Globalised robust bilevel model for multi-commodity distribution and vehicle assignment in post-disaster rescue

Abstract

Post-disaster rescue is the process of managing a series of actions such as commodity distribution and vehicle assignment, to alleviate the suffering of affected people and losses. However, finding the optimal strategy for post-disaster rescue is challenging due to the complexity arising from the hierarchical relationship and uncertainty. A bilevel globalised robust optimisation (GRO) model is built to formulate this joint multi-commodity distribution and vehicle assignment problem. The GRO method is adapted to find the robust solution for all uncertain parameter values by controlling the distance of the parameter from the normal perturbation set. The upper and lower level objectives, which reflect fairness and timeliness, are to minimise the unsatisfied demand and transportation time, respectively. We derive a tractable GRO model and employ Karush-Kuhn-Tucker (KKT) conditions to reformulate the initial model as a single level one solved by CPLEX software. The application of the model is illustrated by a case study of a tornado. Computational results indicate that bilevel optimisation achieves a balance between fair distribution and timely response, and the GRO method can effectively resist uncertainty. Our optimisation approach is beneficial for managers to make efficient decisions in rescue activities.

Highlights

• Uncertain demand and uncertain transportation cost are considered and characterised by perturbation sets.

• Fairness and timeness are considered simultaneously.

• A novel globalized robust bilevel optimisation model is proposed.

• The proposed model is transformed into a computationally tractable single level model, which can be solved by CPLEX.

• A case study about the tornado at Yancheng City is provided to illustrate the effectiveness and practicability of the proposed method.

KEYWORDS:

• Post-disaster rescue
• multi-commodity distribution
• vehicle assignment
• globalised robust optimisation
• bilevel programming

Acknowledgments

Xiaojuan Ma and Yankui Liu have contributed equally to this work. The authors are especially thankful to Editor-in-Chief and anonymous reviewers for their valuable comments, which help us to improve the paper a lot.

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work is supported in part by the National Natural Science Foundation of China [grant number 61773150], the Operations Research and Management Innovation Team of Hebei University [grant number IT2023C02], the Humanities and Social Sciences Research Program of the Ministry of Education [grant number 20YJC630001], the Natural Science Foundation of Hebei [grant number A2022204001], the Science and Technology Project of Hebei Education Department [grant number QN2021080], and the Post-graduates Innovation Fund Project of Hebei University [grant number HBU2022ss008].

Notes on contributors

Xiaojuan Ma

Xiaojuan Ma received the B.S. degree in mathematics from the Department of Mathematics, Hebei Normal University of Science & Technology, Qinhuangdao, China, in 2020. She received the M.S. degree in mathematics from the Department of Mathematics, Hebei University, Baoding, China, in 2023. She is currently a researcher. Her main research interests include robust optimisation theory and its applications, bilevel programming and disaster management.

Yankui Liu

Yankui Liu received the B.S. and M.S. degrees in mathematics from the Department of Mathematics, Hebei University, Baoding, China, in 1989 and 1992, respectively, and the Ph.D. degree in computational mathematics from the Department of Mathematical Science, Tsinghua University, Beijing, China, in 2003. He is currently a Professor with the College of Mathematics and Information Science, Hebei University. He has authored or coauthored more than 100 research papers and 6 monographs. His research interests include theoretical/foundational work, including credibility measure theory and robust credibilistic optimisation methods, algorithmic analysis and design for optimisation problems, such as credibilistic approximation approaches and their convergence, and applications in various engineering and management problems. Prof. Liu was featured among the most cited Chinese Researchers in the fields of computer science (from 2014 to 2019) and management science and engineering (from 2020 till now), based on the citations in the Scopus database.

Xuejie Bai

Xuejie Bai received the B.S. degree from the Department of Mathematics, Hebei Agricultural University, Baoding, China, in 2004. She received the M.S. degree from the Department of Mathematics, in 2010, and the Ph.D. degree in Management Science and Engineering from College of Management, Hebei University, Baoding, China, in 2015, respectively. She is currently an Associate Professor with the College of Science, Hebei Agricultural University. Her main research interests include credibilistic optimisation, emergency management and game theory. She has authored or coauthored over 20 articles on those areas in journals such as Information Sciences, Journal of Cleaner Production, Computers & Industrial Engineering, and Journal of Intelligent Manufacturing.