Genetic algorithms for optimizing two-stage DEA by considering unequal intermediate weights

Evaluating the performance of a system with a network structure as a Decision-Making Unit (DMU) is a significant topic for many researchers and scholars. In this context, an appropriate method to assess the efficiency of a system is Network Data Envelopment Analysis (NDEA). Based on the structure of a corresponding network, which consists of at least two stages, an intermediate factor has an output nature for the first stage and an input nature for the second stage. Therefore, it is not appropriate to consider the same weight for each stage using this factor. Unfortunately, contrary to real-world conditions, all previous conventional NDEA studies have considered the same role for intermediate factors in order to linearize or simplify models. For the first time, this study seeks to determine the efficiency of a two-stage series system and its sub-processes with unequal intermediate product weights. Thus, the proposed model remains in its original nature as a complex combinatorial problem in the Non-Linear Programming (NLP) category of NP-hard problems. A Genetic Algorithm (GA) is utilized as a metaheuristic algorithm, and a novel hybrid GA-NDEA algorithm is presented to solve the problem. It is worth noting that the absence of any restrictions on the inequality of the intermediate weights brings the model closer to the nature of DEA models; consequently, the performance evaluation of DMUs comes closer to reality. Finally, the applicability of the proposed method is tested on non-life insurance companies in Taiwan, and the results are compared with the existing models.