bluuebunny/crossref_metadata_2025 huggingface dataset:
Machine Replacement with Stochastic Costs
Authors: Kalymon Basil A.
Published: November 2008

The machine replacement model studied assumes that, at the end of each discrete interval, the state of deterioration of a machine and the current cost of replacement become known. A decision to keep or to replace must then be made, given that future deterioration and costs are determined by a known Markovian process. A finite set of possible states of deterioration is considered, including a “failed” state at which replacement by a “new” machine must occur. The operating cost is an increasing function of the level of deterioration, and replacement cost is the difference between new machine cost and salvage value. For both a finite and infinite planning horizon, given current cost, the optimality of a “control level” policy is demonstrated. Linear programming and policy iteration methods exploiting problem structure for the calculation of optimal policies are derived.
A Generalized Lagrange Multiplier Algorithm for Optimum or Near Optimum Production Scheduling
Authors: Evans J. P. , Gould F. J.
Published: November 2008

In this paper we apply the concept of generalized Lagrange multipliers, introduced by Everett [Everett, H. 1963. Generalized lagrange multiplier method for solving problems of optimum allocation of resources. Oper. Res. XI 399–417.], to the development of an algorithm for a one-period multi-product production model, where the objective is to maximize profit subject to constraints on aggregate regular time and overtime production. We assume no difference between the cost of idle time and regular time labor, so that the regular time cost is fixed. Overtime cost is variable. The price for each product is constant (independent of quantity sold), and everything produced can be sold. The optimum production schedule (maximum profit) will depend upon revenues, overtime costs, setup times, and productivities.
An Overview of the Mathematical Theory of Games
Authors: Lucas William F.
Published: November 2008

A cursory survey of the theory of games is presented. The basic models for games in extensive form, normal form, and characteristic function form are discussed, and some generalizations and extensions of these models are mentioned briefly. Some general remarks about the applicability of the theory are made in §2, and a few-specific applications are referred to in sections subsequent to the description of the particular models. Mention is made throughout this paper to the other game theoretic articles in this issue in an attempt to place them somewhat within this outline of the subject.
On Gaming and Game Theory
Authors: Shubik Martin
Published: November 2008

Gaming and game theory are two extremely different yet highly related disciplines. It is of considerable use to a practitioner of either of these disciplines that he be aware of the relationship of one to the other. This paper attempts to provide a sketch of game theory for those whose prime concern is gaming.
The Use of Multiple Ranking Procedures to Analyze Simulations of Management Systems: A Tutorial
Authors: Kleijnen Jack P. C. , Naylor Thomas H. , Seaks Terry G.
Published: November 2008

This paper describes the use of multiple ranking procedures to analyze data generated from computer simulation experiments with models of management systems. After outlining the rationale for the use of multiple ranking procedures with computer simulation experiments and defining some basic terminology, we examine several specific multiple ranking procedures. Careful attention is given to the assumptions underlying the different multiple ranking procedures and the extent to which these assumptions are satisfied by the data generated by simulation experiments. An example model is included to illustrate the applicability of multiple ranking procedures to simulation experiments in management science.
A Decision and Value Approach to Research Personnel Allocation
Authors: Childs Martin , Wolfe Harvey
Published: November 2008

A problem which exists in a large research laboratory is the allocation of professional people to work on research projects. Each department manager must allocate his personnel so that effectiveness, value of a given man to a given project, is maximized. Computationally, the transportation technique may be used to solve the problem if it is possible to determine the individual coefficients (or effectiveness values) giving the relative value of the ith man to the jth project, for all i, j. This paper describes a technique for determining these effectiveness values. The effectiveness values are subjective, and reflect the value judgments of the department manager and of those who assign projects. The philosophy used in producing the effectiveness values is to simplify the manager's decisionmaking task in expressing his value judgments to comparing only two alternatives with respect to a single criterion at one time. The results of the ratings taken are reduced to produce a set of normalized effectiveness values. The use of the technique in a model allocation problem is shown. The application of the technique need not be confined to a personnel allocation problem, but can be applied to any resource allocation problem where the objective is to optimize a subjective measure.
On the Evaluation of Shortage Costs for Inventory Control of Finished Goods
Authors: Oral Muhittin , Salvador Michael S. , Reisman Arnold , Dean Burton V.
Published: November 2008

