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Common set of weights in data envelopment analysis: a linear programming problem

CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2012年第2期20卷 355-365页

作者： Davoodi, A. Rezai, H. Zhiani Islamic Azad Univ Dept Math Neyshabur Branch Neyshabur Iran Islamic Azad Univ Dept Math Mashhad Branch Mashhad Iran

Data Envelopment Analysis is used to determine the relative efficiency of Decision Making Units as the ratio of weighted sum of outputs by weighted sum of inputs. To accomplish the purpose, a DEA model calculates the weights of inputs and outputs of each DMU individually so that the highest efficiency can be estimated. Thus, the present study suggests an innovative method using a common set of weights leading to solving a linear programming problem. The method determines the efficiency score of all DMUs and rank them too.

关键词： multiple objective programming Data Envelopment Analysis Common set of weights

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Multiobjective multiproduct parcel distribution timetabling: a real-world application

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2012年第4期19卷 613-629页

作者： Ben-Ayed, Omar Hamzaoui, Salem Optimal Solut Ctr Management Sci Wichita KS USA Univ Kairouan Inst Comp Sci & Business Kairouan Tunisia Univ Sfax Coll Econ & Business Sfax Tunisia

Multiobjective multiproduct parcel distribution timetabling problem is concerned with generating effective timetables for parcel distribution companies that provide interdependent services (products) and have more than one objective. A parcel distribution timetabling problem is inherently multiobjective because of the multitude of criteria that can measure the performance of a timetable. This paper provides the mathematical formulation of the problem and applies the model to a real-world case study. The application shows that without a common ground with the practitioners, it would be impossible to define the actual requirements and objectives of the company;problem definition is as important as model construction and solution method.

关键词： scheduling multiple objective programming integer programming transportation distribution shipping industry postal services practice of OR

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Satisfactory solution concepts and their relations for Stochastic Multiobjective programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 430-442页

作者： Munoz, Maria M. Ben Abdelaziz, Fouad Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Amer Univ Sharjah Grad Program Coll Engn Sharjah U Arab Emirates

This work deals with the concept of satisfactory solution for Stochastic Multiobjective programming (SMP) problems. Based on previous literature, we will introduce different concepts of satisfactory solutions for SMP problems, define a new concept of solution (where the decision maker (DM) sets his/her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels), and establish some relationship between these concepts. The results will aim at featuring these concepts and determine the differences between them. Moreover, the paper proposes a new step by step procedure to exchange information between the analyst and DM prior to solving the problem. Thus, the DM will be able to choose the transformation criterion for each stochastic objective and the aspiration level. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Stochastic programming multiple objective programming Goal programming Decision-maker's preferences Satisfactory solution Probabilistic goal

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Combined forecasts in portfolio optimization: A generalized approach

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COMPUTERS & OPERATIONS RESEARCH 2012年第4期39卷 805-819页

作者： Ustun, Ozden Kasimbeyli, Refail Izmir Univ Econ Fac Engn & Comp Sci Dept Ind Syst Engn TR-35330 Izmir Turkey Dumlupinar Univ Fac Engn Dept Ind Engn TR-43100 Kutahya Turkey

In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-variance-skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Risk management Global optimization Portfolio optimization Conic scalarization F-MSG algorithm

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A Metaheuristic Approach for Supply Chain Network Design Problems

A Metaheuristic Approach for Supply Chain Network Design Pro...

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International Conference of Modeling and Simulation in Engineering, Economics, and Management

作者： Venkatadri, Uday Bose, Soumen Azaron, Amir Reykjavik Univ Dept Financial Engn & Engn Management Reykjavik Iceland Dalhousie Univ Dept Ind Engn Halifax NS Canada Indian Inst Technol Dept Ind Engn & Management Kharagpur W Bengal India Univ Coll Dublin Michael Smurfit Grad Sch Business Dublin Ireland

ISBN: (纸本)9783642304330;9783642304323

We develop a multi-objective stochastic programming model for supply chain design under uncertainty using a metaheuristic approach. This is a comprehensive model, which includes both the strategic and tactical levels. The uncertainty regarding demands, supplies, processing and transportation costs is captured by generating discrete scenarios with given probabilities of occurrence. To solve the problem, we use multi-objective simulated annealing and compare the results against the goal attainment technique. Numerical results show that the proposed metaheuristic approach is a very practical solution technique.

