DEA Sensitivity Analysis for Parallel Production Systems

Abstract

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.