The design and optimization of urban-rural dual-directions logistics network is a substantial important issue, which will directly affect the development of the urban-rural integration in China. A reasonable scheme of logistics network will contribute to supply efficient logistics services to customers scattering in urban and rural areas. In this paper, we consider a variant of the Location-Routing-Problem (LRP), namely the LRP with simultaneous pickup and delivery in specially background (LRPSB). The objective of LRPSB is to minimize the total system cost, including depot location cost and vehicle routing cost, and implement and control the effective dual-direct commodity flow to meet customers requirement by simultaneously locating the depots and designing the vehicle routes that satisfy pickup and delivery demand of customer at the same time. A nonlinear mixed integrated programming model is formulated for the problem. Since such integrated logistics network design problems belong to a class of NP-hard problems, we propose a two-phase heuristic approach based on Tabu Search, tp-TS, to solve the large size problem and an initialization procedure to generate an initial solution for the tp-TS. We then empirically evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions or strong lower bounds, and investigate the effectiveness of the proposed heuristic approach. Computational results show that the proposed heuristic approach is computationally efficient in finding good quality solutions for the LRPSB.
A Meta-heuristic Approach for VRP with simultaneous pickup and delivery incorporated with Weber basis saving method