bluuebunny/crossref_metadata_2025 huggingface dataset:
Decision Rules in Chance-Constrained Programming: Some Experimental Comparisons
Authors: Smith Douglas V.
Published: November 2008

A stochastic programming model for evaluation of investment in irrigation is presented. The model reflects the complex hydrologic and economic interactions that arise from consideration of the conjunctive use of ground and surface water, the need for the provision of drainage to irrigated lands, and the use of some lands for rice cultivation. The implications of stochastic precipitation are discussed. Several decision rules for system operation are presented and discussed in terms of computation requirements and the possibility of field implementation.

Deterministic equivalents to the probabilistic water requirement constraints are derived for zero-order, linear, and two-piece decision rules, and the model is solved with alternate assumptions regarding the form of the rules to be used. An irrigation project proposed for Bangladesh is chosen to illustrate some possible consequences for investment planning of the choice of decision rules. Decision rules in chance-constrained programming are seen as tools for effecting good approximate solutions to stochastic programming problems when used with knowledge of the technical aspects of the investment decisions to be analyzed.
Note—A Note on Decision Making and Replacing Sure Prospects with Uncertain Prospects
Authors: Shubik Martin
Published: November 2008

In the making of decisions where the valuation problem poses the major difficulty an individual may choose to replace a hard-to-evaluate certain prospect with a much easier to evaluate set of uncertain prospects.
Joint Pricing and Inventory Decisions for Constant Priced Items
Authors: Kunreuther Howard , Schrage Linus
Published: November 2008

This paper develops an algorithm for determining the pricing and ordering decisions for a firm that produces one product for which there is a deterministic demand curve that differs from period to period. It is assumed that the firm wants to maintain the same price for the product throughout the season. There is a fixed cost associated with each order placed (or alternatively, each batch produced) in addition to per unit ordering and storage costs for carrying inventory over time.
The Joint Stationary Multivariate Queue Length Distribution in a Single Server Queueing System with N Queues, Arbitrary Priorities, and a General Probabilistic Inter-Queue Transition Matrix
Authors: Wignall T. K. , Enns E. G.
Published: November 2008

In modern telephone systems utilizing computers, the realization of a single server feedback queueing system often arises. In this paper, it is assumed that an originating or transferred call to such a system requires a number of different services before leaving the system as a completed or rejected call. A customer may also repeat a portion of his services, omit some services, or leave the system after any service with some assigned probabilities. In this paper, we present a theorem on the joint multi-variate queue length distribution, in a system with N services or queues, arbitrary priorities, and a general probabilistic transition matrix inter-connecting the various queues.
An Analysis of a Multi-Line Re-Order System Using a Can-Order Policy
Authors: Maher Michael J. , Gittins John C. , Morgan Roger W.
Published: November 2008

This paper analyses an inventory system which employs a “can-order” policy. Under such a policy lines of stock are re-ordered when they run out, and at these times lines which have not run out are also re-ordered if the stock levels in particular lines are below the “can-order level.” The well-known policies of independent and of joint re-orders are extreme cases of a can-order policy. Optimal values of the initial stock level and the can-order level are found, and are given in graphical form for the cases of 2 and 3 identical lines. An approximate method is described which finds these values for higher numbers of lines, and the method is shown to be a significant improvement on the two basic policies. Finally, the extension of the model to the general case, in which each line may have a separate unit holding cost and a separate sales rate, is discussed and some proposals made for optimisation.
The Use of Distribution Functions to Represent Utility Functions
Authors: Berhold Marvin H.
Published: November 2008

This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution.
Representation and Analysis of Multi-Stage Problems in R & D
Authors: Lockett A. G. , Gear A. E.
Published: November 2008

The paper describes a method of representing and analysing the multi-stage, dynamic nature of many types of research and development projects. The method makes use of a number of well-known techniques, decision trees, mathematical programming and simulation in combination.

Each project which could form part of a laboratory portfolio is represented in a modified decision tree format called a “project tree,” and the project trees are then considered in one analysis based on heuristics. The approach is demonstrated using a small illustrative example, and an industrial case study is described, giving attention to computational problems of size.
A Mathematical Programming Model for Test Construction and Scoring
Authors: Feuerman Martin , Weiss Harvey
Published: November 2008

A method is presented for test construction and scoring which utilizes the knapsack model of mathematical programming. The method applies to examinations of the type in which a choice exists in the number of questions the examinee is required to answer. The method has been utilized with respect to a Mathematics examination and computer generated results of this test are provided.
Operating Policies in Multiechelon Dual-Constraint Job Shops
Authors: Fryer John S.
Published: November 2008

In this paper a simulation study to examine the effects of operating policies on the performance of a multiechelon dual-constraint job shop is described. A hypothetical shop in which machines and workers are constraining resources is the setting of the study. The shop consists of divisions comprised of work centers which, in turn, contain machines to which workers are assigned. There are fewer workers than machines. Operating policies consist of rules for dispatching and labor control. There are two levels of labor control—decision rules are used for allocating workers to divisions and then to work centers within divisions. The measures of shop performance are mean flow-time, flow-time variance, and worker transfers between divisions and work centers.

