A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity

Abstract

Having multiple optimal solutions to weights affects to a great extent the consistency of operations related to weights. The cross efficiency method is the most frequently studied topic in data envelopment analysis (DEA) literature. Originally, the cross efficiency method included the efficiency evaluations that were obtained for a decision making unit (DMU) by the classical DEA for the reuse of optimal weights in other DMUs. As the optimal weights in classical DEA solutions usually have multiple solutions, this reduces the usefulness of the cross evaluation. Lam (J Oper Res Soc 61:134-143, 2010) proposed a mixed-integer linear programming (MILP) formulation based on linear discriminant analysis and super efficiency method to choose suitable weight sets to be used in cross efficiency evaluation. In this study, Lam's MILP model has been modified to reduce the steps during the solution process. The model also becomes a linear programming model after the modification to make it easier to use and to reduce the computational complexity. Numerical examples indicate that the proposed weight determination model both reduces the steps and minimizes computational complexity. Furthermore, it has similar performance with Lam's MILP model for the cross efficiency evaluation.

A Fuzzy Approach to Support Evaluation of Fuzzy Cross Efficiency

“…Since the seminal works of Sexton et al [6] and Doyle and Green [7], many cross-efficiency models and applications have been reported in the literature. Örkcü et al [9] and Wu et al [10] provided good reviews on models. Kao and Liu [11] extended the calculation of cross efficiency to two-stage systems.…”

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

“…They develop aggressive (minimal) and benevolent (maximal) formulations to identify optimal weights that not only maximize the efficiency of a particular DMU under evaluation, but also minimize the average efficiency of other DMUs. In addition to the well-known aggressive (minimal) and benevolent (maximal) formulations, other secondary-goal techniques are proposed and investigated [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Since it is possible that these two different formulations produce two different ranking results, decision makers may need to make a choice between these two formulations.…”