A Two-stage DEA Model Considering Shared Inputs, Free Intermediate Measures and Undesirable Outputs

Data envelopment analysis (DEA) has been proved to be an excellent approach for measuring the performance of decision-making units (DMUs) that use multiple inputs to generate multiple outputs. But the allocation problem of shared inputs and undesirable outputs does not arouse attention in this movement. This paper proposes a two-stage DEA model considering simultaneously the structure of shared inputs, additional input in the second stage and part of intermediate products as the final output. In addition, a part of second stage outputs is undesirable which can be fed back as raw materials to the first stage. Cooperative and non-cooperative game theories are discussed in order to determine the upper and lower bounds of the efficiencies of sub-DMUs in different stages to assess the relative performance of the operational units.