A Multiobjective Programming Method for Ranking All Units Based on Compensatory DEA Model

Author:

Cheng Haifang1ORCID,Zhang Yishi1ORCID,Cai Jianhu12ORCID,Huang Weilai1ORCID

Affiliation:

1. School of Management, Huazhong University of Science and Technology, Wuhan 430074, China

2. College of Economics and Management, Zhejiang University of Technology, Hangzhou 310023, China

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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