This paper summarizes work performed in evaluating shortage costs associated with stockouts for each of a manufacturer's seven thousand catalogued line items. A modified version of a decision tree model proposed by Yu Chang is employed in a determination of estimated unit shortage costs for a stratified random sample of items. The data required by this model for describing customer behavior were obtained via direct interviews and an extensive mail survey, while the remaining data were extracted from records of the manufacturer. The results are extended to all items on the basis of an excellent correlation between, the evaluated unit shortage costs and unit gross profits of the items in the sample.
Précis—An Operations Research Approach to the Management of Government Cost-Plus-Award- Fee Contracts
Authors: Thomas John E. , Manton Edgar J. , Stoms James M.
Published: November 2008

This paper, written by authors with experience as both government and contractor managers of CPAF contracts, sets out a simple quantitative model that serves to introduce some objective checkpoints to aid the project manager and government representative in achieving optimum performance under a subjective incentive system.
A Sequential Stochastic Assignment Problem
Authors: Derman Cyrus , Lieberman Gerald J. , Ross Sheldon M.
Published: November 2008

Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a “p” man is assigned to an “X = x” job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy.

In particular, if p1 ≦ p2 ≦ ⋯ ≦ pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's.

The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a “p” man is assigned to an “x” job is given by a function r(p, x).
Multiparametric Linear Programming
Authors: Gal Tomas , Nedoma Josef
Published: November 2008

The multiparametric linear programming (MLP) problem for the right-hand sides (RHS) is to maximize z = cTx subject to Ax = b(λ), x ≧ 0, where b(λ) be expressed in the form [Formula: see text] where F is a matrix of constant coefficients, and λ is a vector-parameter.

The multiparametric linear programming (MLP) problem for the prices or objective function coefficients (OFC) is to maximize z = cT(v)x subject to Ax = b, x ≧ 0, where c(I) can be expressed in the form c(v) = c* + Hv, and where H is a matrix of constant coefficients, and v a vector-parameter.

Let Bi be an optimal basis to the MLP-RHS problem and Ri be a region assigned to Bi such that for all λ ϵ Ri the basis Bi is optimal. Let K denote a region such that K = UiRi provided that the Ri for various I do not overlap.

The purpose of this paper is to present an effective method for finding all regions Ri that cover K and do not overlap. This method uses an algorithm that finds all nodes of a finite connected graph. This method uses an algorithm that finds all nodes of a finite connected graph. An analogus method is presented for the MLP-OFC problem.
Models for the Minimum Cost Development of Offshore Oil Fields
Authors: Devine M. D. , Lesso W. G.
Published: November 2008

Since the cost of developing a single offshore oil field usually runs in the tens of millions of dollars, savings due to better development policies could be quite significant. This paper presents a general model for developing offshore fields at minimum cost. The model applies to any field developed from fixed platforms, and thus could also be used directly for the development of fields on the north slope of Alaska. The basic limitations and possible utility of the model are discussed. The mathematical programming formulation of the problem is shown to be identical in general structure to the well-known warehouse location problem. Algorithms for solving the problem are developed, whereby the algorithm for a particular problem will depend upon the general form of the platform cost function. The algorithms developed are tested and shown to be computationally practical.
Earnings Estimates and the Accuracy of Expectational Data
Authors: Elton Edwin J. , Gruber Martin J.
Published: November 2008

This paper examines the accuracy of forecasts produced by mechanical forecasting techniques and three groups of analysts. The nine mechanical forecasting techniques are variations of exponentially weighted moving averages, naive models, simple moving averages, and regressions. One-, two- and three-year forecasts are used to evaluate these techniques.

The mechanical techniques exhibit statistically significant differences in their ability to forecast earnings per share, with the exponentially weighted moving averages producing the best forecasts. One-year forecasts produced by the best of the mechanical forecasting techniques were compared to the corresponding analysts' projections. No statistically significant difference could be discerned.
A Direct Approach to Choice under Uncertainty
Authors: Kamien Morton I. , Schwartz Nancy L.
Published: November 2008

In a problem of decision making under uncertainty, the payoff is random, obeying some probability distribution. The distribution depends upon both the problem faced and the action taken by the decision maker. For example, in the selection of a portfolio, funds are allocated among securities, each of which has an associated distribution over the return it yields. The allocation results in a composite probability distribution over the total return from the entire portfolio.

Although it is typical to select an action, which in turn implies a resulting distribution, we suggest in the present paper that it may sometimes be appropriate to select a probability distribution directly, or to view the problem abstractly as though the distribution were to be developed directly. We envision the decision maker selecting a most preferred distribution over payoffs via modification of an existing probability distribution at a direct monetary cost. Thus the family of distributions from which the decision maker can choose is implicitly defined by initial wealth, the original distribution, and the modification cost function.

