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Convex Approximations of a Probabilistic Bicriteria Model with Disruptions

INFORMS JOURNAL ON COMPUTING 2013年第1期25卷 147-160页

作者： Rengarajan, Tara Dimitrov, Nedialko Morton, David P. Univ Texas Austin Grad Program Operat Res & Ind Engn Austin TX 78712 USA USN Postgrad Sch Dept Operat Res Monterey CA 93943 USA

We consider a multiperiod system operation problem with two conflicting objectives, minimizing cost and risk. Risk stems from uncertain disruptions to the system during operation. Whereas a general model would hedge against disruptions in each time period, we study special cases in which only a modest number of disruptions occur. To optimize for risk, we employ a convex approximation based on constraint sampling. We develop a stratified sampling scheme based on distributional information on the time of disruption. We establish that our scheme yields significant savings in sampling costs-up to an order of magnitude in the number of time periods-over naive sampling. Moreover, in the absence of distributional information, we exhibit a sampling strategy that has comparable performance to optimal stratification. We numerically demonstrate that stratification improves cost over naive sampling, improving the solution's proximity to the efficient frontier of the bicriteria problem.

关键词： programming, stochastic: probabilistic constraints simulation programming: multiple criteria

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Generating a Representative Subset of the Nondominated Frontier in multiple criteria Decision Making

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OPERATIONS RESEARCH 2009年第1期57卷 187-199页

作者： Karasakal, Esra Koksalan, Murat Middle E Tech Univ Dept Ind Engn TR-06531 Ankara Turkey

In this paper, we address the problem of generating a discrete representation of the nondominated frontier in multiple objective linear problems. We find a surface that approximates the shape of the nondominated frontier. Utilizing the surface, we generate a set of discrete points that is representative of the frontier. Our experience on randomly generated problems demonstrates that the approach performs well in terms of both the quality of the representation and the computation time.

关键词： discrete representation nondominated frontier programming: multiple criteria

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FURTHER DEVELOPMENTS AND TESTS OF A PROGRESSIVE ALGORITHM FOR multiple criteria DECISION-MAKING

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OPERATIONS RESEARCH 1993年第6期41卷 1033-1045页

作者： KORHONEN, P MOSKOWITZ, H SALMINEN, P WALLENIUS, J PURDUE UNIV CTR MANAGEMENT MFG ENTERPRISESW LAFAYETTEIN UNIV JYVASKYLA SF-40100 JYVASKYLAFINLAND

P. Korhonen, H. Moskowitz, and J. Wallenius (1986) developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives. A special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker's (DM's) preference structure or value function. The algorithm is based on progressively sampling the decision space, obtaining preference information from the DM, determining the likelihood of finding possibly/surely better alternatives, and based on this information, continuing the search or terminating it by making the final choice. We describe a computerized implementation and extensive computational tests of the algorithm, as well as some of our experiences in applying and field testing it in practice. We also consider several improvements and developments of the algorithm to further facilitate its use in practice.

关键词： decision analysis: sequential programming: multiple criteria utility/preference: applications multiattribute theory

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SOLVING THE DISCRETE multiple criteria PROBLEM USING CONVEX CONES

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MANAGEMENT SCIENCE 1984年第11期30卷 1336-1345页

作者： KORHONEN, P WALLENIUS, J ZIONTS, S UNIV JYVASKYLA DEPT ECON & MANAGEMENTSF-40100 JYVASKYLA 10FINLAND SUNY BUFFALO SCH MANAGEMENTBUFFALONY 14214

An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.

关键词： decision analysis utility/preference: multiattribute programming: multiple criteria convex cones

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INFERRING PREFERENCES IN multiple criteria DECISION-ANALYSIS USING A LOGISTIC-REGRESSION MODEL

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MANAGEMENT SCIENCE 1984年第9期30卷 1067-1077页

作者： STEWART, TJ CSIR NATL RES INST MATH SCIPRETORIA 0001SOUTH AFRICA

A method is proposed for the analysis of multiple criteria decision making problems in an interactive environment, when decision-maker preferences are inconsistent with a simple utility model and/or are self-inconsistent (e.g., showing intransitivities). A maximum likelihood estimation procedure is invoked which is based on a logistic regression model relating the probability of selecting one decision option over another to a linear function of attribute values. The method is illustrated by application to multi-objective linear programming, where it serves as an alternative to the method of Zionts and Wallenius (Zionts, S., J. Wallenius. 1976. An interactive programming method for solving the multiple criteria problem. Management Sci. 22 652–663.), and allows for inconsistencies which are not satisfactorily handled in the Zionts-Wallenius approach.

