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A visual interactive tolerance approach to sensitivity analysis in MOLP

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第2期142卷 357-381页

作者： Borges, ARP Antunes, CH Coimbra Polytech Inst ISEC P-3030601 Coimbra Portugal Univ Coimbra Dept Elect Engn P-3030030 Coimbra Portugal INESC P-3000033 Coimbra Portugal

This paper deals with the tolerance approach to sensitivity analysis of the weights in multiple objective linear programming (MOLP) problems. A geometric interpretation to compute the results in Hansen et al. [Eur. J. Oper. Res. 38 (1989) 63-69] is presented. Along the same direction, a visual interactive approach based on the analysis of indifference regions corresponding to basic efficient solutions is described. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： multiple objective linear programming sensitivity analysis tolerance approach decision analysis interactive methods

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A multiple objective model to deal with economy-energy-environment interactions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期153卷 370-385页

作者： Oliveira, C Antunes, CH INESC Coimbra P-3000033 Coimbra Portugal Univ Coimbra Dept Engn Electrotecn P-3030030 Coimbra Portugal

An economy-energy-environment multiple objective model based on the linear structure of inter-industry production linkages is presented. Axes of evaluation consistent with sustainable energy strategies, economic growth, social welfare and environmental friendliness are explicitly considered. The aim of this study is to provide decision-makers with a comprehensive model which allows to assess environmental burdens (global warming potential and acidification potential) with respect to changes in economic activities consistent with distinct policy measures. (C) 2003 Elsevier B.V. All rights reserved.

关键词： energy system environmental input output methodology multiple objective linear programming

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On the use of value efficiency analysis and some further developments

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JOURNAL OF PRODUCTIVITY ANALYSIS 2002年第1-2期17卷 49-64页

作者： Korhonen, P Soismaa, M Siljamäki, A Helsinki Sch Econ & Business Adm Helsinki 00101 Finland NumPlan Ltd Nummela 00101 Finland

The purpose of this paper is to discuss the use of Value Efficiency Analysis (VEA) in efficiency evaluation when preference information is taken into account. Value efficiency analysis is an approach, which applies the ideas developed for multiple objective linear programming (MOLP) to Data Envelopment Analysis (DEA). Preference information is given through the desirable structure of input- and output-values. The same values can be used for all units under evaluation or the values can be specific for each unit. A decision-maker can specify the input- and output-values subjectively without any support or (s)he can use a multiple criteria support system to assist him/her to find those values on the efficient frontier. The underlying assumption is that the most preferred values maximize the decision-maker's implicitly known value function in a production possibility set or a subset. The purpose of value efficiency analysis is to estimate a need to increase outputs and/or decrease inputs for reaching the indifference contour of the value function at the optimum. In this paper, we briefly review the main ideas in value efficiency analysis and discuss practical aspects related to the use of value efficiency analysis. We also consider some extensions.

关键词： efficiency analysis data envelopment analysis value efficiency analysis multiple objective linear programming value function efficient frontier interactive multiple objective programming

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Integrating fuzzy goal programming and data envelopment analysis to incorporate preferred decision-maker targets in efficiency measurement

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DECISIONS IN ECONOMICS AND FINANCE 2020年第2期43卷 673-690页

作者： Di Caprio, Debora Ebrahimnejad, Ali Ghiyasi, Mojtaba Santos-Arteaga, Francisco J. Univ Trento Dept Econ & Management Trento Italy York Univ Dept Math & Stat Toronto ON M3J 1P3 Canada Islamic Azad Univ Qaemshahr Branch Dept Math Qaemshahr Iran Shahrood Univ Technol Fac Ind Engn & Management Sci Shahrood Iran Free Univ Bolzano Fac Econ & Management Bolzano Italy

Data envelopment analysis (DEA) is a nonparametric frontier assessment method used to evaluate the relative efficiency of similar decision-making units (DMUs). This method provides benchmarking information regarding the removal of inefficiency. In conventional DEA models, the view of the decision maker (DM) is ignored and the performance of each DMU is solely determined by the observations retrieved. The current paper exploits the structural similarity existing between DEA and multiple objective programming to define a model that incorporates the preferences of DMs in the evaluation process of DMUs. Given the potential unfeasibility of the input and output targets selected by the DM, the model defines an interactive procedure that considers minimum and maximum acceptable objective levels. Given the feasible levels located closer to the targets selected by the DM, a program improving upon the feasible allocations is designed so that the suggested benchmark approximates the requirements fixed by the DM as much as possible. A real-life case study is included to illustrate the efficacy and applicability of the proposed hybrid procedure.

关键词： Data envelopment analysis Fuzzy goal programming multiple objective linear programming Subjective preferences Target setting Efficiency

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On Parallelizing Benson's Algorithm: Limits and Opportunities 18th

On Parallelizing Benson's Algorithm: Limits and Opportunitie...

