategic mobility system problem in reaching decisions for the size of transportation forces for the DOD. A linear programming model provides optimal allocation of overall mobility system vehicles and schedules. Two simulation models, an airlift model and a sealift model, provide productivity estimates and tests of capability.
A Comparison between Two Kinds of Decentralized Optimality Conditions in Nonconvex Programming
Authors: Ten Kate A.
Published: November 2008

Decomposable mathematical programming problems sometimes admit a certain degree of decentralization in the decision process. By an informative interplay between a central authority and a number of subdivisions one hopes to establish the overall best solution. This interplay can be organized in either of two ways: direct or indirect distribution. However, an absolute prerequisite for such procedures to be successful is the availability of an optimality criterion to the centre so as to know when to stop the iterative process. It is well known that for either of two cases the optimality conditions as derived from the Kuhn-Tucker conditions for the overall problem are not satisfactory. The present paper makes a comparison between the shortcomings of the two kinds of conditions. In the case of direct distribution this condition turns out to be necessary but unfortunately not sufficient and for indirect distribution the condition is sufficient but not necessary. The insufficiency in the direct and the absence of necessity in the indirect case, which are caused by eventual nonconvexities of the problem, are explored a bit further. A simple example is presented.
Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios
Authors: Sharpe William F.
Published: November 2008

The characteristic line of a security or portfolio relates its rate of return to that of a “market portfolio.” Several investigators have suggested the desirability of obtaining such a line by minimizing the sum of the absolute deviations rather than the sum of the squared deviations around the line. This paper presents a new algorithm for such a regression problem. The procedure has at least two virtues: it is simple, and it produces useful information as a byproduct of the solution process. Empirical evidence is also presented on the differences in the values obtained with the two regression methods (i.e., mean-absolute-deviation and least-squares). The differences appear to be relatively slight, at least for well-diversified portfolios.
Manpower Planning in Hierarchical Organizations: A Computer Simulation Approach
Authors: Weber Wesley L.
Published: November 2008

A complex system model is presented here as a tool for corporate manpower planning. This approach permits representation of the interrelationships between the behavior of individuals as entities, personnel policy decisions, the labor market, and a large number of individual and organizational outcomes. A computer simulation of the model in the context of a managerial and professional hierarchy is described and tested against hypotheses from the managerial and behavioral science literature. The implications of the results of these tests for the usefulness of this approach for manpower planning and other purposes are discussed.
Bond Refunding with Stochastic Interest Rates
Authors: Kalymon Basil A.
Published: November 2008

The bond refunding problem is formulated as a multiperiod decision process in which future interest rates are determined by a Markovian stochastic process. It is assumed that a single bond is to be outstanding at a given time. Given the future requirements for debt financing, the decision maker must decide whether to keep his current bond or to refund by issuing a new bond at the current market interest rates. Over a finite planning horizon, the structure of policies which minimize expected total discounted costs is studied.
Letter to the Editor—Reply to Nelson's Comments
Authors: Tsao Che S. , Day Richard H.
Published: November 2008

Reply to comments Nelson, Jon P. 1971. Letter to the editor—A note on the economics of metallurgical coke production. Management Sci. 18(4, Part I, December) B-237–B-239.
Experiences with a Sales Districting Model: Criteria and Implementation
Authors: Hess Sidney W. , Samuels Stuart A.
Published: November 2008

Previously reported research documented the analogue between sales districting and legislative apportionment and described the first applications of computer techniques to the redrawing of sales and service areas.

