Positive weights in data envelopment analysis

Abstract

AbstractData Envelopment Analysis (DEA) models give each decision making unit freedom to assign values to the input-output weights maximising its efficiency score. However, there is no guarantee that the optimal weights obtained from a DEA model are always positive which poses a problem, in both theory and practice. This paper offers new linear programming models to deal with the zero weights problem without restricting the weights or placing prior value judgments on them while maintaining the original DEA frontier. These models generate a profile of weights with the maximum number of positive weights applicable to both envelopment and multiplier DEA settings. These linear programs still allow weight flexibility and are independent of the solver. We show how these models can be modified to provide unit-specific positive weights. We illustrate the relevance of our approach using artificial and real world data.