A branch-and-price algorithm for the multi-trip multi-repairman problem with time windows

This study introduces the multi-trip multi-repairman problem with time windows where an integrated traveling cost involving distance-dependent and time-dependent costs needs to be minimized. The problem is formulated as two mixed integer programming models. A branch-and-price algorithm is proposed, in which two route-generating approaches are devised to handle the pricing sub-problem. A large number of instances are randomly generated based on an actual service network of China. The proposed algorithm is validated based on these instances and compared to the direct solving method using Cplex. The comparison to the single-trip mode indicates the advantages of the multi-trip mode.