This paper summarizes what we have learned from these seven applications. We emphasize

—motivation for re-alignment: Better coverage, fairer work load and change in size of sales force,

—criteria for measuring “good” districting: Single, multiple and weighted measures of salesman activity; relationship to sales objectives; and correlation between activity measures,

—implementation: Top management involvement and presentation to the sales force,

—demonstrated effectiveness of the new alignments.
Introduction to a Dedicated Issue on Game Theory and Gaming
Authors: Shakun Melvin F.
Published: November 2008

The emphasis in this issue has been on game theory with six papers on game theory, one on gaming, and one relating game theory to gaming. Collectively, the first three papers present an overview of the subject area. The remaining five papers report on new research.
Optimization of Batch Ordering under Deterministic Variable Demand
Authors: Elmaghraby Salah E. , Bawle Vishwas Y.
Published: November 2008

We consider the problem of the optimal ordering schedule to satisfy a given demand pattern over a finite planning horizon when ordering must be in batches of size Q > 1, with and without “setup” cost. A dynamic programming model is constructed. The number of stages are minimized through the characterization of a “complete” set of periods in which ordering must take place and through consideration of the role of initial inventory. The state space and the decision space at each stage are also minimized through considerations of dominance, bounding and feasibility relative to established properties of the optimal schedule. All this results in a most computational efficient algorithm.
Interactive Goal Programming
Authors: Dyer James S.
Published: November 2008

The use of goal programming for the solution of the multiple criteria problem is discussed. An extension of this use is presented in the form of an algorithm which requires interaction with the relevant decision-maker in order to obtain certain information regarding his utility function defined over the permissible values of the criteria. This algorithm provides a bridge between goal programming and recently suggested interactive strategies for the optimization of the multiple criteria problem.
Dynamic Facility Location
Authors: Wesolowsky George O.
Published: November 2008

This paper extends the static single facility location problem to a model that permits location changes within a planning horizon of r periods. An algorithm is developed to optimize the sequence of locations in order to meet changes in costs, volumes and locations of destinations.
Column Dropping Procedures for the Generalized Programming Algorithm
Authors: Murphy Frederic H.
Published: November 2008

Column dropping procedures are provided for the Generalized Programming algorithm. Nonbasic columns may not be dropped, however, from the restricted master at every iteration for all problems. Conditions are provided under which columns may be dropped from the restricted master. An example is provided where the first of these conditions is satisfied at every iteration.
Lot Size Scheduling on a Single Machine for Stochastic Demand
Authors: Goyal S. K.
Published: November 2008

This paper presents a method for computing the lot size to be produced each time each product is scheduled for production when all products are produced on a single machine. The method also computes the distribution of lot size for each product. The demand for each product is a stochastic variable with known distribution, distributed independently for nonoverlapping time periods and identically for equal time periods.
Scientific Manpower Allocation to New Drug Screening Programs
Authors: Pyle E. B. , Douglas B. , Ebright G. W. , Westlake W. J. , Bender A. D.
Published: November 2008

A mathematical model has been developed for the purpose of assisting R&D management in the crucial task of allocating manpower resources to a set of competing pharmaceutical research programs. The problem is formulated such that the optimal manpower allocations among competing research programs are obtained through the use of a standard dynamic programming algorithm. A utility function is developed which allows for variations in the size, timing, and costs of the potential products from the various research programs. The model has been implemented on a digital computer, and the inputs and outputs are demonstrated through an example case. The model has been in existence for four years and is utilized quite extensively during the planning and budgeting cycles.
Optimal Control of a Single-Server Queue with Balking and Reneging
Authors: Blackburn Joseph D.
Published: November 2008

We consider the problem of controlling a single-server queue by turning the server on and off. In addition to a Poisson arrival process and general service-time distribution, provisions for balking and reneging are included in the models, yielding a variety of applications. Stationary optimal policies which maximize expected discounted reward over an infinite horizon are shown to have a simple critical-number characterization. Algorithms for computing the critical numbers are described.
An Analytical Model of a Two-Product, One-Machine, Production-Inventory System
Authors: Hodgson Thom J.
Published: November 2008

This paper is concerned with the modeling and analysis of a one-machine two-product, integrated production-inventory system. A semi-Markovian model is developed which incorporates a state dependent control system heretofore not used in integrated production-inventory models. Control optimization is achieved through the use of Markov-renewal programming. The model is exercised over a range of parameters in order to determine the characteristics of the system. An analysis of the experimental results leads to the following conjectures about the production-inventory system:

1. For the production-inventory system, the economic manufacturing quantity is greater than that seen in the deterministically derived EMQ. The increase results primarily from increases in expected overtime costs and expected setup costs rather than increases in stockout costs. This is important for applications, since overtime and setup costs are a good deal easier to quantify than stockout costs in a real system.

