A PageRank-like measure for evaluating process flexibility

Abstract

Uncertainty has always been a threat to system performance in both manufacturing and service industries. Although cost-budgeting may limit available resources, a more flexible structure can still improve the system’s ability to deal with uncertainty. In this study, we develop a new measure to help find a more flexible structure without extensive simulation. We create a PageRank-analogous score whereby we can calculate the Flexibility Gap (FG) index to predict the better of two alternative structures with topological information only. We theoretically analyze how the FG index recognizes flexible sparse structures such as expander graphs with high expansion ratios. Numerical experiments show that the FG index is effective in ranking the flexibility performance of different structures in terms of average waiting time and expected lost sales. Moreover, we extend the FG index with minimal modification to accommodate the case of imperfect flexibility (i.e., flexible suppliers with shrinking capacities) and demonstrate that the generalized FG index is still a good predictor of expected lost sales. Our approach provides a novel view to explain flexibility. That is, sparse structures with higher graph expansion ratios disperse the demand fluctuation more “rapidly” among resources to cushion the shock of uncertainty.

Keywords:

• Process flexibility
• flexibility measurement
• expander graph
• PageRank
• shrinking capacity

Additional information

Funding

This work was supported by the National Key R&D Program of China under Grant No.2017YFF0209400 and Ministry of Science and Technology of the People’s Republic of China under Grant No. 2019IM020200.

Notes on contributors

Fengming Cui

Dr. Fengming Cui obtained his doctoral degree from the Department of Industrial Engineering at Tsinghua University. His research interests include modeling and analysis of flexible service and manufacturing systems.

Chen Wang

Dr. Chen Wang is an Associate Professor in the Department of Industrial Engineering at Tsinghua University. She obtained her doctoral degree from the Department of Industrial and Systems Engineering at the University of Wisconsin-Madison. Her research interests include decision analysis, risk analysis, and data-driven modeling.

Lefei Li

Dr. Lefei Li is an associate professor in the Department of Industrial Engineering at Tsinghua University. He is the Deputy Chair of the department and the deputy director of the Tsinghua Smart Logistics and Supply Chain Systems Research Center. He received his B.S. degree in Electronic Engineering from Zhejiang University in 2002, M.S. (2004) degree in Industrial Engineering, and Ph.D. (2006) degree in Systems and Industrial Engineering from the University of Arizona. He joined Tsinghua University in 2006, conducting research in Systems Engineering, Service Operations and Management, Logistics and Complex Systems Modeling and Simulation. He has been serving as an associate editor for the IEEE Transactions on Intelligent Transportation Systems, IEEE Intelligent Systems and Asian Pacific Journal on Operational Research. He is the assistant director of INCOSE Academic Council and the past president of the INCOSE Beijing Chapter.