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18th International Conference on Computational Science and Its Applications (ICCSA)

作者： Buecker, H. Martin Loehne, Andreas Weissing, Benjamin Zumbusch, Gerhard Friedrich Schiller Univ Jena Inst Comp Sci Jena Germany Friedrich Schiller Univ Jena Inst Math Jena Germany Friedrich Schiller Univ Jena Inst Appl Math Jena Germany Friedrich Schiller Univ Jena Michael Stifel Ctr Jena Data Driven & Simulat Sci Jena Germany

ISBN: (纸本)9783319951652;9783319951645

multiple objective linear programming problems frequently arise in various applications of computational and data science. An important class of iterative techniques for numerically solving these problems is based on Benson's algorithm. This algorithm starts with an initial outer approximation of a polyhedron and then iteratively refines these outer approximations until a solution is found. This algorithm is an archetype of a class of methods that have been extensively studied serially. Today, however, there is hardly any discussion in the open literature on the difficulties encountered when executing this algorithm in parallel. To fill this gap, we report on numerical experiences when parallelizing Benson's algorithm on two different shared-memory computers. More precisely, we quantify the performance of a parallelized version of this algorithm on two Intel systems (single socket Core i7-6700 with up to 4 threads and dual socket Xeon E5-2650v4 using up to 24 threads). We show that parallelizing Benson's algorithm has its performance limitations caused by memory bandwidth saturation. We also sketch opportunities for future research directions on techniques that could improve the performance of Benson-type algorithms on parallel computers.

关键词： Mathematical programming Parallel algorithms multiple objective linear programming

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A multiple objective model to deal with economy-energy-environment interactions

A multiple objective model to deal with economy-energy-envir...

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12th Mini Euro Conference

作者： Oliveira, C Antunes, CH INESC Coimbra P-3000033 Coimbra Portugal Univ Coimbra Dept Engn Electrotecn P-3030030 Coimbra Portugal

关键词： energy system environmental input output methodology multiple objective linear programming

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On the application of TRIMAP to problems with multiple decision makers

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Annals of Operations Research 1994年第3期51卷 99-114页

作者： Clímaco, João Antunes, Carlos Henggeler Faculty of Economics University of Coimbra Portugal INESC Coimbra 3000 Rua Antero de Quental 231 cave Portugal Department of Electrical Engineering University of Coimbra Portugal

In this paper the potentialities of TRIMAP to provide decision support in multiobjective problems with multiple decision makers are exploited. TRIMAP is an interactive three-objective linear programming package which enables a progressive and selective learning of the nondominated solution set. The aim is to aid the opposing parties in exploring their own preferences and to explore the dynamic nature of the negotiation process. © 1994 J.C. Baltzer AG, Science Publishers.

关键词： computer graphics group decision support systems interactive methods multiple decision makers multiple objective linear programming negotiation

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A decision support approach to achieve competitive advantage for a hypermarket chain

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Journal of Business Economics 2022年第5期92卷 809-827页

作者： Siljamäki, Aapo Department of Information and Service Management School of Business Aalto University PO Box 1210 Helsinki 00101 Finland

This paper describes the decision support approach used in the development process of the S Group's Prisma hypermarket chain in Finland. The management was looking for a new and sustainable operating model for the rapidly growing chain, and contacted the author to consult in the process. Fierce competition forced the search for new business ideas, tools and methods that would provide a clear competitive advantage. To find new perspectives, we decided to use statistical approaches and various decision support system options, such as multi-criteria modelling. A database was available for research and analysis, including data on purchasing behavior and key performance indicators (KPI). The approach had to take into account the role and impact of customers. It was highly important to include customer behavior in the analysis using shopping basket data. Shopping basket data was central in the current paper. From these, an observation matrix was created combining shopping basket data, product data and customer background information. Using multivariate methods, customer groupings and profiles were created with the data from the observation matrix. Using the customer profile and KPI data, a multi-criteria decision support system was produced to support strategic planning. The decision support system (DSS) model was created together with a market chain operational expert and an external methodological expert. We used the VIG software package developed by Korhonen (Belg J Oper Res Stat Comput Sci 27(3):15, 1987) to solve the problem because it is easy to use and requires no prior knowledge of computers or multi-objective linear programming models. Pareto Race plays a central role in the VIG system. The chain expert easily learned how to use and work with the model. The results were immediately visible and could be used to examine alternatives and assess their appropriateness. It was decided to present five different scenarios to the hypermarket chain management. The main obj

关键词： Customer analysis Hypermarket multiple objective linear programming Multivariate analysis Performance improvement Retail Shopping basket analysis

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VM DP-Program for Solving Optimality Problems in Vector Criterion Markov and Semi-Markov Decision Processes

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Optimization 1991年第2期22卷 239-248页

作者： Novak, J. Economic Institute Prague Dept. of Mathematics United Kingdom

Optimality problems in infinite horizon discrete time vector criterion Markov and semi-Markov decision processes can be expressed as standard problems of multiple objective linear programming. “VMDP” is a FORTRAN program for enumerating the objective function coefficients and constraint coefficients in these problems and finding all nondominated extreme points, i.e. all nondominated pure stationary strategies, and all nondominated edges. Using VMDP, computational experiments are presented. The characteristics of Markov and semi-Markov decision problems (the VMDP code) with those of general muitiple objective linear programming problems (the Steuer Adbase code) are compared.

关键词： Markov decision programming multiple criteria Simplex method multiple objective linear programming

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An all-linear programming relaxation algorithm for optimizing over the efficient set

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Journal of Global Optimization 1991年第1期1卷 83-104页

作者： Benson, Harold P. College of Business Administration University of Florida Gainesville 32611-2017 Florida United States

The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. In this paper a relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved. © 1991 Kluwer Academic Publishers.

关键词： efficient set Global optimization multiple criteria decision making multiple objective linear programming relaxation algorithms

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