Cross-efficiency evaluation and decomposition with directional distance function in series and parallel systems

Abstract

As an extension tool of data envelopment analysis (DEA), cross-efficiency evaluation has been widely applied in ranking decision making units (DMUs). Series and parallel are two basic network structures. Current cross-efficiency evaluation in both the structures has been developed with oriented DEA models that minimize inputs while producing at least the given outputs. The extension proposed here is aimed at providing a non-oriented cross-efficiency evaluation based on measures accounting for input excesses and output shortfalls simultaneously. This paper extends the cross-efficiency evaluation in series and parallel structures for use with the directional distance function (DDF). In the proposed DDF cross-efficiency evaluation, the system cross-efficiency score can be decomposed into a weighted average of process cross-efficiency scores, whether for the series or parallel system. The problem with the alternate optima for the multipliers is also addressed and models of avoiding zero multipliers are provided in this new context. Numerical examples from the literature and an empirical one illustrate the validity of the proposed network cross-efficiency evaluation and decomposition, and the superiority of the models in avoiding zero multipliers.