Non-Cooperative Procedure in Two-Stage Systems with Shared Inputs and Final Outputs in the First Stage: A Slacks-Based Measure Model

In the present world, calculating the efficiency of systems with an internal structure, suchas two-stage systems, is principally imperative. Conventional Data envelopment analysis (DEA) is a non-parametric approach that measures the efficiency of comparable black box systems. There is a weakness in traditional DEA that does not survey the internal structure of systems. Hence, for evaluating the efficiency of the systems with internal structure, Network DEA (NDEA) was presented. Two-stage systems are a special case of network systems. Many procedures were suggested to measure the efficiency of these systems such as slacks-based measure (SBM) approach. In this paper, we will focus on two-stage systems with shared inputs between stages and final output in stage 1 and we shall propose non-cooperative models to calculate the efficiency of these systems based on SBM procedure. Also, we shall indicate the overall efficiency of these systems as the product of the efficiency scores of stages. In the end, to explain the proposed approach, a numerical example will be presented.