关键词： Supply chain management Metaheuristics Stochastic programming multiple objective programming

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A positive approach to estimating the weights for quadratic multiple objective programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2007年第10期58卷 1332-1340页

作者： Yates, C. M. 38 Cutbush Lane Reading RG2 9AH Berks England

This paper integrates positive and normative approaches to modelling. The normative approach uses assumptions associated with multiple objective programming. The positive approach uses past observations to estimate the weights associated with each objective criteria. The technique encompasses both linear and non-linear objectives such as profit, cost and risk as well as quadratic calibration terms. The proposed methodology minimizes the sum of squared errors about the ideal multiple objective function, that is one that would reproduce observed results, rather than to minimize errors between fitted and observed activity levels. The technique removes the need to rely upon the use of abstract restraints normally applied to mathematical programming methods and provides a more objective means of testing the appropriateness of a model than previously. The technique has many applications in the field of mathematical modelling such as forecasting and analysing changes in decision-making and behaviour.

关键词： mathematical programming multiple objective programming economic modelling positive mathematical programming

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Constrained optimization using multiple objective programming

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JOURNAL OF GLOBAL OPTIMIZATION 2007年第3期37卷 325-355页

作者： Klamroth, Kathrin Tind, Jorgen Univ Erlangen Nurnberg Inst Appl Math D-91058 Erlangen Germany Univ Copenhagen Dept Appl Math & Stat Inst Math Sci DK-2100 Copenhagen O Denmark

In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically designed to incorporate such complex preference structures, they gain more and more importance in application areas as, for example, engineering design and capital budgeting. The aim of this paper is to analyze optimization problems both from a constrained programming and a multicriteria programming perspective. It is shown that both formulations share important properties, and that many classical solution approaches have correspondences in the respective models. The analysis naturally leads to a discussion of the applicability of some recent approximation techniques for multicriteria programming problems for the approximation of optimal solutions and of Lagrange multipliers in convex constrained programming. Convergence results are proven for convex and nonconvex problems.

关键词： constrained optimization multiple objective programming lagrange multipliers convergence

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Exact generation of epsilon-efficient solutions in multiple objective programming

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OR SPECTRUM 2007年第2期29卷 335-350页

作者： Engau, Alexander Wiecek, Margaret M. Clemson Univ Dept Math Sci Clemson SC 29634 USA

It is a common characteristic of many multiple objective programming problems that the efficient solution set can only be identified in approximation: as this set often contains an infinite number of points, only a discrete representation can be computed, and due to numerical difficulties, each of these points itself might, in general, be only approximate to some efficient point. From among the various approximation concepts, this paper considers the notion of epsilon-efficient solutions and proposes several new methods for their generation. Supporting theoretical results are established and a numerical example is provided.

关键词： multiple objective programming epsilon-efficient solutions epsilon-Pareto outcomes approximation

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SOLVING THE FUZZY SHORTEST PATH PROBLEM BY USING A LINEAR multiple objective programming

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2007年第5期24卷 360-365页

作者： Yu, Jing-Rung Wei, Tzu-Hao Natl Chi Nan Univ Dept Informat Management 470 Univ Rd Puli Nantou 545 Taiwan

In this paper, we propose a simple linear multiple objective programming to deal with the fuzzy shortest path problem. The proposed approach does not need to declare 0-1 variables to solve the fuzzy shortest path problem because it meets the requirements of the network linear programming constraints. Therefore, the linear programming relaxation can be used to arrive at an integer solution without using the Branch and Bound technique, and the complexity of our proposed method can be reduced. A compromising non-dominated integer optimal solution, the fuzzy shortest path, can be obtained easily without adding extra constraints. This approach not only can obtain a fuzzy shortest path but also can reduce the complexity of solving the basic fuzzy shortest path problem without using 0-1 variables. Three examples with trapezoidal and triangular fuzzy numbers in arc length are used to demonstrate the proposed method in more details.

关键词： shortest path multiple objective programming fuzzy number network optimization

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Comparison of Innovation Diffusion Models: A Case Study on the DRAM Industry

Comparison of Innovation Diffusion Models: A Case Study on t...

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IEEE International Conference on Fuzzy Systems

作者： Jing Rung Yu You Wei Dong Yi Hsuan Chang Fang-Mei Tseng Department of Information Management National Chi Nan University College of Management Yuan Ze University

ISBN: (纸本)9781467315074

The development of technology accelerates the life cycle of products and the rate of product substitution. Dynamic random access memory (DRAM), which is characterized by generation substitution, is an innovation in technology development that enhances competitive capabilities. In this study of the DRAM industry, the Gompertz model, traditional logistic growth model, Norton and Bass model, and fuzzy piecewise logistic growth model are applied to predict the growth trends of eight generations of the DRAM market. The results show that only the fuzzy piecewise logistic growth model and the Norton and Bass model can effectively forecast the growth trends of coming generations in the DRAM industry. Of these two models, only the fuzzy piecewise logistic growth model that detects change points can be used to reasonably explain the phenomenon and status of generation replacement in the DRAM industry at particular times, and provide an overview of the market situation.

关键词： Fuzzy piecewise regression Logistic model multiple objective programming Dynamic Random Access Memory

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