Distributionally Robust Fair Transit Resource Allocation During a Pandemic
Distributionally Robust Fair Transit Resource Allocation During a Pandemic
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DOI：
10.2139/ssrn.3874612
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
Weijun Xie;Luying Sun;T. Witten
中科院分区：
文献类型：
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作者：
Weijun Xie;Luying Sun;T. Witten
研究了Wasserstein模糊集下的分布鲁棒公平公交资源分配模型（DrFRAM），以优化疫情期间的公交资源分配。我们表明，建议DrFRAM是高度非凸和非线性的，它是NP-困难的一般。幸运的是，我们表明，DrFRAM可以重新制定为一个混合整数线性规划（MILP），利用等价表示的分布鲁棒优化和单调性属性，二进制化整数变量，线性化非凸项。为了改善建议MILP制定，我们得到更强的，并开发有效的不等式，利用模型结构。此外，我们开发的方案分解方法，使用不同的MILP配方来解决的情况下的子问题，并引入一个简单而有效的没有一个左为基础的近似算法与可证明的近似保证解决模型接近最优。最后，我们数值证明了所提出的方法的有效性，并将其应用到现实世界的数据提供的布莱克斯堡过境。
This paper studies the distributionally robust fair transit resource allocation model (DrFRAM) under the Wasserstein ambiguity set to optimize the public transit resource allocation during a pandemic. We show that the proposed DrFRAM is highly nonconvex and nonlinear, and it is NP-hard in general. Fortunately, we show that DrFRAM can be reformulated as a mixed integer linear programming (MILP) by leveraging the equivalent representation of distributionally robust optimization and monotonicity properties, binarizing integer variables, and linearizing nonconvex terms. To improve the proposed MILP formulation, we derive stronger ones and develop valid inequalities by exploiting the model structures. Additionally, we develop scenario decomposition methods using different MILP formulations to solve the scenario subproblems and introduce a simple yet effective no one left-based approximation algorithm with a provable approximation guarantee to solve the model to near optimality. Finally, we numerically demonstrate the effectiveness of the proposed approaches and apply them to real-world data provided by the Blacksburg Transit.