2. Under some conditions, deterministically derived rules for the application of overtime have merit in a stochastic system.
A Simulation of Municipal Zoning Decisions
Authors: Davis Otto A. , Rueter Frederick H.
Published: November 2008

This paper reports a study which developed and empirically tested a simulation model of the process by which zoning ordinances are altered to adapt to the changing needs and conditions of a city. The perceived decision rules of the participants are reported in the form of flow charts which utilize language similar to that used by the participants. The body of the paper indicates methods which were used to translate these judgmental rules into a form suitable for a computer. The model was tested by allowing the computer to decide the one hundred twenty-five proposed changes in the zoning map of the City of Pittsburgh during the period 1963 to 1965 inclusive. The results were good in the sense that the computer model decided most of the cases in the same way as did the human participants. Additional tests and managerial implications are also discussed.
Blood Bank Inventory Control
Authors: Jennings John B.
Published: November 2008

Essentially, blood banks are facilities which procure, store, process, and dispense blood. To operate effectively in the face of both random supply and random demand, sizable buffer stocks of blood are maintained. The resulting inventory control problem is an extremely complex one for several reasons: (1) both supply and demand are random; (2) approximately 50 percent of all bloods demanded, “crossmatched,” and held for a particular patient are eventually found not to be required for that patient; (3) blood is perishable, the present legal lifetime being 21 days in most areas; and (4) each blood bank typically interacts with a number of other banks. This paper presents a framework for the analysis of the whole blood inventory problem at the individual hospital as well as at the regional level, presents a realistic model of blood inventories for both the individual and regional cases, and analyzes the effects of several alternative inventory policies.
Hospital Admission Systems: Their Evaluation and Management
Authors: Milsum John H. , Turban Efraim , Vertinsky Ilan
Published: November 2008

The paper presents a holistic analysis of hospital management admission systems. It outlines control strategies which will facilitate a system's effectiveness for various organizational attributes. In particular, attention is focused on bed occupancy levels and on the stability of flows into the hospital as interacting control variables.

The paper surveys the major available mathematical models and evaluates their use vs. the use of simulation. It emphasizes the potential use of an iterative assignment model which explicitly considers the alternative profiles for preferences for service attributes held by the various participants in the admission system. To reconcile conflicting objectives of these participants the DELPHI and the Multi-attribute Reduction methods are proposed.
Approximation Formulae for Estimation of Waiting-Time in Multiple-Channel Queueing System
Authors: Maaløe Erik
Published: November 2008

This article deals with two approximation formulae for estimation of Wq<, mean waiting-time in a M/Ek/R queueing system. It is shown how Wq< for the multiple-channel system with λ = λ, μ = μ is approximately Rth part of Wq−, mean waiting-time in a single-channel system with λ = λ/R, μ = μ. A second approximation applies the exact ratio W</W− for M/M/R and M/M/1-systems to general M/Ek/R-systems This is particularly illustrated in the case of M/M/R and M/D/R-systems.
Optimal Use of Control Charts for Controlling Current Production
Authors: Ladany Shaul P.
Published: November 2008

A model is developed consisting of all the costs incurred when fraction-defective control charts are utilized to control current production: cost of sampling, cost of not detecting a change in the process, cost of false indication of change, and cost of re-adjusting detected changes. It is suggested that such control charts can be utilized in an optimal way, if those combinations of sample size, frequency of sampling and extent of control limits from process average will be used that provide the minimum total cost. It is further suggested that, by applying any specific cost data to this model, these optimal decision values can be easily evaluated by computer enumeration.
Computational Experience with an M-Salesman Traveling Salesman Algorithm
Authors: Svestka Joseph A. , Huckfeldt Vaughn E.
Published: November 2008

