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Open AccessArticle

Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

by Lijun Xu 1, Yijia Zhou 2,* and Bo Yu 3
1
School of Science, Dalian Maritime University, Dalian 116026, China
2
School of Computer & Software, Dalian Neusoft University of Information, Dalian 116023, China
3
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 211; https://doi.org/10.3390/math8020211
Received: 24 December 2019 / Revised: 23 January 2020 / Accepted: 2 February 2020 / Published: 7 February 2020
In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.
Keywords: robust optimization; duality theory; uncertain set; logistics production; inventory process robust optimization; duality theory; uncertain set; logistics production; inventory process
MDPI and ACS Style

Xu, L.; Zhou, Y.; Yu, B. Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process. Mathematics 2020, 8, 211.

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