A queuing-location-allocation model for designing a capacitated bus garage system

The spatial distribution of bus garages determines the total vehicular dead mileage of the transit system because buses must travel between bus garages and terminals at the start or conclusion of a day. By contrast, the size of the garages determines the queuing status when buses enter or leave the garages. Thus, a bus garage system with reasonable distribution and size is required to address these problems. In this article, a queuing–location–allocation model for optimizing a bus garage system is developed. Since a nonlinear objective function is involved, a linearization technique is introduced to convert the proposed model into an equivalent linear form. Next, a Lagrangian relaxation algorithm is designed to solve the linear form model. To validate the proposed algorithm, two groups of randomly generated test instances and a real-life case, the Dalian transit system in China, are applied. The results show that the proposed Lagrangian heuristic is efficient and stable.