An interactive MOLP method for identifying target units in output-oriented DEA models: The NATO enlargement problem

• Target units in DEA are used to improve the performance of the inefficient units.
• Conventional DEA methods do not consider preferences in identifying target units.
• Existing models cannot identify target units when undesirable outputs are produced.
• We obtain a new link between DEA and the weighted minimax reference point.
• We show the applicability of the method in a pilot study for NATO enlargement problem.

Data Envelopment Analysis (DEA) is a mathematical programming technique for identifying efficient Decision Making Units (DMUs) with multiple inputs and multiple outputs. DEA provides a technical efficiency score for each DMU, a technical efficiency reference set with peer DMUs, and a target for the inefficient DMU. The target unit informs the Decision Maker (DM) of the amount (%) by which an inefficient DMU should decrease its inputs and/or increase its outputs to become efficient. However, the conventional DEA models generally do not consider the DM’s preference structure in identifying the target units. Several equivalence models between the output-oriented DEA and Multiple Objective Linear Programming (MOLP) models have been proposed in the literature to take the DMs’ preferences into consideration. However, these models are not able to identify target units when undesirable outputs are produced with desirable outputs in the production process. In this study we obtain a new link between a BCC model and the weighted minimax reference point of the MOLP formulation that simultaneously and interactively considers the increase in the total desirable outputs and the decrease in the total undesirable outputs. We present a pilot study for the North Atlantic Treaty Organization (NATO) enlargement problem to demonstrate the applicability of the proposed method and exhibit the efficacy of the procedures and algorithms.