关键词： programming: multiple criteria multi-attribute utility estimation stochastic choice

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A PARTIAL COVERING APPROACH TO SITING RESPONSE RESOURCES FOR MAJOR MARITIME OIL SPILLS

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MANAGEMENT SCIENCE 1984年第10期30卷 1184-1196页

作者： BELARDO, S HARRALD, J WALLACE, WA WARD, J US COAST GUARD DIV TRAINING & EDUCWASHINGTONDC 20591 RENSSELAER POLYTECH INST SCH MANAGEMENTTROYNY 12181 PURDUE UNIV KRANNERT GRAD SCHW LAFAYETTEIN 47907

In this paper, oil spills occurring near shore in semienclosed waterways are viewed as emergency events. A partial set covering model, similar to those developed for firehouse location analysis, is applied to the problem of locating oil spill response equipment. The model includes both assessments of the relative probability of occurrence and the impact after occurrence of various spill types. A multiple objective approach enables the decisionmaker to evaluate strategies without confounding the probability of occurrence with the impact of occurrence.

关键词： programming: integer set covering programming: multiple criteria environmental management

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CONNECTEDNESS IN multiple LINEAR FRACTIONAL-programming

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MANAGEMENT SCIENCE 1983年第2期29卷 250-255页

作者： CHOO, EU ATKINS, DR SANTA CLARA UNIV SANTA CLARACA UNIV BRITISH COLUMBIA VANCOUVER V6T 1W5BCCANADA

The geometric properties of the sets of efficient and weakly efficient solutions of multiple linear fractional programming problems are investigated. Weakly efficient solutions are path-connected by finitely many line... 详细信息

关键词： programming: multiple criteria

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AN ALGORITHM FOR MULTIOBJECTIVE ZERO-ONE LINEAR-programming

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MANAGEMENT SCIENCE 1983年第12期29卷 1444-1453页

作者： KIZILTAN, G YUCAOGLU, E TURKISH ELECT IND CORP ISTANBULTURKEY

A branch and bound algorithm is presented which is based on the extension of implicit enumeration techniques to multiobjective zero-one linear programming and which appears to be computationally quite efficient. Domination tests, aiming at identifying paths of the enumeration tree that lead to dominated solutions as high up the tree as possible, are developed. Some computational results are also given.

关键词： programming: multiple criteria

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AN INTERACTIVE multiple OBJECTIVE LINEAR-programming METHOD FOR A CLASS OF UNDERLYING NON-LINEAR UTILITY-FUNCTIONS

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MANAGEMENT SCIENCE 1983年第5期29卷 519-529页

作者： ZIONTS, S WALLENIUS, J UNIV JYVASKYLA DEPT ECON & MANAGEMENTSF-40100 JYVASKYLA 10FINLAND

This paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties. The method is an extension of our earlier method published in this journal (Zionts, S., Wallenius, J. 1976. An interactive programming method for solving the multiple criteria problem. Management Sci. 22 (6) 652–663.). Various technical problems present in predecessor versions have been resolved. In addition to presenting the supporting theory and algorithm, we discuss certain options in implementation and summarize our practical experience with several versions of the method.

关键词： programming: multiple criteria utility/preference: multi-attribute

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multiple OBJECTIVE LINEAR FRACTIONAL-programming

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MANAGEMENT SCIENCE 1981年第9期27卷 1024-1039页

作者： KORNBLUTH, JSH STEUER, RE UNIV GEORGIA ATHENSGA 30602

This paper presents a simplex-based solution procedure for the multiple objective linear fractional programming problem. By (1) departing slightly from the traditional notion of efficiency and (2) augmenting the feasible region as in goal programming, the solution procedure solves for all weakly efficient vertices of the augmented feasible region. The article discusses the difficulties that must be addressed in multiple objective linear fractional programming and motivates the solution algorithm that is developed.

关键词： programming: multiple criteria

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