A formulation of the traveling salesman problem with more than one salesman is offered. The particular formulation has computational advantages over other formulations. Experience is obtained with an exact branch and bound algorithm employing both upper and lower bounds (mean run time for 55 city problems is one minute). Due to the special formulation, certain subtours may satisfy the constraints, thus reducing the search. A very good initial tour and upper bound are employed. The determination of these as well as the pathology of the formulation and the algorithm are discussed. No increase in computation time over the one-salesman case is experienced.
A Survey of Management Science in University Operations
Authors: Schroeder Roger G.
Published: November 2008

This survey discusses applications and research of the Management Sciences in institutions of higher education. It includes four specific areas: (1) Planning, Programming and Budgeting Systems, (2) Management Information Systems, (3) Resource Allocation Models, and (4) Mathematical Models. In each of these areas, the major trends and literature are discussed along with numerous references. The survey also provides an integration and synthesis of the recent work from both published and unpublished reports. We conclude with four specific problem areas which are evidently in need of further attention. These areas are (1) stability and suitability of various student flow projections, (2) investigation of decision making processes and the information which should be used, (3) measurement of outputs, and (4) alternative approaches to improve planning methodology.
On the Optimal Inventory Equation
Authors: Bellman R. , Glicksberg I. , Gross O.
Published: November 2008

The purpose of this paper is to discuss a number of functional equations which arise in the “optimal inventory” problem. This is a particular case of the general problem of ordering in the face of an uncertain future demand. Actually, an important aspect of the problem is that of determining a suitable criterion of cost, one which is both realistic and analytically malleable.
A Problem in Optimal Machine Loading
Authors: Salveson M. E.
Published: November 2008

An important managerial problem in manufacturing is to determine the optimum amount and mix of products that can be manufactured from a given set of facilities, such as machine tools. A method is discussed here for handling this problem more effectively in one instance than has been possible. It makes use of several standard procedures, but adapts them and adds others to accommodate the unavoidable difficulty of discreteness in real production situations. The traditional formulation of the economic lot size is shown to be incorrect in the general case and a preferred formulation is presented for the situation studied here. A method of optimizing the amount of in-process inventory to carry in the circumstances of this study also is given.
A Computing Procedure for a Line Balancing Problem
Authors: Jackson James R.
Published: November 2008

In a recent article (Salveson, M. E. 1955. The assembly line balancing problem. J. Indust. Engrg. VI 18–25.), M. E. Salveson discussed various problems concerned with setting up production lines. The purpose of the present paper is to set forth an enumeration procedure for solving one of these problems. The reader is referred to Salveson's article for a detailed discussion of the circumstances in which this problem arises and for remarks concerning the assumptions in its statement.
Some Models of Inventory and an Application
Authors: Naddor Eliezer
Published: November 2008

This paper is concerned with two topics: (1) the development of mathematical models for several simple inventory situations, and (2) an industrial application of a mathematical model of inventory. Because T. M. Whitin has described in detail in this journal the present state of research in inventory control (Whitin, T. M. 1954. Inventory control research. Management Sci. I (November).), no attempt will be made to provide a review here. This paper is not an attempt to solve the “general inventory problem.” On the contrary, the object is to deal with specific situations, and with an illustrative industrial application. The emphasis is on methodology of approach rather than on a general solution.
Planning Human Capital Structure: A Study of Economic, Demographic and Educational Determinants
Authors: Parvin Manoucher
Published: November 2008

There exists a need in less—as well as more—advanced economies for human resource development as an integral part of a planning program and a means of avoiding structural or sectoral unemployment. As a first approximation in planning a human capital structure for a given country, a set of ratios such as students per teacher, inhabitants per physician, nurse or lawyer, etc., may be considered a long-run plan objective. In this paper, economic as well as demographic and educational factors and parameters are used to construct a production function for human capital structure which is called the technical model. The technical model is subsequently used as a constraint in the determination and analysis of the least-cost condition of achieving alternative plans.

