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DISTRIBUTIONALLY ROBUST optimization OF THE VEHICLE ROUTING PROBLEM WITH UNCERTAIN CUSTOMERS

JOURNAL OF INDUSTRIAL AND MANAGEMENT optimization 2025年第3期21卷 1983-2006页

作者： Wang, Xiaopeng Zhao, Jinling Univ Sci & Technol Beijing Sch Math & Phys 30 Xueyuan Rd Beijing 100083 Peoples R China

With the rise of e-commerce, the express logistics industry has been developing rapidly, and the Vehicle Routing Problem (VRP) has been widely concerned. In this paper, we focus on the Vehicle Routing Problem with Uncertain Customers (VRPUC), which introduces the uncertain customers set on the basis of the capacitated vehicle routing problem, where the customers demands are uncertain. We first filter out potential uncertain customers using historical data, and then introduce a distributionally robust optimization model based on the cross-moment ambiguity set that minimizes the Essential Riskiness Index (ERI) of all vehicles, which can help mitigate the magnitude and probability of vehicle overload. The model can be reformulated as a mixed integer semidefinite optimization problem. We employ a branch-and-cut algorithm to tackle a relaxed version of this problem. Once the optimal solution is identified, a callback procedure is initiated to verify whether the current optimal solution meets the positive semidefinite constraint. If it does, the solution is confirmed as optimal for the original problem. If not, a lazy constraint is introduced to exclude the solution from the feasible region. Numerical experiments demonstrate that our model outperforms stochastic programming models across various performance indicators.

关键词： Vehicle routing problem uncertain demands distributionally robust optimization essential riskiness index mixed integer semidefinite optimization

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