Labor control decisions prove to be important in their effect on both flow-time and labor transfer measures. In some cases labor control decisions are more important than dispatching decisions. The effects of dispatching decisions on flow-time measures are consistent with previous job shop research. Dispatching decisions also affect labor transfers.
Control Policies for a Single Server System
Authors: Balachandran K. R.
Published: November 2008

The paper deals with two parametric control policies for a single service facility when the arrivals are distributed as Poisson and the service durations have a general distribution. The N-policy is to turn on the server (i. e., open the service channel for service) when the queue size reaches the number N and turn him off when the system is empty. The D-policy is to turn on the server when the total work to be done reaches the value D instead. The optimum policies are compared for both the policies when the costs assumed are linear. It is shown that for constant service the optimal policies are equivalent and for exponential service the D-policy is not superior to the N-policy.
Tests for Suboptimal Actions in Discounted Markov Programming
Authors: Hastings N. A. J. , Mello J. M. C.
Published: November 2008

A new test for suboptimal actions in discounted Markov decision problems is proposed. The test is discussed in relation to that of MacQueen and Porteus and preferred computational schemes are given.
Simplification Activities in a Network Scheduling Context
Authors: Abernathy William J. , Demski Joel S.
Published: November 2008

Network scheduling activities are usually addressed in a two-stage process of static schedule determination and subsequent control monitoring. A more complete view combines these two subsets of decisions with information acquisition decisions into a dynamic optimization framework. Such a framework is developed and the familiar static schedule-control process is then interpreted as a cost-effective simplification of the more complete dynamic formulation. This provides a framework for highlighting the numerous choices made in specifying the typical two-stage process and for evaluating the various choice alternatives. A simulation example illustrates the simplification and its evaluation with the more complete framework.
A Variational Study of Optimal Resource Profiles
Authors: Cullingford G. , Prideaux J. D. C. A.
Published: November 2008

The paper describes a method of supplementing network analysis by taking a global view of project planning.

The sequencing constraints normally found in a project are condensed into restrictions on the quantity of work performed by any stage in its duration. The objective is to minimise cost, where cost is considered to vary both with project duration and with the instantaneous rate of change of resource.

Variational methods are used to produce optimal work-time and resource-time project profiles. The form of some constraints likely to arise in a project is considered, and the best profiles subject to certain constraints are derived and discussed.

The techniques have been used to obtain a lower bound to project cost and to estimate ideal project duration.
State Substitution and the Estimation of Transition Probabilities
Authors: Dent Warren T.
Published: November 2008

Variants of Markovian decision models are many. Of those concerned with the estimation of transition probabilities, few deal with the case of limited information in which only data on market shares are available. Where such investigations have been undertaken, the assumption of constant transition probabilities has been insurmountable. This paper offers a simple heuristic technique to estimate nonstationary transition probabilities, especially in the case where fluctuations in market shares are felt to reflect the effects of secondary considerations external to the transition probabilities as well as effects of the probabilities themselves. Dynamic and quadratic programming are the suggested tools of analysis.
Note—Economic Ordering Frequency for Several Items Jointly Replenished
Authors: Nocturne Dominique J.
Published: November 2008

We consider a problem typical of the batch processing industry. This problem arises when a product is packaged simultaneously into more than one type container after its manufacture, and when set-up costs are associated with the making of the product as well as the packaging of the various items. We formulate the production inventory problem so as to minimize the total holding and set-up costs and give a graphical solution for the two-item case.
Queuing Processes at Competing Service Facilities
Authors: Sobel Matthew J.
Published: November 2008

The queuing models constructed here have the feature that a service facility tends to lose its customers if they often encounter lengthy delays. Structurally, the arrival processes are assumed to depend on past waiting times, hence on past arrival and service processes. The cases investigated include a service facility with several competitors and a facility with very many competitors; these correspond roughly to oligopoly and to perfect competition in micro-economics. For the duopoly case, approximate analytical solutions are presented along with graphs for numerical solutions. A data sample is given that is moderately consistent with the duopoly model.
Steel Management on Two Continents
Authors: Harbison Frederick H. , Köchling Ernst , Cassell Frank H. , Ruebmann Heinrich C.
Published: November 2008

