TY - JOUR
T1 - Facility location design under continuous traffic equilibrium
AU - Ouyang, Yanfeng
AU - Wang, Zhaodong
AU - Yang, Hai
N1 - Funding Information:
The first author conducted this research while he was a visiting scholar in the Department of Civil and Environmental Engineering at the Hong Kong University of Science and Technology. This research was supported by the Research Grants Council of the Hong Kong Special Administrative Region of China through Project HKUST620913 , and the U.S. National Science Foundation through Grant CMMI-1234085 . The helpful advice from Professor S.C. Wong (University of Hong Kong) on the finite element method is gratefully acknowledged.
Publisher Copyright:
© 2015 Elsevier Ltd.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
KW - Continuum approximation
KW - Facility location
KW - Finite element method
KW - Lagrangian relaxation
KW - Mixed-integer program
KW - Traffic equilibrium
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U2 - 10.1016/j.trb.2015.05.018
DO - 10.1016/j.trb.2015.05.018
M3 - Article
AN - SCOPUS:84940505370
VL - 81
SP - 18
EP - 33
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
SN - 0191-2615
IS - P1
ER -