Optimising two-stage robust supplier selection and order allocation problem under risk-averse criterion

Abstract

This paper studies the supplier selection and order allocation (SS&OA) problem, where risks include a series of disruption scenarios with uncertain probability of occurrence. It is a challenge for industry decision-makers to balance the average cost and the level of risk under the ambiguity set for probabilities. To address this challenge, a two-stage distributionally robust (DR) Mean-CVaR model is presented for the SS&OA problem. A procedure is developed for constructing the ambiguity set, and Polyhedral and Box ambiguity sets are constructed to characterise the uncertain probabilities. The worst-case Mean-CVaR criterion is employed for the second-stage cost within the ambiguity set to trade off the expected cost and CVaR value. Three measures are incorporated to increase the resilience of the supply chain. The proposed robust model is reformulated into two mixed-integer linear programming models. A real case of the Huawei cell phone manufacturer is used to illustrate the validity of the proposed approach in numerical settings. Experimental results show that the new optimising approach can provide a robust SS&OA solution to immunise against the influence caused by uncertain probabilities. By comparative analyses, some management insights are obtained for industry decision-makers.

KEYWORDS:

• Supplier selection and order allocation problem
• disruption risks
• mean-CVaR criterion
• distributionally robust optimisation
• ambiguity set

Acknowledgements

Yuqiang Feng and Yanju Chen contributed equally to this work. The authors are especially thankful to Editor-in-Chief, Associate Editor 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, further reasonable inquiries can be directed to the corresponding author.

Notes

1 https://finance.eastmoney.com/a/202106111957465278.html

2 https://zhuanlan.zhihu.com/p/157520487

3 https://www.idc.com/getdoc.jsp?containerId=prAP47424421

4 https://map.baidu.com/

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant no. 61773150 and grant no. 71801077] and the Social Science Foundation of Hebei province [grant no. HB21YJ029].

Notes on contributors

Yuqiang Feng

Yuqiang Feng received his M.S. degree in mathematics from Hebei University, Baoding, China, in 2022. He is currently a PhD student in the School of Management, Northwestern Polytechnical University in China. His main research interests include Robust Optimisation, Supply Chain Network Design, Location-Allocation. His previous research has been published in journals such as Computers & Industrial Engineering and Expert Systems With Applications.

Yanju Chen

Yanju Chen received the B.S. and M.S. degrees in mathematics from the Department of Mathematics, Hebei University, Baoding, China, in 2002 and 2005, respectively. She received the Ph.D. degree in Management Science and Engineering from School of Management, Hebei University, in 2019. Currently, she is an Associate Professor in College of Mathematics and Information Science, Hebei University. Her recent research interests include equilibrium optimisation, robust optimisation, supply chain planning, and supply chain network design. She is the author of over 30 articles on those areas in journals such as IEEE Transactions on Fuzzy Systems, Applied Mathematical Modelling, Expert Systems With Applications, Computers & Industrial Engineering.

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 optimisation methods, algorithmic analysis and design for optimisation problems, such as 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.