Total and Partial efficiency indexes in data envelopment analysis

Introduction: Data envelopment analysis (DEA) is a data-oriented method for measuring and benchmarking the relative efficiency of peer decision making units (DMUs) with multiple inputs and multiple outputs. DEA was initiated in 1978 when Charnes, Cooper and Rhodes (CCR) demonstrated how to change a fractional linear measure of efficiency into a linear programming format. This non-parametric approach solves an LP formulation per DMU to obtain an aggregate efficiency score to each DMU. A new variety of efficiency as partial efficiency has been faced in this paper.  Aim: The current paper studies the problem of partial efficiency in DEA. By using a DEA model, the paper determines a sharing matrix of inputs to optimize the aggregate efficiency of DMU under consideration. Material and methods: Toward this end, we have used the well-known non-parametric technique DEA.   Results: In this paper, we introduced a DEA model to (i) maximize the aggregate efficiency score and (ii) to determine the partial efficiency of each output. Conclusion: Traditional DEA models give an overall efficiency score to each operational unit based on the observed inputs and outputs. In the current study, new efficiency indexes are introduced. These partial indexes are referred to as partial efficiency of outputs. The paper gives the best resource allocation to maximize the aggregate efficiency of DMUs.