Selective vehicle routing problem with reserved requests and time windows

This paper focuses on a sub-problem in distributed collaborative delivery known as the Selective Vehicle Routing Problem with Time Windows and Reserved Requests (SVRPRRTW). First, we present a mixed-integer programming model for the SVRPRRTW and emphasize the importance of finding an exact solution. We have developed a branch-and-price algorithm that converts the initial problem into a master problem and sub-problems. Next, we devise a dynamic programming algorithm for the sub-problem. We provide detailed information regarding the branch strategies, node selection strategies, and lower bound generating heuristics in the branch-and-bound framework to yield integer solutions. We also introduce additional strategies to increase the algorithm’s speed. A series of numerical experiments demonstrate that although compared with commercial solvers, our algorithm is significantly more efficient for this problem. Additionally, for our proposed instances, our method can yield optimal solutions within acceptable time frames.