A formal statement of a class of problems for which our direct approach may be appropriate is developed, followed by examples. The illustrations cover problems of preventive maintenance for a machine subject to failure, pricing of a product under threat of rival entry, and planning a risky R and D project.
Allocating Resources between Research and Development: A Macro Analysis
Authors: Gaver D. P. , Srinivasan V.
Published: November 2008

This paper attempts to coordinate at the macro level the research potential and the development capability of an organization in a competitive environment. New product ideas generate from various sources of research which are then processed (preliminary screening, market appraisal, technical development etc.) by the development section. In view of the randomness present in the above process, a backlog of ideas will normally be present awaiting development. The longer the delay in processing them, the greater are the chances of a competitor introducing the product in the meantime.

Simple queueing models are set up which abstract the essence of the problem, and reveal the causal relationships of the underlying structure. The decision variable (relationship of the research rate to the development rate) is optimized, and its sensitivity to changes in the parameters describing the environment is examined. Generalizations of the approach using Monte-Carlo methods arc also indicated.
Variance Minimization in Single Machine Sequencing Problems
Authors: Merten Alan G. , Muller Mervin E.
Published: November 2008

The variance of flow-time and variance of waiting-time performance measures are analyzed for the single machine sequencing problem. These measures are compared and contrasted to the performance measures of mean flow-time and mean waiting-time. In particular, while the two mean performance measures attain their minimums at the same job sequence, it is shown that the sequence that minimizes the variance of flow-time is antithetical to the sequence that minimizes the variance of waiting-time. However, the minimum values of the two variance measures are equal. Relationships are also derived for the special problems where either all the job processing-times are equal or all the job weights are equal.
Assembly Line Balancing using Best Bud Search
Authors: Nevins Arthur J.
Published: November 2008

A general purpose heuristic program (which has been applied to deductive question-answering and theorem proving) has now been applied to the problem of balancing assembly lines. The results indicate that the program is quite effective in its role as an assembly line balancer.
Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate
Authors: Crabill Thomas B.
Published: November 2008

This paper derives the form of a minimal cost rate stationary operating policy for an M/M/I queueing system with K possible service rates. The two costs of the system are a general cost rate dependent on the state of the system and a cost rate associated with each of the possible service rates. The optimal policy is completely characterized by if K − 1 numbers. The optimal service rate is shown to be nondecreasing in the state of the system.
Higher Order Tree Dual Approximation Methods for the Distribution Problem
Authors: Glover Fred , Klingman Darwin
Published: November 2008

This paper develops efficient algorithms for obtaining a dual feasible starting basis for the capacitated distribution problem. The motivation for the development of such a technique is threefold. Firstly, although efficient dual methods for solving such problems have been developed, none of these methods have addressed themselves to the problem of efficiently determining a dual feasible starting basis. Secondly, no counterpart method exists for obtaining a primal feasible starting basis for the capacitated problem; furthermore, the development of such a counterpart procedure is unlikely. Finally, because our approach provides a dual feasible basis that is both legitimate (i.e., nonartificial) and good (in terms of the dual functional), the synthesis of our procedure with one of the dual distribution methods should provide a more efficient computational algorithm for solving capacitated distribution problems than primal counterpart methods.
Dialectical Decision Theory: A Meta-Theory of Decision-Making
Authors: Mitrofff Ian I. , Betz Frederick
Published: November 2008

This paper presents a meta-logic of decision theory. It utilizes a dialectical formulation [Churchman, C. W. 1966. Hegelian inquiring systems. Internal Working Paper 49, Space Sciences Laboratory, Social Sciences Project, University of California, Berkeley, September; Mason, R. O. 1969. A dialectical approach to strategic planning. Management Sci. 15(8, April) B-403–B-414; Mitroff, I. I. 1971. A communication model of dialectical inquiring systems—A strategy for strategic planning. Management Sci. 17(10, June) B-634–648.] as a prescriptive methodology for minimizing statistical decision errors of the third kind; i.e., the error of solving the “wrong” decision problem when one should have solved the “right” problem. The dialectical formulation is chosen because it is the only existent methodological form which both utilizes conflict over value issues in a productive fashion and ensures a minimal sense of completeness in the decision-space of possible problem choice [Mitroff, I. I. On the general problem of building a generalized model of general models (in preparation).]. The result is the development of a meta-theory of decision-making. It is argued that the concept of a Dialectical Inquiring System [Mitroff, I. I. 1971. A communication model of dialectical inquiring systems—A strategy for strategic planning. Management Sci. 17(10, June) B-634–648; Mitroff, I. I. On the general problem of building a generalized model of general models (in preparation).] is to our meta-theory of decision-making as the concept of a lottery [Pratt, J. W., H. Raiffa, R. Schlaifer. The foundations of decision under uncertainty: An elementary exposition. J. Amer. Stat. Assoc. 59 353–375.] is to the ordinary theory of decision-making.
Substitution Effects in Geometric Programming
Authors: Theil Henri
Published: November 2008

