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

Estimating and decomposing most productive scale size in parallel DEA networks with shared inputs: A case of China’s Five-Year Plans Saeed Assani1,2* · Jianlin Jiang1 · Ahmad Assani3 · Feng Yang2 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

This work is supported by the National Natural Science Foundation of China (No. 71631006, 11571169).

• Saeed Assani saeedassani@nuaa.edu.cn
  Tel: +8615077820900 Jianlin Jiang jiangjianlin@nuaa.edu.cn Ahmad Assani ahmad.assani@hs-karlsruhe.de Feng Yang fengyang@ustc.edu.cn 1 College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 2 School of Management, University of Science and Technology of China, Hefei 230026, China 3 Faculty of Computer Science and Business Computer Systems, Karlsruhe University of Applied Science, Karlsruhe, 76133, Germany 2

two FYPs among the others. Keywords: Data envelopment analysis·Most productive scale size·Parallel Network · Industry · Agriculture· Five-Year Plans 1 Introduction Data envelopment analysis (DEA) is a mathematical method for measuring the relative efficiency of decision making units (DMUs) which may have multiple inputs and outputs (Charnes, Cooper, & Rhodes, 1978). DEA was accorded this name because of the way it envelops the DMUs to identify an efficiency frontier that is used to evaluate the DMUs. On the efficient frontier, there is a unit at which the average productivity of the DMU inputs and outputs mix is maximized. This point is called the most productive scale size (MPSS), and it is first introduced to standard DEA by (Rajiv D. Banker, 1984). (Joe Zhu & Zhao-Han Shen, 1995) showed that the MPSS concept can always be used to estimate RTS without any adjustments unless a set of efficient DMUs exhibit linear dependency, i.e., it is the DMU itself that causes the MPSS concept not to work. Also, they pointed out that the MPSS concept itself is independent of assuming a linear production function in the CCR model. Cooper et al. (1996) proposed a measure of scale which is “dimensionless” (i.e., it does not depend on the units of measure used). (Zhu, 2000) gave a further discussion on linear production functions and DEA, where MPSS was the main research discussion. Later, (Rajiv D. Banker, Cooper, Seiford, Thrall, & Zhu, 2004) discussed RTS in DEA for each of the presently available types of models. In recent years, (Wang & Lan, 2013) defined the MPSS concept from a pessimistic perspective. Then they used a double frontier approach to integrate the optimistic and pessimistic measures of MPSS in one term. (Lee, 2016) proposed a multi-objective mathematical program with DEA constraints to set an efficient target that shows a trade-off between the MPSS benchmark and a potential demand fulfillment benchmark. The classic data envelopment analysis requires that the values for all inputs and outputs be known exactly. However, this assumption may not be true, because data in many real applications cannot be precisely measured. One of the important methods to deal with imprecise data is considering stochastic data in DEA. Therefore, Khodabakhshi (2009) studied the most productive scale size by considering stochastic data in 3

DEA. To that end, he extended the work of (Jahanshahloo & Khodabakhshi, 2003) in stochastic data envelopment analysis. To solve the stochastic model, a deterministic equivalent is obtained. Although the deterministic equivalent is no

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