  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.