The success of any industrial enterprise is obviously dependent upon the effectiveness of its managerial organization and its supervisory personnel. There are differences in management in different industries and even within the same industry in a single country. And these managerial differences may be the single most important competitive difference. But, the differences may be even greater and more significant when comparisons are made on a cross-national basis. In Europe, for example, the concept of the function of management is quite different from that in the United States, as are the variances in the avenues of access to managerial positions.
The Uses of Game Theory in Management Science
Authors: Shubik Martin
Published: November 2008

Since the war, there has been a great growth in interest in the theory of organization. The size of many modern organizations has brought to the surface problems of communication and decision-making of a very different nature to those confronted by smaller groups. A large organization appears to be both quantitatively and qualitatively different from a small one. Information flows and decisions that could be comfortably handled by one “jack-of-all-trades” executive in a small organization or in a dictatorial system, where wastage may be no problem, must be broken down and handled by many specialists. In many cases they may never reach the one-man decision level but are finally acted upon by groups. The need to understand these vital processes of decision-making has impelled us to lay emphasis upon the gathering and study of information, the evaluation of goals, and the role of the individual decision-maker.

The new methods of game theory appear to provide an important approach to many of the problems of decision-making. In this survey of areas of application of game theory some problems which have been completely formulated, solved, and are of immediate practical value have been discussed in Sections 4 and 5. However, for those interested in the deeper and more important long-range problems which confront the researcher in the behavioral sciences, Section 6 indicates where some of the work of yesterday has taken place and where much of the work of tomorrow must lie.
Inventory Control and Price Theory
Authors: Whitin T. M.
Published: November 2008

In spite of the high level of interest in inventory control that has sprung up recently among statisticians, economists, and businessmen, very little has been written that indicates the fundamental connection between price theory and inventory control. Most of the inventory control systems now in operation assume a given price structure. The analysis is frequently restricted to cost minimization. Economic theorists, on the other hand,~have concerned themselves with profit maximization but have not ordinarily concerned themselves with the realistic details underlying the construction of their curves. Only in the event that other variables external to the cost minimization problem are assigned optimal values will the cost minimization problem be equivalent to profit maximization.
Recent Advances in Linear Programming
Authors: Dantzig George B.
Published: November 2008

As interest grows rapidly in industry on the potentialities of mathematical programming techniques, it appears worthwhile to have a paper devoted to some of the more promising developments which may speed up the transition from interest to use. Three topics have been selected (in three sections that follow) which have recently come into prominence: uncertainty, combinatorial problems, and large scale systems. The reader will find in the course of their discussions that a survey—though perhaps not a systematic survey—has been made of current techniques in the linear programming field.
Current Status of the Industrial Use of Linear Programming
Authors: Smith L. Wheaton
Published: November 2008

The 1955 Conference on Business Statistics (Held in Philadelphia, June 9 and 10, 1955, sponsored by the Wharton School of the University of Pennsylvania, and by the American Statistical Association. The panel on linear programming was organised by M. M. Flood.) included a two-day panel discussion on “The Current Uses of Linear Programming in American Business.” The participants in the panel represented a wide enough segment of those who have been active in linear programming to permit brief coverage of a major portion of the active applications. Consequently, this report attempts to summarize the “state of the art” on the basis of that conference (The report is based in part on a verbal summary at the close of the panel discussions by a committee which consisted of A. Orden, L. Wheaton Smith, Jr., and H. H. Cauvet.).
The Objectives of TIMS
Authors: Flood Merrill M.
Published: November 2008

Article II of the Constitution of The Institute of Management Sciences provides that: “The objects of The Institute shall be to identify, extend, and unify scientific knowledge that contributes to the understanding and practice of management.” This evening, I shall offer a few personal views and convictions concerning possible paths through the future to these goals.
N-Job, One Machine Sequencing Problems Under Uncertainty
Authors: Blau Roger A.
Published: November 2008

N jobs simultaneously arrive at a machine where they are to be processed. It is assumed that the processing times and due dates for the jobs are independent random variables whose distributions are known. The problem is to determine the optimal sequences of jobs, before processing begins, for various criteria of tardiness. It is shown that solutions are obtainable by ascertaining the optimal paths through a particular deterministic network. Furthermore, one may utilize a branch and bound technique to find these paths. For special classes of distributions, the solution procedure degenerates, whereby the optimal sequences may be determined by inspection.
Note—A Note on Least Squares Fitting of Functions Constrained to be Either Nonnegative, Nondecreasing or Convex
Authors: Dent Warren
Published: November 2008

