Estimating and decomposing most productive scale size in parallel DEA networks with shared inputs: A case of China's Five-Year Plans

Abstract: Attaining the optimal scale size of production systems is an issue frequently found in the priority questions on management agendas of various types of organizations. Determining the most productive scale size (MPSS) allows the decision makers not only to know the best scale size that their systems can achieve but also to tell the decision makers how to move the inefficient systems onto the MPSS region. This paper investigates the MPSS concept for production systems consisting of multiple subsystems connected in parallel. First, we propose a relational model where the MPSS of the whole system and the internal subsystems are measured in a single DEA implementation. Then, it is proved that the MPSS of the system can be decomposed as the weighted sum of the MPSS of the individual subsystems. The main result is that the system is overall MPSS if and only if it is MPSS in each subsystem. MPSS decomposition allows the decision makers to target the non-MPSS subsystems so that the necessary improvements can be readily suggested. An application of China's Five-Year Plans (FYPs) with shared inputs is used to show the applicability of the proposed model for estimating and decomposing MPSS in parallel network DEA. Industry and Agriculture sectors are selected as two parallel subsystems in the FYPs. Interesting findings have been noticed. Using the same amount of resources, the Industry sector had a better economic scale than the Agriculture sector. Furthermore, the last two FYPs, 11th and 12th, were the perfect two FYPs among the others.