The impact of price changes in geometric programming is analyzed in terms of technological substitution relationships. The method can also be applied to sensitivity analysis, which is illustrated by means of a numerical example.
Uncertain Value Functions
Authors: White D. J.
Published: November 2008

Value theory plays an essential role in the formal solution of decision problems, but the experimental determination of value functions is subject to errors of various kinds. Sensitivity analyses are methodologically invalid. An attempt is made to overcome the uncertainties in derivation of value functions, in a manner which is similar to the economist's “Pareto optimality” approach.

Results are presented for the 2-dimensional situation, and extended to the more general n-dimensional case. In the case when preferences and indifferences are certain the usual results follow.

It is shown how the results can be used to cut down the region of initial feasible solutions to a region within which the decisionmaker makes no initial discrimination, when the boundary regions are convex.

A comparison is made with the approaches of Luce and Aumann, whose work is of a similar, but not equivalent, nature.
On Hyperbolic Programming with a Single Constraint and Upper-Bounded Variables
Authors: Elmaghraby S. E. , Arisawa S.
Published: November 2008

The hyperbolic (or fractional) linear programming problem with only one aggregate constraint is solved by a simple and extremely efficient algorithm. The core step in the iterative procedure is the optimization of a linear function subject to a single linear constraint.
Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem
Authors: Albright Chris , Derman Cyrus
Published: November 2008

Certain sets of numbers {ain}, i = 0,…, n, n = 1, 2,…, are known characterize an optimal sequential assignment policy. In this paper the limiting behavior as n → ∞ of the ain's is studied.
A Measure of an Individual's Power in a Group
Authors: Hofshi Rami , Korsh James F.
Published: November 2008

A mathematical model is presented for assigning numerical weights to each individual of an organization. The model is based on verbal definitions presently used in the social sciences to describe an individual's power or influence within a group of individuals. Thus the numerical weights derived can be interpreted as measures of the power or influence that individuals have in an organization.

The model is not meant to be generally descriptive of group dynamics. It can be used, however, to obtain a group preference structure from individual preference structures.
The Minimum Covering Sphere Problem
Authors: Elzinga D. Jack , Hearn Donald W.
Published: November 2008

The minimum covering sphere problem, with applications in location theory, is that of finding the sphere of smallest radius which encloses a set of points in En. For a finite set of points, it is shown that the Wolfe dual is equivalent to a particular quadratic programming problem and that converse duality holds. A finite decomposition algorithm, based on the Simplex method of quadratic programming, is developed for which computer storage requirements are independent of the number of points and computing time is approximately linear in the number of points.
Technology and Environment
Authors: Simon Herbert A.
Published: November 2008

The solution of today's major social problems will come from more and better technology—not from less technology. For technology is just another name for human knowledge. We need to deepen our scientific knowledge, broaden our repertory of alternatives, and strengthen our technology of decision procedures. Above all, we need a more profound understanding of Man himself, for all human problems have their roots in our own nature.
The ORSA New Orleans Address on Compact City
Authors: Dantzig George B.
Published: November 2008

The failure of urban planners, politicians, and bureaucrats to cope with urban crises and come up with solutions that work, stems from a fundamental inability to deal with complexity. The urban environment is complex, inter-related, highly dynamic. Nothing less than a total-system approach using the tools of mathematical and computer simulation models can hope to attack the problems of urban over growth.

It is important to develop analytic, computer and simulation type models of the total urban system and of detailed subsystems in order to compare various arrangements such as the current megalopolis with its sprawl, and new satelite towns and cities built to make more effective use of vertical space and the round-the-clock use of facilities. Cities that make effective use of the vertical dimension and time, represent a viable alternative and should be given serious consideration.
Management Science, Ecology, and the Quality of Life: The Law and the Legal Process
Authors: Duggan Michael A.
Published: November 2008

The Law and the Legal Process are important ingredients in any attempt to insert “Quality of Life” inputs within an environmental control system. This paper discusses the interface between Environmental Concern and the Legal Process. It does not focus on current legislative enactments and proposals but rather upon the ontological constraints.
Necessary Conditions for Optimality for Paths Lying on a Corner
Authors: Speyer Jason L.
Published: November 2008

