Branch-and-Price-and-Cut for the Vehicle Routing and Truck Driver Scheduling Problem

Many governments worldwide have imposed hours of service regulations for truck drivers to ensure that break and rest periods are regularly taken. Transport companies have to take these into account and plan the routes and schedules of their truck drivers simultaneously. This problem is called vehicle routing and truck driver scheduling problem (VRTDSP). With their paper “An exact method for vehicle routing and truck driver scheduling problems” [Technical Report No. 33, Jacobs University, School of Engineering and Science, Bremen, Germany] Goel and Irnich presented the first exact approach to the VRTDSP. They include hours of service regulations in a vehicle routing problem with time windows and use a branch-and-price algorithm to solve it. The main contribution of the paper at hand is to present a sophisticated branch-and-price-and-cut algorithm for the VRTDSP that is based on the parameter-free auxiliary network and the resource extension functions (REFs) defined in the work of Goel and Irnich. Their labeling algorithm is extended by means of defining backward REFs in order to build a bidirectional labeling. Feasible routes are constructed by a non-trivial merge procedure. Different acceleration techniques are used to speed up the solution process of the pricing problem. In addition, several classes of known valid inequalities are used to further strengthen the LP-relaxation of the master program. We present a detailed computational study to analyze the impact of the different techniques. The resulting algorithm is able to solve all VRTDSP benchmark instances with 25 customers and 44 out of 56 instances with 50 customers in two hours of computation time to proven optimality.