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Abstract
This paper proposes a distributionally robust chance constrained programming model for an emergency medical system location problem with uncertain demands. By minimising the total expected cost, the location of emergency medical stations, the allocation of the ambulances and demand assignments of system are optimised. The Wasserstein-metric is employed to construct the ambiguity set centred at an empirical distribution with a proper radius, which contains all the probability distributions of the uncertainties. We introduce a big-M technique to reformulate distributionally robust chance constrained programming into a corresponding mixed integer programm, which can be inner and outer approximated by Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR). Numerical experiments are illustrated to demonstrate the effectiveness of the formulations.
Acknowledgements
The authors would like to thank the editor and the anonymous reviewers for their valuable suggestions and comments which have led to a much improved paper.
Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
Notes on contributors
Yuefei Yuan
Yuefei Yuan received the B.S. and M.S. degrees in Mechanical Engineering from Universitt Duisburg-Essen, Duisburg, Germany, in 2016 and 2018, respectively. He is currently pursuing the Ph.D. degree with the School of Economics and Management, Chongqing Jiaotong University, Chongqing, China. His current research interests include transportation management and optimisation of transportation systems.
Qiankun Song
Qiankun Song was born in 1964. He received the B.S. degree in Mathematics in 1986 from Sichuan Normal University, Chengdu, China, the M.S. degree in Applied Mathematics in 1996 from Northwestern Polytechnical University, Xi'an, China, and the Ph. D. degree in Applied Mathematics in 2010 from Sichuan University, Chengdu, China. From July 1986 to December 2000, he was with Department of Mathematics, Sichuan University of Science and Engineering, Sichuan, China. From January 2001 to June 2006, he was with the Department of Mathematics, Huzhou University, Zhejiang, China. In July 2006, he moved to the Department of Mathematics, Chongqing Jiaotong University, Chongqing, China. He is currently a Professor at Chongqing Jiaotong University.
He is currently serving as an Editorial Board Member for Neurocomputing, Neural Processing Letters, Systems Science and Control Engineering, Journal of Applied Mathematics, British Journal of Mathematics & Computer Science, ISRN Applied Mathematics, Asian Journal of Mathematics and Computer Research, and a reviewer for Mathematical Reviews. He is the author or coauthor of more than 100 journal papers and two edited books. His current research interests include stability theory of neural networks and chaos synchronisation.
Bo Zhou
Bo Zhou received the B.Sc. degree in applied mathematics and the M.Sc. degree in computer application from Chongqing Jiaotong University, Chongqing, China, in 2010 and 2013, respectively, and the Ph.D. degree in applied mathematics from Southwest University, Chongqing, in 2016. From 2014 to 2015, he was a Program-Aid with Texas A&M University at Qatar, Doha, Qatar. Since 2016, he has been with the College of Mathematics and Statistics, Chongqing Jiaotong University, where he is currently a Professor. His current research interests include mathematical modelling, computer simulation, and optimisation of transportation systems.