Hudson [Hudson, D. J. Least-squares fitting of a polynomial constrained to be either non-negative, non-decreasing or convex. J. R. Statist. Soc. B. 31 113–118.] has described a complicated algorithm for least-squares fitting of polynomials constrained to be either nonnegative, nondecreasing, or convex. Alternate quadratic programming formulations which approximate general functions (not necessarily polynomials) by polygonal segmentation are presented here. The technique is simpler, more general and of wider applicability than that proposed of Hudson.
Empirical Comparison of Models for Short Range Forecasting
Authors: Groff Gene K.
Published: November 2008

Results of a simulation study of the short-range forecasting effectiveness of exponentially smoothed and selected Box-Jenkins models for sixty-three monthly sales series are presented. Brown's exponentially smoothed constant, linear and six- and eight-term harmonic models are compared with two seasonal factor models and ten Box-Jenkins models. The seasonal factor models are Winters' three parameter model and a single parameter model developed by the author. The forecasting errors of the best of the Box-Jenkins models that were tested are either approximately equal to or greater than the errors of the corresponding exponentially smoothed models. Test results indicate that the four exponentially smoothed seasonal models yield approximately equivalent accuracy for most data series. If a sharply defined pattern exists, the seasonal factor models can yield smaller forecast errors than the harmonic models. If no seasonal pattern exists, the errors of the exponentially smoothed models with seasonal components are only slightly greater than those of the constant and linear models.
Another Look at the PERT Assumptions
Authors: Kotiah T. C. T. , Wallace N. D.
Published: November 2008

A maximum entropy approach leads to a truncated normal distribution for the activity time in PERT analysis. Three different methods of fit are discussed, and a comparison with the standard assumption of a Beta distribution is made. The results suggest new ways of performing the PERT analysis.
Alternative Formulation of the Job Shop Problem with Due Dates
Authors: Holloway Charles A. , Nelson Rosser T.
Published: November 2008

The classical formulation of the static job shop scheduling problem with job due dates implies that the question of interest to the manager is: What is the best that can be done to meet due dates with fixed resources? Here, two alternative formulations of the problem are proposed; one because of its practical appeal, the other because of its methodological appeal. The latter is used to develop a multi-pass heuristic scheduling procedure aimed at providing a practical tool for attacking any of the three formulations of the problem. This paper describes the basic structure of the scheduling procedure, the machine coding of a specific version of the procedure, and computational experience with a set of test problems ranging in size up to fourteen jobs and seven machines.
An Imbedding Approach to Additive Value Zero-One Problems
Authors: White D. J.
Published: November 2008

Existing approaches to the determination of the parameters for zero-one additive value functions can involve a large amount of work. This paper considers an alternative imbedding approach which allows the parameters to be determined to within an error range 1/K within K steps. In considering the method itself specific elements of theory are developed relating to the existence of additive values for imbedding sets X · Y*, X · Ỹ where X is a subset of zero-one vectors, Y* is a countable subset of numbers in the range −∞ < y < ∞, and Ỹ is a connected open interval of the range −∞ < y < ∞. In seeking further approximation methods, it is necessary to investigate properties of the component value, u(·) over Y* and Ỹ. The coefficients of the zero-one variables are shown to be unique for Y* once two values have been preset. Under certain circumstances it can be demonstrated that a continuous u(·) over Ỹ exists, and that considerable variations in u(·) may be compatible with the specified preference structures, although in special circumstances u(·) is unique over Ỹ.
Descriptive Aspects of Team Theory: Observation, Communication and Decision Heuristics in Information Systems
Authors: MacCrimmon Kenneth R.
Published: November 2008

To examine the descriptive validity of the economic theory of teams and, more particularly, to study observation, communication, and decision behaviors, sixty business and government executives were asked to make recommendations for the optimal design of a hypothetical sugar plantation information system. Few of the subjects made mathematical calculations; instead they used observation, communication, and decision heuristics which seem representative of behavior occurring in real situations. Ten percent recommended the optimal team theory solution while the remainder exhibited inefficient and sometimes mutually inconsistent heuristics. In some cases too little information was collected and distributed: (1) information expected at particular communication or decision centers was not available at that center, and (2) information observed or communicated was not extensive enough to yield maximum expected net profits. In other cases too much information was collected and distributed: (1) the information, when used, did not yield big enough improvements to cover its cost, (2) the information, when used, resulted in a lower expected gross profit due to interdependencies, and (3) the information observed or communicated was never used. Implications of the results for both theory and practice are discussed.
A Weather Model for Simulating Offshore Construction Alternatives
Authors: Rothkopf M. H. , McCarron J. K. , Fromovitz S.
Published: November 2008

