A distributionally robust optimisation model for last mile relief network under mixed transport

Abstract

The last mile relief network is the final stage of the relief chain but the most critical stage for ensuring the timely delivery of relief supplies after a disaster. Due to the suddenness of the disaster, balancing the shortages of relief supplies and the high demands of victims is a serious problem. We introduce a mixed transport way of relief supply transportation between points of distributions and demand nodes in our problem to face the manpower and resource limitations. We establish a bi-objective distributionally robust optimisation model to balance transportation time and transportation safety, where the demand, transportation time, freight and safety coefficient are assumed to be uncertain variables with partial distribution information. We also deduce the refinement robust counterparts under the ambiguous sets to prove the safe tractable approximations of chance constraints. Finally, we conduct a case study of Tonghai county earthquake to illustrate the efficiency of our proposed distributionally robust model.

Keywords:

• Last mile relief network
• mixed transport
• manpower and resource limitation
• distributionally robust optimisation
• safe approximation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61773150,71801077] and Natural Sciences and Engineering Research Council of Canada [grant number RGPIN-2014-03594,RGPIN-2019-07115] and High-Level Innovative Talent Foundation of Hebei University [grant number 521000981073] and Top-notch talents of Heibei province [702800118009].

Notes on contributors

Peiyu Zhang

Peiyu Zhang received her M.S. degree in mathematics from Heibei University, Baoding, China, in 2020. She is currently a PhD student in Transportation Science and Engineering from Beijing University of Aeronautics and Astronautics. Her main research interests include Emergency Management, Vehicle Platoon Control, Internet of Vehicles and Robust Optimization. Her previous research has been published in journals such as Annals of Operations Research and Soft Computing.

Yankui Liu

Yankui Liu received the B.S. and M.S. degrees from the Department of Mathematics, Hebei University, Baoding, China, in 1989 and 1992, respectively. He received the Ph.D. degree in computational mathematics from Department of Mathematical Science, Tsinghua University, Beijing, China, in 2003. He is a Professor with the College of Mathematics and Information Science, Hebei University, Baoding, China. Professor Liu is the author of seventy research papers and five monographs. His work ranges from theoretical/foundational work including credibility measure theory and robust credibilistic optimisation methods, to algorithmic analysis and design for optimisation problems such as credibilistic approximation approaches and their convergence, and to applications in various engineering and management problems. Based on the citations in Scopus database, he is featured among the Most Cited Chinese Researchers in the field of computer science since 2014.

Guoqing Yang

Guoqing Yang received the B.S. and M.S. degrees from the Department of Mathematics, Hebei University, Baoding, China, in 2009 and 2013, respectively. He received the Ph.D. degree in Management Science and Engineering from College of Management and Economics, Tianjin University, Tianjin, China, in 2016. Currently, he is an Associate Professor in School of Management, Hebei University. His research interests include supply chain network design, emergency management, intelligent algorithms, uncertain optimisation and data-driven optimisation. He has authored or coauthored over 20 articles on those areas in journals such as Annals of Operations Research, Journal of the Operational Research Society, IEEE Transactions on Fuzzy Systems, Applied Mathematical Modelling, Applied Soft Computing, and so on.

Guoqing Zhang

Guoqing Zhang is a Professor in Industrial Engineering, the director of supply chain and logistics optimisation research lab at Department of Mechanical, Automotive & Materials Engineering, University of Windsor. He received the Ph.D. degree in management sciences from City University of Hong Kong in 2000. His recent research interests include supply chain management and optimisation, logistics, warehouse management, algorithms design and development, operations research, data-driven optimisation and intelligent decision support systems. He has published over 70 articles on those areas in journals such as Operations Research, Eur. J. Oper. Res., IIE Transactions, Transport Res B-Meth and E-Log, Omega, Int. J. Prod. Res., Int. J. Prod. Econ., Comput Oper Res., and so on. Dr Zhang has provided consulting to several world leading companies on Automotive, Energy, Airline, and Foods industries. Dr. Zhang and his team won the first place in the Canadian Operations Research Society Practice Prize competition in 2015.