Risk-averse two-stage distributionally robust optimisation for logistics planning in disaster relief management

Abstract

Relief logistics is vital to disaster relief management. Herein, a risk-averse two-stage distributionally robust programming model is proposed to provide decision support for planning disaster relief logistics. It is distinct from the conventional disaster relief logistics planning problem in that (i) the facility location-inventory model and the multi-commodity network flow formulation are integrated; (ii) the probability distribution information of the supply, demand, and road link capacity is partially known, and (iii) the two-stage distributionally robust optimisation (DRO) method based on the worst-case mean-conditional value-at-risk criterion is developed. For tractability, we reformulate the proposed DRO model as equivalent mixed-integer linear programs for box and polyhedral ambiguity sets, which can be directly solved to optimality using the CPLEX software. To evaluate the validity of the proposed DRO model, we conduct numerical experiments based on a real-world case study addressing hurricane threats in the Gulf of Mexico region of the United States. Furthermore, we compare the performance of the proposed DRO model with that of the conventional two-stage stochastic programming model. Finally, we report the managerial implications and insights of using the risk-averse two-stage DRO approach for disaster relief management.

Keywords:

• Disaster relief logistics
• distributionally robust optimisation
• uncertainty
• conditional value-at-risk
• ambiguity sets

Acknowledgements

The authors are grateful to Emilia Grass for providing us with the data/information for the case study. The authors thank the editor and the reviewers for their highly constructive comments on the manuscript.

Data availability statement

The data sets for the case study can be found at https://zenodo.org/record/1012684.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Nos. 71942006, 71621001, 71825004 and 71890972/71890970] and the Fundamental Research Funds for the Central Universities [No. 2020JBM031].

Notes on contributors

Duo Wang

Duo Wang received the B.S. and M.S. degrees in Mathematics from Henan University of Science and Technology, Luoyang, China, in 2016. She is currently a Ph.D. student in System Science from Beijing Jiaotong University. Her main research interests include emergency management, supply chain network design and distributionally robust optimisation. Her previous research has been published in Evolution Equations and Control Theory.

Kai Yang

Kai Yang received the M.S. degree in Applied Mathematics from the Hebei University, Baoding, China, in 2012 and Ph.D. degree in Management Science and Engineering from the Tianjin University, Tianjin, China, in 2015. He is currently an Associate Professor at School of Traffic and Transportation, Beijing Jiaotong University, China. His interesting researches include stochastic programming and robust optimisation, and their applications in transportation planning.

Lixing Yang

Lixing Yang received the B.S. and M.S. degrees from the Department of Mathematics, Hebei University, Baoding, China, in 1999 and 2002, respectively. In 2005, he received Ph.D. degree from the Department of Mathematical Sciences, Tsinghua University, Beijing, China. He is currently a Professor at State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China. His current research interests include uncertain programming, intelligent systems, and applications in transportation planning and rail traffic control systems.