Robust optimization is a new modeling method to study uncertain optimization problems, which is to find a solution with good performance for all implementations of uncertain input. This paper studies the optimal location allocation of processing plants and distribution centers in uncertain supply chain networks under the worst case. Considering the uncertainty of the supply chain and the risk brought by the uncertainty, a data-driven two-stage sparse distributionally robust risk mixed integer optimization model is established. Based on the complexity of the model, a distribution-separation hybrid particle swarm optimization algorithm (DS-HPSO) is proposed to solve the model, so as to obtain the optimal location allocation scheme and the maximum expected return under the worst case. Then, taking the fresh-food supply chain under the COVID-19 as an example, the impact of uncertainty on location allocation is studied. This paper compares the data-driven two-stage sparse distributionally robust risk mixed integer optimization model with the two-stage sparse risk optimization model, and the data results show the robustness of this model. Moreover, this paper also discusses the impact of different risk weight on decision-making. Different decision makers can choose different risk weight and obtain corresponding benefits and optimal decisions. In addition, the DS-HPSO is compared with distribution-separation hybrid genetic algorithm and distributionally robust L-shaped method to verify the effectiveness of the algorithm.
Citation: Zhimin Liu. Data-driven two-stage sparse distributionally robust risk optimization model for location allocation problems under uncertain environment[J]. AIMS Mathematics, 2023, 8(2): 2910-2939. doi: 10.3934/math.2023152
Robust optimization is a new modeling method to study uncertain optimization problems, which is to find a solution with good performance for all implementations of uncertain input. This paper studies the optimal location allocation of processing plants and distribution centers in uncertain supply chain networks under the worst case. Considering the uncertainty of the supply chain and the risk brought by the uncertainty, a data-driven two-stage sparse distributionally robust risk mixed integer optimization model is established. Based on the complexity of the model, a distribution-separation hybrid particle swarm optimization algorithm (DS-HPSO) is proposed to solve the model, so as to obtain the optimal location allocation scheme and the maximum expected return under the worst case. Then, taking the fresh-food supply chain under the COVID-19 as an example, the impact of uncertainty on location allocation is studied. This paper compares the data-driven two-stage sparse distributionally robust risk mixed integer optimization model with the two-stage sparse risk optimization model, and the data results show the robustness of this model. Moreover, this paper also discusses the impact of different risk weight on decision-making. Different decision makers can choose different risk weight and obtain corresponding benefits and optimal decisions. In addition, the DS-HPSO is compared with distribution-separation hybrid genetic algorithm and distributionally robust L-shaped method to verify the effectiveness of the algorithm.
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Zhimin Liu. Data-driven two-stage sparse distributionally robust risk optimization model for location allocation problems under uncertain environment[J]. AIMS Mathematics, 2023, 8(2): 2910-2939. doi: 10.3934/math.2023152
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