The time and cost required for offshore construction operations are often dominated by the influence of weather, particularly wave heights. Historical wave height data can be summarized in a simple probabilistic model that can be used in a Monte Carlo simulation of the construction operations. Such a simulation has been used effectively to evaluate alternative bids on pipeline projects in the Gulf of Mexico. This paper describes the Markovian wave height model we have incorporated in the simulation.
A Transshipment Model for Cash Management Decisions
Authors: Srinivasan V.
Published: November 2008

The cash management problem is concerned with optimally financing net cash outflows and investing net inflows of a firm while simultaneously determining payment schedules for incurred liabilities. The problem is formulated as a transshipment model to minimize the total cost of allocating sources of funds to different uses while retaining the possibility of transferring cash between sources. A numerical example is formulated using this model and its optimal solution is shown to be essentially the same as that of a linear programming formulation proposed by Orgler. Extensions of the methodology for examining the effects of different “minimum cash balance” requirements and for incorporating other institutional constraints are also outlined. The transshipment formulation is useful in organizing data for financial control. It is intuitively appealing and computationally more efficient (by a factor of about 30 to 1) than the linear programming formulation of the problem.
Set Partitioning and Chain Decomposition
Authors: Nemhauser G. L. , Trotter L. E. , Nauss R. M.
Published: November 2008

There is given a finite set I and a family of subsets of I. We consider the problem of determining a minimum cardinality subfamily that is a partition of I. A branch-and-bound algorithm is presented. The bounds are obtained by determining chain decompositions of directed acyclic graphs. The computation time required to determine a bound is bounded by a polynomial in the cardinality of I. Some computational experience is reported and relationships with other methods are discussed.
Note—A Note on Majority Rule under Transitivity Constraints
Authors: Blin J. M. , Whinston A. B.
Published: November 2008

In a recent paper [Bowman, V. J., C. S. Colantoni. 1973. Majority rule under transitivity constraints. Management Sci. 19 (9, May) 1029–1041.] Bowman and Colantoni have described an optimization model which they relate to problems of majority voting in the theory of social choice. Their optimization model was a linear integer programming problem. The purpose of this note is to indicate that an alternative view may be more useful viz. formulating the problem as a quadratic assignment type. We have discussed this in detail elsewhere [Blin, J. M., K. S. Fu, K. B. Moberg, A. B. Whinston. 1973. Optimization theory and social choice. Proceedings of the Sixth Hawaiian International Conference on Systems Science. Supplement on Urban and Regional Systems: Modelling Analysis and Decision Making. University of Hawaii.] and will limit ourselves here to some brief comments.
Further Comments on Majority Rule Under Transitivity Constraints
Authors: Bowman V. Joseph , Colantoni C. S.
Published: November 2008

In their note [Blin, J. M., A. B. Whinston. 1974. A note on majority rule under transitivity constraints. Management Sci. 20 (11) 1439–1440.], Blin and Whinston indicate that the linear integer programming formulation of the majority voting problem can also be formulated as a quadratic assignment problem. We wish to point out that both of these formulations are a result of the fact that majority decision functions can be linearized over the set of integer solutions to the linear program.
Nonlinear Effluent Charges
Authors: Ferrar Terry A.
Published: November 2008

This work derives an effluent taxation structure for meeting a specified level of regional environmental quality. It is demonstrated that the nonlinearity of the proposed charge scheme flaunts equilibrium results identical to linear user-charge programs but elicits superior dynamic characteristics. Moreover, through the use of an iterative stimulus-response algorithm we are able to minimize the technical information transfer among sectors by mapping response surfaces for polluter behavior. These continuously updated response patterns are then used to guide the system to a social optimum. Recognizing that the optimal allocation of environmental resources is likely to be a vacillating target, and that the existence of adjustment lags must be reckoned with in any operational context, we argue that meaningful policing of environmental quality will require the nonlinear taxation approach.
Allocation Processes with Variable Channel Queues
Authors: Hersh Marvin
Published: November 2008

A dynamic model is formulated for determining optimum operating policies in a variable channel queuing situation. Such policies are required when workers must be allocated to one of several jobs which have associated with them different waiting costs. In this model, two such jobs are considered: (a) a “queue job” i.e., serving customers in a queue, and (b) performing another task which does not involve waiting customers (called “fixed work”). The criterion of the model is a minimization of the sum of these costs: the cost of customer waiting, the cost of fixed work, and the cost of changing tasks.

