Inverse DEA under inter-temporal dependence using multiple-objective programming

•Modeling inverse DEA under inter-temporal dependence assumption.•Input-estimation and output-estimation under inter-temporal dependence.•Introducing a new optimality notion for MOP, periodic weak Pareto optimality.•Using periodic weak Pareto optimality in inverse DEA.•Characterizing periodic weak Pareto solutions.

This paper deals with the inverse Data Envelopment Analysis (DEA) under inter-temporal dependence assumption. Both problems, input-estimation and output-estimation, are investigated. Necessary and sufficient conditions for input/output estimation are established utilizing Pareto and weak Pareto solutions of linear multiple-objective programming problems. Furthermore, in this paper we introduce a new optimality notion for multiple-objective programming problems, periodic weak Pareto optimality. These solutions are used in inverse DEA, and it is shown that these can be characterized by a simple modification in weighted sum scalarization tool.