One of the theoretical results here is that such ratios become larger as the average percentage of student “dropouts” per year increase. The model shows that the marginal cost of improving the quality of human capital (by a requirement for a longer training period or by the establishment of stiffer educational standards) is an increasing function of such educational variables. Finally, the model gives an explicit algebraic expression for the qualitative-quantitative transformation-professional expertise vs. the number of personnel produced-existing in the production of human capital for equal or comparable costs. The model can be used for regional as well as global planning and in a mixed capitalist as well as a socialist economy.
An Optimum Budget Allocation Model for Dynamic, Interacting Market Segments
Authors: Gensch Dennis H. , Welam Ulf Peter
Published: November 2008

This paper formulates a model for determining the optimal allocation of a given advertising budget over M interacting market segments and a time domain of T periods. Guidance for budget size optimization is provided via a shadow price. The basic input parameters are in terms of sales saturation levels and advertising elasticities, concepts experienced advertising executives understand and are willing to estimate. Economic and political developments in Western Europe are increasing the interactions among geographically defined segments, and recent development in discrimination techniques may soon make market segmentation a practical strategy for the United States market.

In relation to the time domain, the simplistic and often unrealistic constraint of a constant carryover effect is relaxed in that current advertising is hypothesized to generate sales both by creating new customers and by interacting with the residual effects of past advertising (goodwill) thus reinforcing preferences of past customers. This interactive formulation relating past and future expenditures allows a model user greater flexibility in specifying the relationship between advertising and sales. The mathematical programming technique used is a form of convex programming.
Determination of Economic Packaging Frequency for Items Jointly Replenished
Authors: Goyal S. K.
Published: November 2008

The model described in this paper is typically applicable to the batch processing industry where a batch of a product is packaged into several container types immediately after manufacture. An example involving 10 jointly replenished items has been solved for illustrating the recommended approach.
A Holistic View of Problem Solving
Authors: Bartee Edwin M.
Published: November 2008

The limited view of the problem-solving space that is held by the world of science is criticized. A problem solution is considered to be achieved when a perceived present situation and a perceived desired situation become the same. The problem-solving space is three dimensional, and its three vectors are concerned with problem taxonomy, problem-solving modes, and problem-solving process. The space takes on greater meaning when it is related to the fourth dimension called the chronology of problem solving. This chronology includes four primary phases: personalization, collaboration, institutionalization, and socialization. A case is made that the scientific or rationalistic view of problem solving is limited in the collaboration phase and has no relevance in the institutionalization and socialization phases. A holistic view of problem solving is concerned with the relationship between the problem-solving chronology and the ultimate implementation of solutions.
A Note on Offshore Oil Field Development Problems and Suggested Solutions
Authors: Lilien Gary L.
Published: November 2008

This Note reviews some aspects of an approach to modeling the problem of developing offshore oilfields. An alternative method of solution is suggested and an associated problem, that of determining an optimal drilling schedule, is described.
Computer Based Decision Systems in Xerox Corporate Planning
Authors: Seaberg Ronald A. , Seaberg Charlotte
Published: November 2008

The whole concept of modelling has caught on aided immeasurably by the considerable progress in computer technology. Mini-computers, timesharing systems, remote terminals, and graphical displays have placed computer power directly into the hands of the decision maker.

This paper presents a corporate decision-aiding system, a family of timeshared models, developed for Xerox of Canada Limited (XCL) in an effort to link the functional areas for communication, planning, and control purposes. Using the approaches of statistical forecasting, heuristics, and simulation, the XCL Decision System assists and guides management all the way from deriving product demand forecasts to simulating the day-to-day operations of the firm to formulating divisional financial statements to preparing corporate operating and medium-range plans. Developed in a short time span and at low cost, the system is used extensively in Canada and has been adopted, in part, by U.S. corporate and regional offices.
A Planning Model for a Water Quality Management Agency
Authors: Taylor Anthony C.
Published: November 2008

