Modelling the semi-additive production technology in DEA

The semi-additive production technology allows for the aggregation of production units in the process of efficiency analysis using data envelopment analysis (DEA). This means that one must consider not only the full set of decision-making units (DMUs), but as well the entire power set, that is the set of all aggregations of the set of DMUs. Specifically, for n DMUs the number of variables involved is 2(n), hence requiring one to solve a set of linear programming problems, each of size O(2(n)). In a big data sense, such a problem becomes prohibitive as n increases. The current paper proposes a new model that significantly decreases the computational complexity of models based on the semi-additive production technology. We show that the proposed semi-additive methodology allows the number of variables to be decreases from 2(n) to n, and the complexity of the algorithm to be reduced from O(2n)to O(n). Three numerical and graphical examples are presented to illustrate the methodology. (C) 2020 Elsevier Ltd. All rights reserved.