Most productive scale size decomposition for multi-stage systems in data envelopment analysis

The most productive scale size (MPSS) of decision systems has been measured for the whole system by using conventional data envelopment analysis (DEA) methodology. This paper investigates the MPSS measurements for systems consisting of multiple stages connected in series by taking into account the interrelationship of the stages within the system. New models are proposed for determining the MPSS of the system and of the individual stages. Mathematical analysis proves that the MPSS of the system can be decomposed as the sum of the MPSS values of the individual stages. As a result, the system is overall MPSS if and only if it is MPSS in each stage. With MPSS decomposition, the decision maker can identify the non-MPSS stages and make subsequent improvements. For these improvements, an approach to project the non-MPSS system onto the MPSS region is proposed. Numerical examples are provided to show the applicability of the proposed methods in both estimating MPSS and deriving MPSS projections.