Inputs and Outputs Estimation in Inverse DEA

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 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 answer this question. Using (weak) pareto solutions of multiple-objective linear programming, necessary and sufficient conditions for inputs and outputs estimation are established. 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: semipareto and semi-weak pareto optimal notions. The aforementioned solutions are used to answer the above question.