Abstract
The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this paper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.
Highlights
Nowadays, a China high-speed rail network has been formed, it is an urgent problem to design the Passenger Train Operation Plans (PTOP) based on networks, which is different from the general PTOP based on lines
In a forthcoming article, we studied a new kind of OPDP, named One-to-one Pickup and Delivery Problems with Shortest-path Transport (OPDPST), in which each pd-pair must be transported along the shortest path, and a new kind of modeling method was proposed for the OPDPST according its new route constructions
A new Pickup and Delivery Problem with new route structure, the OPDPSTRP, which is proposed in real-life connected graphs, is introduced and formulated in a new way
Summary
A China high-speed rail network has been formed, it is an urgent problem to design the Passenger Train Operation Plans (PTOP) based on networks, which is different from the general PTOP based on lines. Each vehicle starts at a given location and ends at the final delivery point of the pd-pairs transported by the vehicle, and cannot visit (stop at or pass through) any point more than once, namely each vehicle should travel along a real-life path. Constraints, such as vehicle load capacities, vehicle travel distances, and vehicle stops, need to be considered. Since each pd-pair must be transported along the shortest path and vehicle stops need to be considered, the OPDPSTRP will be studied based on connected graphs, which shouldn’t be abstracted into complete graphs.
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