Expansion of the cross-efficiency evaluation by using the equations forming the efficient frontier in DEA

Abstract

In this paper, we propose an algorithm to calculate cross-efficiency scores which used the equations forming the efficient frontier in data envelopment analysis (DEA). In many standard DEA models, each decision-making unit (DMU) is evaluated by using the advantageous weight for itself. Then, many DMUs are evaluated as efficient, and those efficient DMUs are not ranked by the models. The cross-efficiency evaluation is a method to rank DMUs by using the advantageous weights for all DMUs. Previously, the cross-efficiency scores based on different ideas are calculated by solving multiple linear or nonlinear programming problems. However, it is often hard to solve such a nonlinear programming problem. Therefore, by analysing the efficient frontier, we construct an algorithm to calculate alternative cross-efficiency scores.

Keywords:

• data envelopment analysis
• efficient frontier
• production possibility set
• cross-efficiency
• facet

AMS Subject Classification:

• 46N10
• 93B15