A class of optimization problems is investigated in which some of the functions, continuous in all their arguments, have continuous right- and left-hand derivatives but are not equal at a point called the corner. For this nonclassical problem, a set of first order necessary conditions for stationarity is determined for an optimal path which may have arcs lying on a corner for a nonzero length of time. Enough conditions are provided to construct an extremal path. This, in part, is achieved by noting that the corner defines a manifold in which the derivatives of all the functions are uniquely defined. Three examples, two of which represent possible aggregate production and employment planning models, illustrate the theory.
On a Discounted Replacement Problem with Arbitrary Repair Time Distribution
Authors: Sivazlian B. D.
Published: November 2008

The functional equation technique is applied to obtain explicit expressions for the long-term total expected discounted cost in replacement problems incorporating the downtime effect associated with the repair state of the failed component. Necessary and sufficient conditions for an optimal replacement policy are obtained and some asymptotic results are derived.
Erratum—A Note on Sharpe's Algorithm for Minimizing the Sum of Absolute Deviations in a Simple Regression Problem
Authors: Rao M. K. , Srinivasan V.
Published: November 2008

Erratum to the authors' paper “A Note on Sharpe's Algorithm for Minimizing the Sum of Absolute Deviations in a Simple Regression Problem”, Vol. 19, No. 2 (October 1972), pp. 222–225.
Forecasting and Systems Approach: A Frame of Reference
Authors: Jantsch Erich
Published: November 2008

Long range forecasting for social systems deals with complex feedback interactions between all sectors and elements of such systems, and thus inherently implies facing the challenge of the systems approach. The latter may be characterised as an attempt to understand the self-organizing behaviour of social systems and to grasp its potential dynamic implications. It aims at integration at least along four coordinates: horizontal (conceptual systems dimensions and different views and attitudes), vertical (planning levels), time/causality (exploratory and normative directions), and action-orientation (forecasting as the “inventive core” of planning and rational change processes). In this process of integration, forecasting finds a variety of tasks which are briefly enumerated.
Square Root Laws for Fire Engine Response Distances
Authors: Kolesar Peter , Blum Edward H.
Published: November 2008

An inverse square-root function is developed for the relation between average response distance and the number of locations at which response units are stationed in a region. Analysis of theoretical models, simulation data, and empirical measurements are used to confirm the square-root model.

The square-root response distance model is combined with response distance—response time relations to resolve decision problems important to the management of urban fire departments. The results can be used to find optimal resource allocations given resource constraints and response time standards, or to describe the response time consequences of proposed allocation plans.
A Time-Sharing Computer Program for the Solution of the Multiple Criteria Problem
Authors: Dyer James S.
Published: November 2008

This note presents a description of a time-sharing computer program written to implement a man-machine interactive algorithm for the solution of the multiple criteria problem. The interactive algorithm was suggested in a recent paper by Geoffrion, “Vector Maximal Decomposition Programming,” Working Paper No. 164, Western Management Science Institute, University of California, Los Angeles, September 1970. A unique feature of this program is the man-machine dialog which obtains information from the decision-maker through a series of simple, ordinal comparisons.
Media Scheduling: A Stochastic Dynamic Model Approach
Authors: Zufryden Fred S.
Published: November 2008

A stochastic model is developed with application to both the study of consumer behavior and the scheduling of advertising media. This model incorporates a stochastic response behavior model which examines changes in brand purchase probability over time through the integration of consumer advertising exposure response, purchase incidence behavior and purchase-event feedback constructs. The response behavior model provides the basis for the objective function of a general media scheduling model that is formulated as a binary integer mathematical programming system. Among the factors considered or reflected in the media model are the sales potentials of the target audience and respective market segments, advertising budget, media timing, exposure probabilities, and time patterns (e.g., advertising carry-over, forgetting and saturation effects). Finally, efficient heuristic programming techniques are proposed for solving the media model.
A Model for Cash Balance Management
Authors: Heyman Daniel P.
Published: November 2008

A model for minimizing the average cash balance subject to a constraint on the probability of stock-out is presented. The cash balance is described as an inventory process that changes because of deterministic and stochastic events. Recursive systems of equations are given to find (1) the distribution function of the cash level at any time and (2) the probability that all demands during some time interval are met. Then we examine the problem: minimize the expected time average cash balance subject to the condition that the probability that all demands are satisfied is at least some given number. It is shown that the optimal policy has a very simple form, which can be expressed verbally as, “never have any more cash on hand than is necessary to satisfy the constraint.”
Determination of Excess Stock Quantities
Authors: Hart Anthony
Published: November 2008