The Canada Water Act provides for the establishment of regional management agencies in areas designated as water quality management areas. These agencies must establish water quality standards within their area and design a control program to meet these standards efficiently. This paper describes a model for planning an efficient water quality program within a river basin. The waste abatement control employed is called the rent allotment control, whose merit is that its implementation provides a solution to the information problem of efficient waste abatement. The control is implemented through a bargaining process or game between the agency and the waste dischargers that may be characterized as an n-person prisoner's dilemma. The game provides the agency with information about individual waste abatement costs, and terminates in a set of agreements on rents and allotments which depend upon the bidding strategies adopted by each player. “Optimal” bidding strategies are examined under the assumption that waste dischargers are risk averse and cost minimizing. An example of the operation of the control is provided using data from the Ottawa River Basin.
Practical Solution of Large Mixed Integer Programming Problems with Umpire
Authors: Forrest J. J. H. , Hirst J. P. H. , Tomlin J. A.
Published: November 2008

In this paper we discuss some branch and bound methods implemented in the UMPIRE mathematical programming system for solving practical integer programming problems and give details of computational experience with these methods. We have found that the nontrivial integer programming problems we encounter tend to fall into two classes. The first class of problems is characterized by a relatively small number (less than 100) of binary integer variables embedded in a very large and difficult linear program, with a few thousand constraints and complex matrix structure. The second class of problems tends to have many more integer variables (perhaps several hundred), frequently organized into special ordered sets and expressing complex logical relationships, but embedded in a much simpler linear program with 500–1,000 constraints. Problems in the first group in particular do not generally behave well using a simple-minded “penalty” approach for reasons we will make clear and a number of heuristic estimation procedures are used to guide the branch and bound search. The most important devices used are “priorities,” the “best projection criterion” and “pseudo-costs.” Some or all of these heuristics can also be very useful in tackling the second group of problems, where it is important to reach a good solution quickly to limit the search.
Simulation Testing of Aggregate Production Planning Models in an Implementation Methodology
Authors: Lee William B. , Khumawala Basheer M.
Published: November 2008

The planning of production, inventories, and work force at an aggregate level to respond to fluctuating demands on a production system has received substantial theoretical treatment in the literature for several years. However, widespread implementation of the available analytical techniques has not occurred. The objectives of this research are to explore this implementation problem: (1) by developing a simulation model of an operating firm, (2) by using this simulation to compare the performance of aggregate production planning models, and (3) by formulating a generalized methodology for implementing quantitative planning models into the decision procedures of operating firms.
A Consumer-Based Methodology for the Identification of New Product Ideas
Authors: Shocker Allan D. , Srinivasan V.
Published: November 2008

This paper suggests a procedure which analytically ties a model to predict users' predispositions to purchase different “brands” in a product-market together with a search process to identify optimal new product ideas. Brands, conceptualized as attribute bundles, are located in a prespecified attribute space. The painwise preference judgments of each individual in a representative sample drawn from the population of users are analyzed using the authors' LINMAP procedure (LINear programming techniques for Multidimensional Analysis of Preferences) to determine his ideal point and salience weights for the attributes of the space. A distance model of choice is postulated for each user and used to predict his probability of choosing nonexisting products. The models developed for each user are tied to methods for searching the product space to find “best” locations for new products. The proposed procedures are discussed and evaluated in the light of relevant conceptual and empirical research. The paper concludes with a discussion of additional applications of the behavioral framework of LINMAP to other marketing decision areas.
An Algorithm for Optimal Inventory Policies For Systems with Joint Setup Costs
Authors: Hartfiel D. J. , Curry G. L.
Published: November 2008

This paper presents an algorithm inventory policies for a class of multi-product dependent setup cost problems. The operational policy under consideration is to replenish jointly, at a reduced cost, all products of the dependent class which are to be ordered in a scheduling period. Demands are assumed to be random with known probability distributions. Convergence of the iterative algorithm, to the optimal solution under suitable hypotheses is proven. Comparisons with the results of a simpler algorithm by Simmons demonstrate the cost advantages of our method.
Decision Analysis Expert Use
Authors: Morris Peter A.
Published: November 2008

This paper is the first in a series of articles introducing a new conceptual and methodological framework for the use of experts in decision situations. Presented is the first theory of expert resolution wholly consistent with the Bayesian or subjectivist view of probability. The approach taken rests philosophically on the foundations of decision analysis. The results form practical tools for solving expert resolution problems.

