A Branch and Price Algorithm for the Two-Agent Heterogeneous Fleet Vehicle Routing Problem with Time Windows

In this paper, a two-agent heterogeneous fleet vehicle routing problem with time windows (TAHF_VRPTW) is considered. The objective of the first agent is to minimize the total tardiness and the objective of the second agent is to minimize the total transportation cost. A new mixed integer programming model (MILP) is built for this problem, and then a new branch and price algorithm (NBAPA) is proposed to address it. In the NBAPA, a genetic algorithm (GA) is developed to construct the initial columns, and a label algorithm is designed to exactly solve sub-problems. If the optimal solution obtained by column generation contains real elements, this solution should be used for branch operation. Extensive computational experiments are conducted on the Solomon benchmark instances. The results show that within the specified time, compared with the standard BAP algorithm (i.e., theBAPwithout usingGAto generate initial columns), theNBAPA can reduce the computation time by an average of 28.32% and the average number of branches by 42.29%.