Fair ranking of the decision making units using optimistic and pessimistic weights in data envelopment analysis

Ranking all of the decision making units (DMUs) is one of the most important topics in Data envelopment analysis (DEA). Provided methods for ranking often rank the efficient units. Ranking inefficient units by early DEA models has some weaknesses since slacks are ignored. One of the methods presented in the ranking of all DMUs is Khodabakhshi and Ariavash’s method [M. Khodabakhshi and K. Ariavash, Appl. Math. Lett. 25 (2012) 2066–2070.] in this method, the maximum and minimum efficiency values of each DMU are measured by considering the sum of all efficiencies equal one. Finally, the rank of each DMU is determined in proportion to a convex combination of its minimum and maximum efficiency values. But optimistic and pessimistic weights of the other DMUs are not considered in ranking of the evaluated DMU. In this paper, a fair method to rank all DMUs, using Khodabakhshi and Ariavash’s method is proposed. In the proposed method optimistic and pessimistic efficiency values will be assessed, not only by the optimal weights of evaluated DMU but also by considering the optimistic and pessimistic optimal weights of all DMUs. The obtained optimistic and pessimistic efficiency values are supposed as criterion for the ranking. The proposed method is illustrated by a numerical example.