The present paper develops a structure in which the expert resolution problem may be logically formulated and conceptually solved. A framework is developed which enables a decision maker to encode his state of information concerning an expert. Application of the tools of Bayesian inference provides a mechanism by which a decision maker can incorporate an expert's opinion into his own.

The more complicated case in which a decision maker is confronted with the diverse judgments of more than one expert is also addressed in detail. Additionally, the problem of determining the economic worth of one or a panel of experts is presented.
A Production Scheduling Problem with Sequencing Considerations
Authors: Prabhakar T.
Published: November 2008

A type of production scheduling problem with sequencing considerations existing in several manufacturing facilities in chemical industry is formulated as a mixed integer programming problem and solved using a branch and bound search algorithm. The problem has two unusual sequencing aspects, namely, (1) a product to be sequenced can be split up amongst the reactors which, described in sequencing literature as job-splitting, is not usually allowed in machine sequencing problems and (2) the number of products to be sequenced on a given equipment as well as the product sequence need to be simultaneously determined. Some computational experience is reported.
Preference Order Dynamic Programming
Authors: Mitten L. G.
Published: November 2008

The dynamic programming recursive procedure has provided an efficient method for solving a variety of multi-stage decision problems in which the objective is measured by a real valued utility function. In this paper we propose that the real valued objective function be replaced by preference relations. Sufficient conditions are given on the structure of the preference relations to insure that the recursive dynamic programming procedure yields an optimal sequence of decisions.

The solution method is well adapted to an interactive mode of implementation in which there is a dialogue between the decision maker and a source of information and analysis (e.g., a computer). The “computer” collects, analyzes, and presents information on a set of alternatives to the decision maker who then communicates to the “computer” his choice of the best alternatives in the set. The process is repeated, stage by stage, thus generating an optimal sequence of decisions.

The approach should be particularly useful in dealing with multi-stage decision problems involving design and/or operation of facilities and multi-period public projects where a variety of desiderata must be considered (i.e., a simple cost or benefit function is inadequate).
A Note on the Ratio of Two Normally Distributed Variables
Authors: Hayya Jack , Armstrong Donald , Gressis Nicolas
Published: November 2008

This note is a continuation of a previous paper on normal approximations of standard forms. The standard form treated here is the ratio of two normally distributed variables. It is found that a suitable transformation of this ratio is approximately normally distributed provided that the coefficient of variation of the denominator is less than 0.39.
A Model for Manpower Management
Authors: Lilien Gary L. , Rao Ambar G.
Published: November 2008

A model for manpower management is presented based upon the study of a large technical department of a corporation. The model can be used in an optimization mode to determine recruiting plans, given manning needs, and in a simulation mode to project the results of changes in salary structure or advancement policies. The model explicitly recognizes different levels of performance at each job level, and the fact that certain sources of employees are more likely to produce “better” employees than others. Also modelled is the phenomenon of the “learning period”—the time it takes for a person to approach his potential in a given job. Several numerical examples of the use of the model based on observed data are presented.
A Computer-Based Corporate Planning System
Authors: Hamilton William F. , Moses Michael A.
Published: November 2008

The key to effective analytical support of the strategic planning process is not simply a corporate model, but an integrated system of models with appropriate software support. This paper describes a computer-based corporate planning system which combines the analytical power of optimization with simulation capabilities and more specialized planning models as elements of an interactive management system. The system has been designed to aid both periodic and ad hoc planning decisions in a large multi-national firm and can be implemented in a wide variety of corporate contexts.
Solving the “Marketing Mix” Problem using Geometric Programming
Authors: Balachandran V. , Gensch Dennis H.
Published: November 2008

