A game theoretic approach to modeling undesirable outputs and efficiency decomposition in data envelopment analysis

The changing economic conditions have challenged many organizations to search for more effective performance measurement methods. Data envelopment analysis (DEA) is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogeneous decision making units (DMUs) by evaluating their relative efficiency. Performance measurement in the conventional DEA is based on the assumptions that inputs should be minimized and outputs should be maximized. However, there are circumstances in real-world problems where some output variables should be minimized. We consider the concepts of technical efficiency (the ratio of the desirable outputs to inputs) and ecological efficiency (the ratio of the desirable outputs to undesirable outputs) in DEA. We then introduce a new measure called process environmental quality efficiency (the ratio of the inputs to the undesirable outputs) and use game theory to integrate these three different efficiency scores into one overall efficiency score. The cooperative and non-cooperative game theory concepts are used to integrate different efficiency ratios into a linear model. We also present a case study to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed models.