Abstract
•Traditional data envelopment analysis measures technical (radial) efficiency.•The input and output status of each performance measure is assumed known.•The data associated with each performance measure is assumed non-negative.•A new non-radial directional distance model is proposed to relax these assumptions.•A case study in the automotive industry demonstrates the efficacy of this approach.
Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units that convert multiple inputs into multiple outputs. Traditional DEA models measure technical (radial) efficiencies by assuming the input and output status of each performance measure is known, and the data associated with the performance measures are non-negative. These assumptions are restrictive and limit the applications of DEA to real-world problems. We propose a new extended non-radial directional distance model, which is a variant of the weighted additive model, to cope with negative data. We then extend our model and use flexible measures, which play the role of both inputs and outputs, to cope with the unknown status of the performance measures. We also present a case study in the automotive industry to exhibit the efficacy of the models proposed in this study.