A Branch-and-Price Heuristic Algorithm for Vehicle Routing Problem with Soft Time Windows

A branch-and-price based heuristic algorithm (B&P_HA) is presented to solve the vehicle routing problem with soft time window (VRPSTW), whose objective is to minimize the total cost. In the B&P_HA, the linear problem (LP) relaxation of the set partitioning reformulation of the VRPSTW is solved by column generation. Specifically, a heuristic algorithm with greedy rules is firstly developed to construct initial columns, and then feasible columns are generated by using the special designed label correcting algorithm to solve the pricing subproblem (i.e., the single vehicle pricing subproblem). Furthermore, the branching scheme introduced is implemented when the LP's solution is fractional. Experimental results show that the B&P_HA algorithm outperforms the traditional branch-and-price algorithm.