EVALUATING DECISION MAKING UNITS WITH STOCHASTIC DATA BY THE MULTIPLIER MODEL IN DEA

Data Envelopment Analysis (DEA) is a linear (and mathematical) programming method, generally used in dealing with several inputs and outputs. It is used for computing the relative efficiency of a set of similar units, usually referred to as Decision Making Units (DMUs). DEA successfully separates DMUs into two groups: efficient and inefficient DMUs. DEA requires exact information for all inputs and outputs but under many circumstances, exact information is insufficient to model actual-life states. Hence, in this paper, we first use the concept of chance constrained programming to evaluate DMUs with stochastic data by the multiplier model. Next, we develop its deterministic equivalent which is a nonlinear program. Also, we prove that the deterministic equivalent of the stochastic multiplier model can be transformed to a quadratic program. The concept considered in this paper is illustrated using Khodabakhshi's (2010) data on Iranian electricity distribution units.