Decision rules involving the assignment of workers depended upon the number of waiting customers, the anticipated arrival pattern, and the amount of uncompleted fixed work remaining. The model was run using arrival and service data obtained from a medium sized suburban bank together with implicitly derived cost data.
On a Class of Stochastic Optimization Problems with a Specified Growth Pattern
Authors: Nakamura Masao
Published: November 2008

We consider a system which consists of several subsystems. The outputs of these subsystems satisfy linear difference equations which specify the growth pattern of the output of the system over time. The state of each subsystem is described by a finite Markov chain, the transition probabilities of which are subject to our control. Associated with the Markov chain of each subsystem is a cost per unit output of the subsystem, and the cost is incurred as the subsystem occupies one of J states in each epoch. The problem of minimizing the total expected cost with respect to the transition probabilities over a sufficiently long period of time is shown under certain conditions to reduce to a collection of n independent programs. Each of these can be solved by column generation techniques.
A Long-Range Selection and Timing Analysis System for Facility Location: Implementation
Authors: Meyer Carl F.
Published: November 2008

This paper describes the application of a mixed-integer program to the problem of providing strategic decisions for the selection and timing of a set of proposed facilities to serve distinct geographic regions. Solutions to this selection-timing process are obtained by the system presented so as to maximize the ratio of total net revenues to total assets. In addition, a series of optimal integer solutions to a large-scale problem is included with discussion and analysis.
A Bayesian Sequential Multi-Decision Problem
Authors: Noe N. H. , Ehrenfeld S.
Published: November 2008

A formal Bayesian framework is provided for the problem where some possibly contaminated data item can be collected periodically and where additional information about each period's true data value can be obtained at some cost. A decision is made each period with loss depending on the true data value and the decision. The special case with normal distributions and quadratic loss is formulated as a dynamic programming problem, and results include proof that the optimum policy structure calls for a more expensive form of data collection initially with less expensive data collection after the process parameters are better known.
Bounded Production and Inventory Models with Piecewise Concave Costs
Authors: Love Stephen F.
Published: November 2008

An n period single-product single-facility model with known requirements and separable piecewise concave production and storage costs is considered. It is shown using network flow concepts that for arbitrary bounds on production and inventory in each period there is an optimal schedule such that if, for any two periods, production does not equal zero or its upper or lower bound, then the inventory level in some intermediate period equals zero or its upper or lower bound. An algorithm for searching such schedules for an optimal one is given where the bounds on production are −∞, 0 or ∞. A more efficient algorithm assumes further that inventory bounds satisfy “exact requirements.”
Statistical Analysis for Queueing Simulations
Authors: Fishman George S.
Published: November 2008

This paper presents a method for estimating the variances of sample performance measures in queueing simulations, for removing the bias in these sample measures due to initial conditions and for deriving approximating confidence intervals for the true performance measures. It also describes how a variance reduction can be achieved using the method when comparing performance measures for two queue disciplines. The approach requires only that every time the system passes through the empty and idle condition future behavior is independent of past behavior.
Profit Analyses and Sequential Bid Pricing Models
Authors: Kortanek K. O. , Sodeni J. V. , Sodaro D.
Published: November 2008

A bid pricing strategy based upon opportunity costs is presented for the firm confronted with the problem of competitively pricing a sequence of sealed tenders for future undifferentiated but interrelated contract work. Each contract, if awarded, will require the expending of predetermined amounts of several restricted resources at a later time. A goal of the bidding strategy is to determine a price structure of the winning bids which maximizes the total contribution over direct costs associated with the time period of resource utilization. According to various levels of complexity of data, several models of the problem are developed together with optimal bid price rules. Each optimal rule involves scarce resource “cost” charges for future opportunities and competitive advantages according to the general bid rule form: OPTIMAL BID PRICE = DIRECT COSTS + OPPORTUNITY COSTS + COMPETITIVE ADVANTAGE FEE.

Experiences are also given of an adaptive and conditional implementation of the general bid rule for a major chemical manufacturer in a complex business area where sales orders are determined by competitive bidding.
Note—On the Weber Problem with Rectangular Distance: A Comment
Authors: Huriot J. M. , Perreur J.
Published: November 2008

A comment about Watson-Gandy, C. D. T. 1972. A note on the centre of gravity in depot location. Management Sci. 18 (8, April) B 478–B 481.
Inventory Policy and Trade Credit Financing
Authors: Haley Charles W. , Higgins Robert C.
Published: November 2008

