bluuebunny/crossref_metadata_2025_split huggingface dataset:
Optimal Maintenance and Sale Age for a Machine Subject to Failure
Authors: Kamien Morton I. , Schwartz Nancy L. 
Published: November 2008

A problem of optimal machine maintenance policy is studied. The value of the machine's output is independent of age, but the natural probability of machine failure increases with age. Preventive maintenance can be applied to reduce the probability of machine failure (but a failed machine can only be junked). The machine may be sold at any time providing it is still effective. The problem is to select an optimal preventive maintenance policy for the period of ownership and a planned sale date at which the machine will be sold providing it has not yet failed. The optimal policy calls for a continuous nonincreasing maintenance rate, although not necessarily a decreasing rate of maintenance expenditure. The necessary condition for machine age at sale is critical in the determination of optimal maintenance policy. The necessary conditions for an optimal maintenance policy are shown to be sufficient as well. The novelty of the approach lies in the explicit distinction between the machine's “natural” failure rate and the actual failure rate resulting from selection of preventive maintenance policy.
Proximal Decision Analysis
Authors: Howard Ronald A. 
Published: November 2008

This paper presents simplified techniques for analyzing the effect of uncertainty in large decision problems. Starting with the development of approximate expressions for the moments of a value lottery, we show that the probabilistic assessments of jointly related random variables necessary for these approximations are quite reasonable in number. The concepts of risk aversion, certain equivalent, and exponential utility function then permit writing useful approximations for the certain equivalent of the value lottery. Deterministic sensitivity analyses are described first for the case when the decision variables are fixed and then for the case when they can be changed to compensate for variations in state variables. The approximate effect and value of clairvoyance (revelation of ultimate values of uncertain variables) is derived from the original probabilistic assessment and the results of the deterministic sensitivity analysis. We next determine the approximate value of wizardry (changing uncertain variables into decision variables). The amount by which decision variables must be adjusted to account for risk aversion is established from earlier results. The final portion of the paper discusses a simple economic example that illustrates the application of the development.
Flows in Arborescences
Authors: Glover Fred 
Published: November 2008

This paper gives efficient methods for solving four specially structured network problems that arise in connection with certain integer programming methods developed by Cook and Cooper, Hillier, and Glover. Such problems have also independently been studied in inventory theory by Ignall and Veinott, who have developed extensive qualitative (nonalgorithmic) implications of their structures. In the integer programming context, special subclasses of these network problems are generated and solved as part of a strategy for solving more general integer linear programs. By providing particularly efficient methods for accommodating somewhat broader network structures, our results enable the development of related integer programming solution strategies that generate more complex subproblems. We show that the first of the four network problems can be solved by a procedure that assigns each variable a value exactly once, without subsequent revision. Properties of optimal solutions for the remaining problems are developed that enable the algorithm for the first to be extended to the second and then, by suitable transformation of variables, to the third and last problems as well. Moreover, while the last three problems involve an additional linear constraint that nullifies the “integer extreme point property,” we show that optimal integer solutions to these problems can nevertheless easily be obtained from the optimal continuous solutions.
Estimating Sample Size in Computing Simulation Experiments
Authors: Fishman George S. 
Published: November 2008

A method is described for estimating and collecting the sample size needed to estimate the mean of a process (with a specified level of statistical precision) in a simulation experiment. Steps are also discussed for incorporating the determination and collection of the sample size into a computer library routine that can be called by the ongoing simulation program. We present the underlying probability model that enables us to denote the variance of the sample mean as a function of the autoregressive representation of the process under study and describe the estimation and testing of the parameters of the autoregressive representation in a way that can easily be “built into” a computer program. Several reliability criteria are discussed for use in determining sample size. Since these criteria assume that the variance of the sample mean is known, an adjustment is necessary to account for the substitution of an estimate for this variance. It is suggested that Student's distribution be used as the sampling distribution, with “equivalent degrees of freedom” determined by analogy with a sequence of independent observations. A bias adjustment is described that can be applied to the beginning of the collected data to reduce the influence of initial conditions on events in the experiment. Four examples are presented using these techniques, and comparisons are made with known theoretical solutions. One unfortunate shortcoming of the proposed procedure is that its performance is directly linked to the initially chosen sample size. Our results show that as this sample size increases, the procedure gives results which agree more closely with predicted results.
Extensions of the Group Theoretic Approach in Integer Programming
Authors: Wolsey Laurence A. 
Published: November 2008

