decomposition of cost efficiency, given the set of price and cost production possibilities in data envelopment analysis

Data envelopment analysis (dea) science can deal with the most important management and economic concepts which identify the source of energy-wasting inefficiencies in decision making units (dmus).in addition to the input and output values of the dmus, if the price of each input unit is known, one can introduce three production possibility sets (ppss): the pps made by the input and outputs; the pps made by the prices and outputs; the cost pps obtained from the multiple of optimal inputs and optimal prices derived from the two input and price sets. this study presents two ways for decomposing the efficiency and opportunities lost: first, the condition in which the technical inefficiencies and congestion are first resolved in the pps made by inputs, and then, they are resolved in the price, and second, the condition in which the technical efficiencies and congestion are first resolved in the price pps, and then, they are resolved in the input pps, and finally, in both conditions, the cost inefficiencies are resolved in the cost pps.