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In the context of the increasing demands for home delivery of fresh food, this article addresses the terminal distribution problem in an urban environment, which is called the vehicle routing problem with flexible time windows and order release dates (VRPFTWRD). This study develops a mathematical model and presents a set of valid inequalities based on the problem characteristics. According to the model and the inequalities, a branch-and-cut algorithm (B&amp;C) is proposed for solving the problem. To verify the effectiveness of B&amp;C, a set of test problems of different sizes is generated. The results show that the VRPFTWRD problem with up to 55 nodes can be solved to be optimality within one hour. Furthermore, B&amp;C is used to solve vehicle routing problem (VRP) variants, and the results demonstrate that B&amp;C can effectively solve VRP variants within a reasonable time.

The vehicle routing problem with release dates and flexible time windows