It is common business practice to purchase inventory on open account. Consequently, purchased inventory can be considered to be financed in whole or in part with trade credit. This paper investigates the relationship between inventory policy and trade credit policy in the context of the basic lot-size model. It demonstrates that, in general, optimality requires order quantity and payment time decisions determined simultaneously. The conditions under which the standard solutions are optimal are also developed.
Analysis of the Allocation of Resources in Family Planning Programs
Authors: Lawrence Charles E. , Mundigo Axel I. , Revelle Charles S.
Published: November 2008

The reduction of population growth rates through family planning programs is being attempted in many of the developing nations of the world. This activity lends itself aptly to mathematical modelling. Building from the well-known difference equation model of population growth, a model is constructed which integrates population dynamics, program activities and resource consumption. The model may be used predictively to assess the outcome of various program activities. Alternatively, it may be used to determine the pattern of activities which yields the greatest reduction in births under the projected resource constraints. A further use of the model is the identification of the parameters to which predictions are most sensitive; such information provides valuable insights to those gathering the input data. The model is here applied to two family planning programs currently in progress. An evaluation of the feasibility of the program's goals is provided, as well as information on limiting resources, data sensitivity and the most important ages for contraceptive acceptance. The model's generality is such that it can be applied to most birth control programs which are planned at the national or regional level.
Letter to the Editor—On Lawler's K Best Solutions to Discrete Optimization Problems, 2
Authors: Marshall James
Published: November 2008

Comment on Lawler, Eugene L. 1972. A procedure for computing the K best solutions to discrete optimization problems and its application to the shortest path problem. Management Sci. 18 (7, March) 401–405.
Financing Public Hospitals in Ontario: A Case Study in Rationing of Capital Budgets
Authors: Jackman H. W.
Published: November 2008

A real system is described where the normal assumptions of capital rationing are violated. A goal programming model of this system is developed which allows a decision maker to choose the basis upon which an objective could be computed. The major part of this model is an integer programming algorithm leading to selection of the projects which optimize the system according to the basis chosen yet can be used on a relatively small computer. Finally, speculation on the possible use of this tool in other public sector decision making activities is presented.
Preface and Guide
Authors: Geoffrion A. M.
Published: November 2008

My objective in assembling this issue was to garner articles that would be of clear and present interest to those who professionally develop or apply mathematical programming techniques. It was not enough for a prospective paper to be competent, original, or even a dazzling display of intellectual prowess. Rather, each paper selected had to satisfy the more difficult criterion of usefully supporting, illuminating, or advancing the current state-of-the-art of applicable mathematical programming.
NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems
Authors: Klingman D. , Napier A. , Stutz J.
Published: November 2008

The purpose of this paper is to describe the development, implementation, and availability of a computer program for generating a variety of feasible network problems together with a set of benchmarked problems derived from it. The code “NETGEN” can generate capacitated and uncapacitated transportation and minimum cost flow network problems, and assignment problems. In addition to generating structurally different classes of network problems the code permits the user to vary structural characteristics within a class.

Problems benchmarked on several codes currently available are provided in this paper since NETGEN will also allow other researchers to generate identical problems. In particular, the latter part of the paper contains the solution time and objective function value of 40 assignment, transportation, and network problems varying in size from 200 nodes to 8,000 nodes and from 1,300 arcs to 35,000 arcs.
Mathematical Programming Book Reviews: 1965–1972
Authors: Gerber Fred
Published: November 2008

Approximately two hundred books on mathematical programming have been published during the past eight years. Most workers in this field have immediate access to only a minor fraction of these, but would have at least vicarious access to many of the rest through book reviews if only they knew where to look. That is the primary motivation for this bibliography of book reviews published during the years 1965–1972. A secondary reason is simply to furnish a reasonably comprehensive list of recent books on mathematical programming.
Erratum: N Job, One Machine Sequencing Problems Under Uncertainty
Authors: Blau Roger A.
Published: November 2008

An erratum to “N job, one machine sequencing problems under uncertainty”, Vol. 20, No. 1 (September 1973), pp. 101–109.
Erratum: On Characterizing the Extrema of a Function of Two Variables, One of Which if Discrete
Authors: Kumin Hillel
Published: November 2008

An erratum to “On characterizing the extrema of a function of two variables, one of which if discrete”, Vol. 20, No. 1 (September 1973), pp. 126–129.
A Diet Model with Protein Quality Variable
Authors: Smith Victor E.
Published: November 2008

