01660519

Component

Ng and Lo formulated the housing supply allocation problem with a bi-level program, in which the upper level maximizes the housing profit by determining the optimal housing supply, while the lower level constitutes a combined bid-rent and residence choices equilibrium model. The lower level involves not only the conventional user equilibrium conditions as in the network design problem (NDP), but also the bid-rent process which describes the competition among residents bidding for housing. Similar to the classical NDP, this bi-level problem belongs to the class of mathematical program with equilibrium constraints (MPEC), whose solution global optimality is not guaranteed. This paper proposes a global optimal solution algorithm to solve such problems, including the continuous NDP (CNDP) as a special case. Specifically, the original housing supply allocation problem is reformulated and relaxed into a mixed-integer linear program (MILP) through the process of piecewise linear relaxation of the original nonlinear functions. The MILP provides a global solution to the linearized original problem through the iterative solution algorithm developed in this paper. Extending the work of Polisetty, the proposed updating process of the linearized problem and the information from the original problem at each iteration step assure convergence of the global optimal solution. This paper provides a proof of the global optimality of the solution, and numerical studies to demonstrate its promising results, in solution accuracy and computational speed.

This paper was sponsored by TRB committee ADB30 Standing Committee on Transportation Network Modeling.

18-03897

English

4p

2018

Transportation Research Board 97th Annual Meeting

Digital/other

References

Algorithms; Choice models; Mixed integer programming; Network analysis (Planning); Optimization; Rent; Residential location; Stochastic processes; Traffic assignment

Planning and Forecasting; Transportation (General)

Transportation Research Board Annual Meeting 2018 Paper #18-03897

TRIS, TRB, ATRI

Jan 8 2018 10:58AM