By relaxing the nonnegativity constraints on a set of basic variables, an integer programming problem can be reduced to a shortest route problem over a finite Abelian group. Here it is shown how given a similar relaxation on any set of variables, a structurally simpler problem is obtained, which can be regarded as a shortest route problem over an Abelian (but not necessarily finite) group. In particular if the non-negativity constraints are relaxed on all but one of a set of basic variables, a knapsack (or very close to knapsack) problem is obtained, which either gives the solution of the integer problem, or when solved by dynamic programming provides bounds at least as strong as those provided by the above group problem. The difficulty that arises when the order of groups encountered is very large is also considered in the same framework, and by further relaxation it is shown how the groups can be reduced to manageable size, which can be used to provide simple bounds for the above group problem. Finally applications of these results are suggested with reference to various existing integer programming algorithms.
Infinite Horizon Programs
Authors: Grinold Richard C. 
Published: November 2008

Several difficulties arise when multistage optimization problems with linear constraints are extended to an infinite horizon. For linear objectives the weak duality theorem fails, duality gaps exist, complementary slackness is not a sufficient condition for optimality, and the total reward may diverge. This paper presents verifiable conditions on the problem that guarantee the existence of optimal solutions and equilibrium prices for linear and nonlinear objectives. In addition, it is ascertained that the Kuhn-Tucker conditions are sufficient for optimality if additional restrictions are imposed. If the constraints are Leontief and the objective is convex (in a maximization problem), then the existence of an extreme point optimal solution can be verified. The decision taken in each period is an extreme point of the set of solutions that are feasible in that period. The Leontief case also yields a horizon theorem. All sufficiently long finite horizon problems produce a first decision that is optimal for the infinite horizon problem.
Set Covering and Involutory Bases
Authors: Bellmore Mandell , Ratliff H. Donald 
Published: November 2008

Some new properties associated with the special class of integer programs known as weighted set covering problems are derived. While it is well known that an optimal integer solution to the set covering problem is a basic feasible solution to the corresponding linear program, we show that there exists an optimal basis which is involutory (i.e., B = B−1). This property and others are used to develop a new algorithm which uses strong cutting planes. The cutting planes are strong in the sense that they exclude both integer and noninteger solutions. Computational experience is presented.
The Labor Assignment Decision and Application of Work Flow Structure Information
Authors: Holstein William K. , Berry William L. 
Published: November 2008

The movement of workers among machines is a tactic often employed by job shop managers to break bottlenecks and smooth the flow of work. Despite its common occurrence in industrial practice, the problem has only recently received attention in the management science literature. The purposes of this paper are (1) to discuss the nature of the labor assignment problem in job shops, and (2) to suggest a procedure for making labor assignments at the time of actual production. The significant features of the specific rules suggested are that they use aggregate information on work flow patterns in the shop, and that they make fewer labor transfers than other rules which have been suggested.
A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem
Authors: Lawler Eugene L. 
Published: November 2008

A general procedure is presented for computing the best, 2nd best,…, Kth best solutions to a given discrete optimization problem. If the number of computational steps required to find an optimal solution to a problem with n(0, 1) variables is c(n), then the amount of computation required to obtain the if best solutions is O(Knc(n)). The procedure specializes to published procedures of Murty and of Yen for the assignment problem and the shortest path problem, respectively. A method is presented for reducing the required amount of storage by a factor of n, compared with the algorithms of Murty and of Yen. It is shown how the K shortest (loopless) paths in an n-node network with positive and negative arcs can be computed with an amount of computation which is O(Kn3). This represents an improvement by a factor of n, compared with Yen's algorithm.
Inventory Systems with Imperfect Asset Information
Authors: Iglehart Donald L. , Morey Richard C. 
Published: November 2008

An inventory stock record is in error when the stock record is not in agreement with the physical stock. Such discrepancies may be introduced due to time lags between flow of information and material, pilferage, incorrect unit of issue, inaccurate physical inventory counts, etc. The primary impact of these errors is that the system fails to order when it should, resulting in “warehouse denials,” i.e., the stock records show a balance sufficient to issue a given material release order, but for which insufficient units of stock can physically be found. The object of this paper is to select the proper frequency and depth of inventory counts, together with modifications to a given stocking policy, so as to minimize the total cost per unit time, subject to the likelihood of a warehouse denial between inventory counts being below a prescribed level. The goal has been to obtain results easily implementable and leads to formulae comparable to those of the classical economic lot-size models. A numerical example is included to illustrate the procedure.
A Note on the Use of Nonparametric Statistics in Stochastic Linear Programming
Authors: Tintner Gerhard , Rama Sastry M. V. 
Published: November 2008

