DEA Sensitivity Analysis for Parallel Production Systems

In this paper, we introduce systems consisting of several production units, each of which include several subunits working in parallel. Meanwhile, each subunit is working independently. The input and output of each production unit are the sums of the inputs and outputs of its subunits, respectively. We consider each of these subunits as an independent decision making unit(DMU) and create the production possibility set(PPS) produced by these DMUs, in which the frontier points are considered as efficient DMUs. Then we introduce models for obtaining the efficiency of the production subunits. Using super-efficiency models, we categorize all efficient subunits into different efficiency classes. Then we follow by presenting the sensitivity analysis and stability problem for efficient subunits, including extreme efficient and non-extreme efficient subunits, assuming simultaneous perturbations in all inputs and outputs of subunits such that the efficiency of the subunit under evaluation declines while the efficiencies of other subunits improve.