Malnutrition is a serious obstacle to development in many countries. To deal with it effectively we must know how to provide adequate nutrition in an economical way. Linear programming will determine the most economical set of foods or production activities if the set of nutrients needed can be specified in absolute amounts or as fixed ratios, but this will not suffice for one of the most pressing nutritional problems—the protein problem. It is impossible to specify the quantity of protein required in this way. That quantity depends upon the concentration of protein in the diet and the “quality” of the protein (its amino acid composition). The greater the concentration, the less efficiently the protein is used; the better the quality, the more efficiently. For a least-cost diet, quality and quantity must be determined simultaneously, but the relationships are nonlinear. This paper presents a model, with one nonlinear restraint, that determines a least-cost diet in which the quality and the quantity of the protein are jointly and optimally determined.
Health Manpower Systems: An Application of Simulation to the Design of Primary Health Care Teams
Authors: Uyeno Dean H.
Published: November 2008

A method was developed for the evaluation of alternative primary health care team compositions and for the examination of skill levels for new categories of personnel. This procedure determines the appropriate composition of primary health care teams for differing demand levels and facility availabilities.

A simulation model of a general primary health care delivery unit was developed as part of this procedure. This simulation model, given demand schedules, team compositions, and facility levels, produces information relating to the efficiency and effectiveness of that alternative.

An application of the simulation model and the evaluation procedure was made to the area of pediatrics. A time study was taken of pediatric office practice. The data gathered therein were analyzed and used to create various demand schedules. Task-capability lists were created for various proposed categories of allied child health personnel, and these personnel were incorporated into various alternative team compositions and tested against varying facility and demand levels. Results indicate there are instances where a team structure is inappropriate and that the first member added to aid the physician is probably a person to assume lower level repetitive tasks.
A Horizon-Varying, Zero-One Approach to Project Scheduling
Authors: Patterson James H. , Huber Walter D.
Published: November 2008

Bounding techniques similar to those used with branch and bound procedures are used in this study in conjunction with zero-one programming to produce minimum duration schedules for the resource constrained, project scheduling problem. The algorithms developed consist of examining the feasibility of a series of zero-one programming problems rather than solving one zero-one problem optimally. Computational results demonstrate the advantage of this method over using zero-one programming without employing any form of bounding. A comparison with other exact procedures for solving the resource constrained, project scheduling problem is also given.
A Modified Linear Learning Model of Buyer Behavior
Authors: Lilien Gary L.
Published: November 2008

A stochastic model of individual buyer behavior is developed from a set of postulates about the buying process. The postulates are shown to imply a linear learning model modified by a term to explain response to pricing stimuli. Thus, a customer's purchasing probability is modelled as a combination of the effect of his past purchasing behavior plus the effect of price-variation in the market. Methods are developed to calculate short- and long-term probabilistic properties of the process. A method for parameter estimation is included. The model differs from past modelling efforts in this area in that a controllable variable, product price, is explicitly included in the model-structure, allowing the model to be used to aid in pricing decision making under a certain set of assumptions about competitive behavior in a market situation.
A Multi Product Joint Ordering Model with Dependent Setup Cost
Authors: Chern Chung-Mei Ho
Published: November 2008

A multi product, continuous review inventory model with dependent setup cost is studied and a joint ordering policy is defined. The development of the model is based on the independent (R, Q) policy. A can order point is derived for each product such that if the inventory level of one product drops to its reorder point, all products with inventory level less than or equal to their can order points are ordered together. The analytic results are given for the unit Poisson demands. Simulation experiments are used to compare the joint ordering policy with the independent ordering policy for the case of Stuttering Poisson demands. It is learned that the joint ordering policy achieves a substantial saying in total cost over the independent ordering policy.
Erratum—Tests for Suboptimal Actions in Discounted Markov Programming
Authors: Hastings N. A. J. , Mello J. M. C.
Published: November 2008

Erratum—Tests for Suboptimal Actions in Discounted Markov Programming (Vol. 19, No. 9 (May 1973), pp. 1019–1022).
Job Shop Scheduling with Due Dates and Variable Processing Times
Authors: Holloway C. A. , Nelson R. T.
Published: November 2008

A multi-pass heuristic scheduling procedure developed for job scheduling problems with deterministic processing times is tested with processing times that are random variables. The heuristic procedure, which uses expected processing times, typically generates a delay schedule (i.e., a schedule in which some operations are delayed while the machine to process these operations is kept idle awaiting the arrival of another operation). Simulation is employed to compare the performance of the schedule generated by the heuristic procedure, a nondelay transformation of that schedule, and the nondelay schedules obtained with four single-pass dispatching rules. The criteria employed are fraction of jobs tardy, mean tardiness, variance of tardiness, and maximum tardiness. The delay schedule produced by the heuristic procedure was found to be markedly superior under certain conditions. Under other conditions, the relative performance of the scheduling rules appears highly problem dependent. Implications of these results are discussed with respect to further research.