A procedure is described which can be used as an aid in solving the following problem: given excess stock of an inventory item, how much should be disposed of at a scrap price, and how much should be retained for regular sale, in order to minimize the present value of all the relevant costs. The minimum cost retention quantity is determined using a sequential search procedure based on the “Golden Section.” For each retention quantity considered, a procurement schedule is determined heuristi-cally according to a set of rules based on economic order quantities and economic “bridging” quantities. The costs associated with the determined procurement schedule and the scrap and retention quantities are discounted and summed to give the total present value cost. The heuristic method of determining procurement schedules is compared with a dynamic programming method. The results of applying the procedure to some inventory items are given.
A Note on the Possibility of Decentralization in a Model of Allocation of Resources
Authors: Maiti Pradip , Sengupta Ramprasad
Published: November 2008

The decomposition algorithm for the solution of large-scale linear programmes has been interpreted by Baumol and Fabian (Management Science, September, 1964) as a procedure for decentralized decision by the multi-division company or the multi-sector economy. While commenting on the possibility of decentralization in this context, they maintain that an economy's optimum point will not in general yield a sectoral optimum. The present note demonstrates that this contention is not valid.
Management Sciences in an Underdeveloped Country: The Case of Operations Research in Peru
Authors: Sagasti Francisco R.
Published: November 2008

This paper examines the development of management sciences in Peru, with particular reference to the introduction and diffusion of operations research in the 1960's. The reactions of government officials and executives in private industry to management science are analyzed. The educational and institutional aspects of the future of OR are also examined. The paper ends with a discussion of the methodological aspects of operations research work in underdeveloped countries.
On Normal Approximations of the Frequency Functions of Standard Forms Where the Main Variables are Normally Distributed
Authors: Hayya Jack C. , Ferrara William L.
Published: November 2008

Risk analysts frequently encounter functional relationships concerning costs and revenue which can be expressed as standard algebraic forms. The forms are quadratic, product, or mixed functions of variables which are normally distributed and not necessarily statistically independent. (The ratio functions will hopefully be the subject of a paper that follows this.) Generally, interest focuses on the construction of 2σ or 3σ probability intervals for each form. Since probability distributions of these forms, as far as the risk analyst is concerned, are neither tabled nor easily derived, the desired probability intervals are not easily constructed.

This paper shows through analysis, review of previous research, and simulation, that under ordinary conditions the probability distribution of these forms can be approximated by more population distributions (e.g., gamma or normal). The paper suggests rules of thumb that allow one to make probability statements about each form without recourse to costly simulation. An application to a financial planning model for an industrial firm augments the theoretical discussion.
Engineering Design Optimization Under Risk
Authors: Weisman Joel , Holzman A. G.
Published: November 2008

Since engineering designs generally involve a number of elements about which only partial information is available, design optimization should be conducted under conditions of risk. Utility is nonlinear with cost or revenue; consequently, the enterprise's view of risk is considered through utilities assigned to costs or revenues which deviate from the mean. This is termed “risk programming” to distinguish it from previous contributions in this area. General forms of the objective function, yielding expected utility, are derived for utility functions of two types. When the total cost distribution is normal, an exact solution requiring only a knowledge of expected total cost and the cost variance is obtained. For nonnormal cost distributions, an upper bound of the objective function, requiring knowledge only of the same two quantities, is obtained. A model for engineering design, which provides both the expected total cost and cost variance, is developed based upon division of the elements of variability into several categories. With this division, a reasonable computational procedure is possible. The procedure has been incorporated into a modified direct search optimization program capable of solving large-size design problems.
A Central Limit Theorem for Present Values of Discounted Cash Flows
Authors: Mantell Edmund H.
Published: November 2008

A renewal process is defined to represent the present value of a stream of money payments occurring at random times.The objective is to partially close a gap in the state of knowledge regarding the properties (asymptotic behavior) of certain cashflow models, scheduling models, and inventory models, all of which can be embedded in the context of replacement-reliability theory in general. The contribution of this paper is a characterization of the asymptotic distribution of a general capitalized random variable as the time-invariant rate of discount approaches zero. The main result is a central limit theorem demonstrating that the standardized distribution of the discounted random variable converges to the unit normal as the discount rate approaches zero.
Municipal Bond Coupon Schedules with Limitations on the Number of Coupons
Authors: Weingartner H. Martin
Published: November 2008