This paper investigates the optimal allocation of the marketing budget within the marketing-mix decision variables so that sales (or profit) is maximized in a planning horizon. Since the influence of marketing mix variables upon sales are, in reality, nonlinear and interactive, a geometric programming algorithm is used that solves this problem. A procedure to estimate a functional of sales on the marketing mix and environmental variables utilizing the experienced judgments of the firm's executives and the raw data is provided. The derived functional is later optimized by the Geometric Programming algorithm under a constraint set consisting of budget and strategy restrictions imposed by a firm's marketing environment, and conditions under which the optimal solution is either local or global are identified. An empirical application for a large midwestern brewery is provided which utilizes and illustrates both the estimation an optimization procedures.
Optimum Checking Schedules for Systems Subject to Random Failure
Authors: Keller Joseph B.
Published: November 2008

An optimum checking schedule is one that minimizes the expected cost, which is the sum of the cost of checking and the expected loss due to an undetected failure. The problem is made tractable by supposing that checking is so frequent that it can be described by a continuous density n(t) of checks per unit time. The optimum n(t) is found by the methods of the calculus of variations. An explicit result is given when the loss is proportional to the duration of an undetected failure. A minimax solution is also given for the case in which the probability of failure is not known.
Flowshop Sequencing Problem with Ordered Processing Time Matrices
Authors: Smith M. L. , Panwalkar S. S. , Dudek R. A.
Published: November 2008

A flowshop sequencing problem having an ordered processing time matrix is defined. Job and machine characteristics resulting in processing time relationships that have logical and practical bases are discussed. An optimizing solution procedure for a special class of ordered matrix problem is presented along with proof of optimality.
Note—A Computational Survey of Methods for the Set Covering Problem
Authors: Christofides Nicos , Korman S.
Published: November 2008

This paper is a survey of available methods for the solution of the Set Covering Problem. The prime objective has been to establish the computational efficiency and relative merits of the various algorithms that have been proposed. To this end five methods have been programmed and tested on the same set of 33 test problems some of which can be found in the literature and the rest of which were randomly generated. Some of the methods examined have—as far as the authors are aware—never been previously tested, and in some cases some surprising results have been noted.

In addition, one type of tree search method has been studied in some greater detail and new techniques involving multiple dominance tests, and the calculation of a better lower bound have been suggested to limit the search. This resulting algorithm was found to be better than the original one by orders of magnitude in both computation times and numbers of tree-nodes generated, and has proved to be the most efficient of the methods tested.
Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions
Authors: Philippatos George C. , Gressis Nicolas
Published: November 2008

Conditions of equivalence are established among the following portfolio selection criteria: (1) Mean-Variance (E-V), (2) Second-Degree Stochastic Dominance (SSD), and (3) Mean-Entropy (E-H), for portfolios whose returns are characterized by-Uniform, Normal, and Lognormal probability distributions. We also assume that all portfolios derive from the same family of distributions and consider only the cases where the cumulative density functions intersect. In comparing the three selection criteria, under the three posited probability distributions, we utilize a combination of mathematical and graphical analyses. It is concluded that the three efficiency criteria are equivalent for uniformly and normally distributed portfolio returns. For lognormally distributed portfolio returns, the SSD criterion is optimal. Its efficiency, however, is sufficient but not necessary to establish efficiency for E-V and E-H. On the other hand, given the empirical similarities between E-V and SSD derived portfolios, and the close correspondence between the E-V and E-H criteria, the potential use of E-H becomes more appealing because of its distribution free nature.
Note—A Note on “A Simple CPM Time-Cost Tradeoff Algorithm”
Authors: Goyal S. K.
Published: November 2008

A Note on “A Simple CPM Time-Cost Tradeoff Algorithm” (Siemen, N. 1971. A simple CPM time-cost tradeoff algorithm. Management Sci. 17 (6, February) 354–363.).
Zero-Sum Games with “Almost” Perfect Information
Authors: Ponssard Jean-Pierre
Published: November 2008

The present paper generalizes the concept of perfect information to games in which the players, while moving sequentially, remain uncertain about the actual payoff of the game because of an initial chance move. It is proved that the value of such games with “almost” perfect information can still be computed using backward induction in the game tree. The optimal behavioral strategies obtained by a dynamic procedure may, however, require randomization. A typical illustration of such games is poker.