An ordinary linear programming problem is formulated as [Formula: see text] under the constraints [Formula: see text] where A is a matrix with m rows and n columns, x and c are column vectors with n elements, and b is a column vector with n elements. The theory of stochastic linear programming first suggested by Tintner [Tintner, G. 1955. Stochastic linear programming with applications to agricultural economics. Sympos. Linear Programming, Vol. 1. National Bureau of Standards, Washington, D. C., 197 ff.] uses the following approach. The elements of b, c and the matrix A are assumed to be random variables with a known probability distribution. Two possible ways of deriving the distribution of z are known as direct and indirect methods. In this article, some nonparametric statistics were applied to test the difference between the distributions derived by the direct and indirect methods. The non-parametric tests include the Kolmogorov-Smirnov statistic and Alfred Rényi's statistics.
A Comparative Study of Methods for Long-Range Market Forecasting
Authors: Armstrong J. Scott , Grohman Michael C. 
Published: November 2008

The following hypotheses about long-range market forecasting were examined: H1 Objective methods provide more accuracy than do subjective methods. H2 The relative advantage of objective over subjective methods increases as the amount of change in the environment increases. H3 Causal methods provide more accuracy than do naïve methods. H4 The relative advantage of causal over naïve methods increases as the amount of change in the environment increases. Support for these hypotheses was then obtained from the literature and from a study of a single market. The study used three different models to make ex ante forecasts of the U.S. air travel market from 1963 through 1968. These hypotheses imply that econometric methods are more accurate for long-range market forecasting than are the major alternatives, expert judgment and extrapolation, and that the relative superiority of econometric methods increases as the time span of the forecast increases.
Methods for Allocating Urban Emergency Units: A Survey
Authors: Chaiken Jan M. , Larson Richard C. 
Published: November 2008

An urban emergency service system provides mobile units (vehicles) to respond to requests for service which can occur at any time and any place throughout a city. This paper describes the common characteristics and operational problems of these systems and surveys the various methods, both traditional and recently developed, which may be used for allocating their units. Aspects of allocation policy discussed include (1) determining the number of units to have on duty, (2) locating the units, (3) designing their response areas or patrol areas, (4) relocating units, and (5) planning preventive-patrol patterns for police cars. Typical policy changes which may be suggested by the use of quantitative allocation models include selective queuing of low priority calls, varying the number of units on duty (and their locations) by time of day, dispatching units other than the closest ones to certain incidents, relocating units as unavailabilities begin to develop, and assigning police cars to overlapping patrol sectors. As a result of making such changes, it is often possible to reduce queuing and travel time delays, improve the balance of workload among units, and enhance the amount of preventive patrol where needed.
Semi-Markov Decision Processes with Unbounded Rewards
Authors: Lippman Steven A. 
Published: November 2008

We consider a semi-Markov decision process with arbitrary action space; the state space is the nonnegative integers. As in queueing systems, we assume that {0, 1, 2, …, n + N} is the set of states accessible from state n in one transition, where N is finite and independent of n. The novel feature of this model is that the one-period reward is not required to be uniformly bounded; instead, we merely assume it to be bounded by a polynomial in n. Our main concern is with the average cost problem. A set of conditions sufficient for there to be an optimal stationary policy which can be obtained from the usual functional equation is developed. These conditions are quite weak and, as illustrated in several queueing examples, are easily verified.
A Linear Decision Rule for Production and Employment Scheduling
Authors: Holt Charles C. , Modigliani Franco , Simon Herbert A. 
Published: November 2008