The optimum coupon schedule for serial bonds issued by municipalities has been solved as a knapsack problem, and is widely implemented in bank and nonbank underwriting firms. A large subset of issues carries the additional requirement that limits the number of distinct coupons which the underwriters may assign to the issue. The paper formulates this problem as a dynamic programming model and discusses the computational aspects relating to this formulation by comparing it with a direct 0/1 integer programming model. Some computational experience is also provided.
A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital
Authors: Warner D. Michael , Prawda Juan
Published: November 2008

The Nursing Personnel Scheduling Problem is defined as the identification of that staffing pattern which (1) specifies the number of nursing personnel of each skill class to be scheduled among the wards and nursing shifts of a scheduling period, (2) satisfies total nursing personnel capacity, integral assignment, and other relevant constraints, and (3) minimizes a “shortage cost” of nursing care services provided for the scheduling period. The problem is posed as a mixed-integer quadratic programming problem, which is decomposed by a primal resource-directive approach into a multiple-choice programming master problem, with quadratic programming sub-problems. Initial results suggest that a linear programming formulation, with a post-optimal feasibility search scheme, may be substituted for the multiple-choice master problem. The model is tested on six wards of a 600-bed general hospital, and results are presented.
Chromatic Scheduling and the Chromatic Number Problem
Authors: Brown J. Randall
Published: November 2008

The chromatic scheduling problem may be defined as any problem in which the solution is a partition of a set of objects. Since the partitions may not be distinct, redundant solutions can be generated when partial enumeration techniques are applied to chromatic scheduling problems. The necessary theory is developed to prevent redundant solutions in the application of partial enumeration techniques to chromatic scheduling problems with indistinguishable partitions and distinct objects. The chromatic number problem, which is the problem of finding the chromatic number of any graph, is a particular case of the chromatic scheduling problem. Two algorithms, basic and look-ahead, are developed for the chromatic number problem. Computational experience is given for each algorithm.
Discussion
Authors: Hertz David B.
Published: November 2008

Information technology, as emphasized by Charnes, Kozmetsky and Ruefli, will undoubtedly influence the formulation of urban goals significantly. The more that is known and disseminated about the condition of man, his hopes, aspirations and fears in an increasingly urban world, the more broadly based will be the goals he sets for himself. And yet, will this “explosion” of information technology lead to more effective choices of end objectives? One can only hope so, but the Charnes, Kozmetsky and Ruefli paper does not provide any clear evidence that this will be the case.
Discussion
Authors: Flax Michael J.
Published: November 2008

I want to begin by stating that I am doing research at one of the institutions that was formed in an attempt to cope with the a rapid changes occurring in information technology about which Dean Kozmetsky was talking in the paper he wrote with Professors Charnes and Ruefli. The Urban Institute is a problem oriented, multi-disciplinary research organization investigating urban problems. Many of the staff, including myself, have had experience in the “systems approach” which was used so extensively by defense research agencies.
Information Requirements for Urban Systems: A View into the Possible Future?
Authors: Charnes A. , Kozmetsky G. , Ruefli T.
Published: November 2008

The successful management of urban systems is becoming increasingly a matter of successful information about the urban area and its environment. Using information as a basis for developing a structure for, and outlining the flows in, an urban area, this paper develops a dual hierarchy of information requirements and management activities. Each level of the hierarchy is discussed in terms of the emergent problems and requirements that are likely to confront management scientists and urban administrators in the future. As the information requirements of urban areas become more complex and as the components of the urban system become more highly interrelated, developments in information technology can be expected to have a direct impact on the activities of urban area administrators. This development is illustrated here through the presentation of a selected number of possible impacts of information technology developments upon the information and management hierarchies of urban systems.
The Delivery of Ambulatory Care to the Poor: A Literature Review
Authors: Lave Judith R. , Leinhardt Samuel
Published: November 2008

The authors review the literature on the delivery of ambulatory care to the urban poor by isolating the crucial variables affecting the supply and demand for such services and organizing the literature around these concepts. The state of health of the poor, perception of health, and cost of care are examined as factors influencing demand. Then the consequences of various policies designed to intervene in the market are considered. Since little systematic date have been collected on the costs and benefits of these programs, the authors conclude by discussing an alternative to the current system of delivering ambulatory care to the poor and raise several issues for future research.
An Inverse-Basis Method for Beale's Quadratic Programming Algorithm
Authors: Land A. H. , Morton G.
Published: November 2008

This paper presents a version of Beale's Quadratic Programming Algorithm [Beale, E. M. L. 1959. On quadratic programming. Naval Res. Logist. Quart. 6 227–243; Beale, E. M. L. 1967. Numerical methods. J. Abadie, ed. Nonlinear Programming. Amsterdam.] for solving a problem of maximising a quadratic function under linear constraints. The modification discussed here makes it possible to retain the “inverse basis” tableau which has to be augmented by additional constraints to be called “auxiliary.” The algorithm has been successfully tested on a computer.
Improved Combinatorial Programming Algorithms for a Class of All-Zero-One Integer Programming Problems
Authors: Pierce John F. , Lasky Jeffrey S.
Published: November 2008

In an earlier paper [Pierce, J. F. 1968. Application of combinatorial programming to a class of all-zero-one integer programming problems. Management Sci. 15 (3, November) 191–209.] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical “and” and “or” operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds.

