A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model
In order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a comp...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2014/807843 |
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doaj-005a5e3bacac45d2b0f4148a08777c822020-11-24T22:54:20ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/807843807843A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA ModelHaifang Cheng0Yishi Zhang1Jianhu Cai2Weilai Huang3School of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaSchool of Management, Huazhong University of Science and Technology, Wuhan 430074, ChinaIn order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a compensatory DEA model for ranking all units, point out the existing problem for solving the model, and present an improved algorithm for which an approximate global optimal solution of the model can be obtained by solving a sequence of linear programming. Then, we applied the key idea of the compensatory DEA model to develop the MOP model in which the objectives are to simultaneously maximize all common weights under constraints that the sum of efficiency values of all DMUs is equal to unity and the sum of all common weights is also equal to unity. In order to solve the MOP model, we transform it into a single objective programming (SOP) model using a fuzzy programming method and solve the SOP model using the proposed approximation algorithm. To illustrate the ranking method using the proposed method, two numerical examples are solved.http://dx.doi.org/10.1155/2014/807843 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Haifang Cheng Yishi Zhang Jianhu Cai Weilai Huang |
spellingShingle |
Haifang Cheng Yishi Zhang Jianhu Cai Weilai Huang A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model Mathematical Problems in Engineering |
author_facet |
Haifang Cheng Yishi Zhang Jianhu Cai Weilai Huang |
author_sort |
Haifang Cheng |
title |
A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model |
title_short |
A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model |
title_full |
A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model |
title_fullStr |
A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model |
title_full_unstemmed |
A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model |
title_sort |
multiobjective programming method for ranking all units based on compensatory dea model |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2014-01-01 |
description |
In order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a compensatory DEA model for ranking all units, point out the existing problem for solving the model, and present an improved algorithm for which an approximate global optimal solution of the model can be obtained by solving a sequence of linear programming. Then, we applied the key idea of the compensatory DEA model to develop the MOP model in which the objectives are to simultaneously maximize all common weights under constraints that the sum of efficiency values of all DMUs is equal to unity and the sum of all common weights is also equal to unity. In order to solve the MOP model, we transform it into a single objective programming (SOP) model using a fuzzy programming method and solve the SOP model using the proposed approximation algorithm. To illustrate the ranking method using the proposed method, two numerical examples are solved. |
url |
http://dx.doi.org/10.1155/2014/807843 |
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