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

Keywords: Data envelopment analysis Target unit Undesirable output Multiple objective linear programming Minimax method a b s t r a c t 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. Data Envelopment Analysis (DEA), initially introduced by Charnes et al. [9], is a widely used mathematical programming approach for comparing the inputs and outputs of a set of homogenous Decision Making Units (DMUs) by evaluating their relative efficiency. DEA generalizes the usual efficiency measurement from a single-input single-output ratio to a multiple-input multiple-output ratio by using a ratio of the weighted sum of outputs to the weighted sum of inputs. Although DEA does not provide a precise mechanism for achieving efficiency, it does quantify the magnitude of change required to make the inefficient DMUs efficient and hence contributes to productivity growth. A DMU is considered efficient when no other DMU can either produce the same outputs by consuming fewer inputs, known as the ''input-orientated approach'', or produce more outputs by consuming the same inputs, known as the ''output-orientated approach''.