The decision problems involved in setting the aggregate production rate of a factory and setting the size of its work force are frequently both complex and difficult. The quality of these decisions can be of great importance to the profitability of an individual company, and when viewed on a national scale these decisions have a significant influence on the efficiency of the economy as a whole. This paper reports some of the findings of a research team that has been developing new methods to enable production executives to make better decisions and to make them more easily than they can with prevailing procedures. With the cooperation of a manufacturing concern, the new methods have been developed in the context of a set of concrete production scheduling problems that were found in a factory operated by the company. The new method which is presented in this paper, involves: (1) formalizing and quantifying the decision problem (using a quadratic approximation to the criterion function) and (2), calculating a generalized optimal solution of the problem in the form of a (linear) decision rule. Like a rule of thumb, an optimal decision rule prescribes a course of action when it is applied to a particular set of circumstances; but, unlike most rules of thumb, an optimal decision rule prescribes courses of action for which the claim can be made that the decisions are “the best possible,” the meaning of “best” being clearly specified. The ultimate test, of course, must be whether the new decision methods do or do not outperform prevailing decision methods when full allowance is made for the cost of obtaining the optimal decisions.
Derivation of a Linear Decision Rule for Production and Employment
Authors: Holt Charles C. , Modigliani Franco , Muth John F. 
Published: November 2008

An application of linear decision rules to production and employment scheduling was described in the last issue of this journal [Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October).]. The hypothetical performance of these rules represented a significant improvement over the actual company performance as measured by independent cost estimates and other managerial measures of efficiency. The quadratic cost function which was used should be applicable to production and employment scheduling decisions in many other situations. Also the general approach of approximating decision criteria with quadratic functions and obtaining linear decision rules can usefully be extended to many decision problems. In the present paper we will demonstrate (a) how optimal (i.e., minimum expected cost) decision rules may be derived for a quadratic cost function involving inventory, overtime, and employment costs, and (b) how the numerical coefficients of the rules may be computed for any set of cost parameters.
Planning Horizons for Production Smoothing with Deterministic Demands
Authors: Kunreuther Howard C. , Morton Thomas E. 
Published: November 2008

In Part I of this paper, we develop an algorithm for finding planning horizons for the deterministic production smoothing problem when all demand must be met from regular production, under rather general assumptions for the production, production smoothing, and holding cost functions. (In Part II, planning horizons will be developed when the model is extended to include backlogging and overtime.) The techniques developed here are essentially forward-looking and marginal-cost-balancing in nature, rather than total-cost-minimizing and backward-looking such as dynamic programming, or total-cost-minimizing and omni-looking in nature such as linear programming. The fact that the planning horizon theorems do not depend on having discount rates less than one illustrates that the approach developed here is fundamentally different from ordinary infinite horizon dynamic programming techniques. The algorithm is “user oriented” in the sense that only a small amount of forecasting work and computation ordinarily must be done to determine the horizon; the nature of the algorithm also makes the exact dependence of the horizon on the forecast clear for sensitivity analysis. Firms facing a seasonal demand pattern will often find that the horizon occurs within the first several periods after the peak period if there is a sufficient enough drop in demand afterwards. This result complements the findings of Modigliani and Hohn and provides insight into the nature of the optimal policy for stochastic planning problems.
The Political Properties of Crystalline H2O: Planning for Snow Emergencies in New York
Authors: Savas E. S. 
Published: November 2008

A major snowstorm produced a serious snow emergency and a political crisis in New York City. Mayor Lindsay asked for an analysis of the problem to prevent its recurrence. His management science unit studied four basic questions: (1) How much snow falls on New York City? (2) How much work has to be done to clean it up? (3) What is the capacity for performing this work? (4) What improvements are needed to correct any imbalance between work load and work capacity? The surprising findings eliminated most of the remedies that had been offered earlier. A low-cost snow emergency plan was prepared, calling for some additional equipment, better deployment, and a strategy for more rapid mobilization. The recommendations were implemented promptly, and with due regard for political impact, in the midst of a mayoralty election campaign.
Airline Seat Share: A Study in False Optimization
Authors: Barcun Seymour D. , Jeming Peter 
Published: November 2008

An interactive model is developed which correctly predicts the problems faced by the airline industry today. The function of the model is to simulate the decision making process of determining the number of seats (and therefore planes) a competitor will fly in a given “market.” (A market is a city pair, e.g., the Washington-Chicago market.) This model of competition in a regulated industry considers the interaction of seat share, market share and profitability as major determinants of policy. Simulated data is presented for three cases in a two-competitor market. Case 1 supposes this model is used to determine policy only by one airline. Case 2 assumes the model is used by both competitors, but neither will fly a market if losses are encountered. Case 3 assumes that the model is used by both competitors, and losses will be taken to insure a favorable market share for future profitability.