Inputs and Outputs Estimation in Inverse DEA

Abstract

The present study addresses the following question: if among a group of decision making units, the decision maker is required to increase inputs and outputs to a particular unit in which the DMU, with respect to other DMUs, maintains or improves its current efficiency<br />level, how much should the inputs and outputs of the DMU increase? This question is considered as a problem of inverse data envelopment analysis, and a method is introduced to<br />answer this question. Using (weak) pareto solutions of multiple-objective linear programming, necessary and sufficient conditions for inputs and outputs estimation are established.<br />An application of inverse DEA using real data (for choosing a suitable strategy for spreading educational departments in a university) is presented. In addition, two new optimal notions are introduced for multiple-objective programming problems: semi-pareto and semi-weak pareto optimal notions. The aforementioned solutions are used to answer the above question.