Facility location design under continuous traffic equilibrium
Facility location design under continuous traffic equilibrium
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DOI：
10.1016/j.trb.2015.05.018
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发表时间：
2015-11
影响因子：
6.8
通讯作者：
Y. Ouyang;Zhaodong Wang;Hai Yang
中科院分区：
文献类型：
--
作者：
Y. Ouyang;Zhaodong Wang;Hai Yang
本文提出了在客户需求弹性和连续空间交通均衡的情况下，中间型设施选址设计的两种建模方法。第一种方法遵循连续介质近似方案，建立在无限均匀平面的特殊情况下，其中交通平衡可用常微分方程式描述。这种同质情况的解，有时是封闭形式的，然后被用来开发更一般情况的近似解(例如，在异质空间中的情况)。该模型提供了一种计算效率高的方法来获得管理洞察力和接近最优的解决方案，特别是对于大型问题实例。我们还开发了一个更传统的混合整数规划形式的离散选址模型，该模型直接建立在客户交通平衡的非线性偏微分方程描述的基础上。我们开发了一种基于拉格朗日松弛的求解方法，并嵌入了有限元子程序，以分离和求解选址决策以及交通平衡。通过数值实验验证了所提模型的适用性，并比较了两种互补建模方法的性能。
This paper presents two modeling approaches for median-type facility location design under elastic customer demand and traffic equilibrium in a continuous space. The first approach, following the continuum approximation scheme, builds upon the special case of an infinite homogeneous plane where traffic equilibrium can be described by an ordinary differential equation. The solution to this homogeneous case, sometimes in a closed form, is then used to develop approximate solutions to more general cases (e.g., those in a heterogeneous space). This model provides a computationally efficient way to obtain managerial insights and near-optimal solutions, especially for large problem instances. We also develop a more traditional discrete location model in the form of a mixed-integer program, which builds directly upon a nonlinear partial differential equation description of customer traffic equilibrium. We develop a Lagrangian relaxation based solution approach with an embedded finite-element method subroutine, to separate and solve the location decisions as well as the traffic equilibrium. Numerical experiments are conducted to illustrate applicability of the proposed models and to compare performance of the two complementing modeling approaches.