In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions.
A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem
Authors: Schwarz Leroy B.
Published: November 2008

A one-warehouse N-retailer deterministic inventory system is examined. The objective is to determine the stocking policy which minimizes average system cost per unit time over the infinite time horizon. Necessary properties of an optimal policy are derived, and optimal solutions for the one-retailer and N identical retailer problems are given. Heuristic solutions for the general problem are suggested, tested against analytical lower bounds and, on the basis of these tests, found to be near optimal.
Continuous-Review (s, S) Inventory Models with State-Dependent Leadtimes
Authors: Gross Donald , Harris Carl M.
Published: November 2008

This paper describes the development of a continuous-review (s, S) inventory model with complete backordering and state-dependent, stochastic leadtimes. The demand on the inventory system is assumed to be a Poisson process, and the order-filling portion of the replenishment leadtime is allowed to depend on the number of outstanding orders (i.e., to be state dependent). The inventory state probabilities which are required in order to optimize the cost function with respect to s and S can be obtained via a queuing analysis on the order-filling process. Orders are assumed to arrive at a single-channel service facility, where the service may be state dependent in either one of two ways: (1) the instantaneous probabilities at an arbitrary point in time of an order being filled (i.e., a service completed) in an infinitesimal interval of length Δt is μ(m)Δt + o(Δt), where m is the number of outstanding orders (instantaneous state dependence); and (2) the order-filling time is an exponentially distributed random variable with distribution function Bn(t) = 1 − e−μ(n)t, where n is the number of outstanding orders just after the previous order has been filled (departure-point state dependence). The μ(·) used to illustrate the methodology is two state; that is, μ(·) = μ1 if only one order is outstanding and μ if more than one is outstanding. The appropriate queuing model describing the ordering process turns out to be a Poisson input, batch-service model with batch size Q = S − s. The instantaneous state-dependent model is analyzed using a Chapman-Kolmogorov approach, while the departure-point state-dependent model utilizes an imbedded-Markov-chain approach. The computational aspects of the models are illustrated for a specific set of values of the appropriate parameters.
The Effectiveness of Three Heuristic Rules for Job Sequencing in a Single Production Facility
Authors: Haynes R. D. , Komar C. A. , Byrd Jack
Published: November 2008

This paper examines the effectiveness of three heuristic rules used in production sequencing where the objective is to minimize the downtime due to setup changes. The effectiveness of these heuristic rules was evaluated under various conditions of job size and setup time distribution. The results of this analysis indicate that job conditions do affect the effectiveness of these three rules.
Note—A Comment on the Use of Simplex Method for Absolute Value Problems
Authors: Ravindran Arunachalam , Hill Thomas W.
Published: November 2008

The linear programming approach to the absolute value problem is to transform the unrestricted variable by the difference of two nonnegative variables. This transformation creates an unbounded feasible region which may lead to erroneous solution. To avoid this, Kaplan [Kaplan, Seymour. 1971. Comment on a précis by Shanno and Weil. Management Sci. 17 (11, July) 778–780.] introduced a new constraint to bound the feasible region and suggested a solution scheme using the simplex method. We shall give two counter examples to the proposed scheme and discuss the difficulties involved with this particular class of problem.
A Note on Parametric Network Flows
Authors: Minieka Edward
Published: November 2008

In their paper [Doulliez, P. J., M. R. Rao. 1971. Maximal flow in a multi-terminal network with any one are subject to failure. Management Sci. 18 (1, September) 48–58.], Doulliez and Rao present algorithms that solve two flow problems for a single source, multi-terminal network. The first problem that they solve is the construction of a flow that maximizes the value of t, where the demand at each sink is a nondecreasing, linear function of t. Given such a flow, the second problem that they solve is the construction of a flow that maximizes the value of t when the capacity of an arc is reduced. This paper supplies a finiteness proof for the first algorithm and sketches a finiteness proof for the second algorithm. The proofs are based on the well-known fact that a network possesses only a finite number of different spanning trees.