An Iterative Route Construction and Improvement Algorithm for the Vehicle Routing Problem with Soft and Hard Time Windows

The joint solution of routing problems with soft and hard time windows has valuable practical applications. Simultaneous solution approaches to both types of problems are needed when: (a) the number of routes needed for hard time windows exceeds the number of available vehicles, (b) a study of cost-service tradeoffs is required or the dispatcher has qualitative information regarding the relative importance of hard time window constraints across customers. A new Iterative Route Construction and Improvement (IRCI) algorithm of average run time performance 2 ( ) O n is proposed to sequentially solve Vehicle Routing Problems with Soft Time Windows (VRPSTW) and Hard Time Windows (VRPHTW). Due to its modular and hierarchical design, the IRCI algorithm is intuitive, easy to code, and able to accommodate general cost and penalty functions. The solution quality and computational time of the new algorithm is compared against existing results on benchmark problems for the VRPHTW and VRPSTW. Furthermore, the algorithm can be used to obtain faster simultaneous solutions for both VRPHTW and VRPHTW problems using the soft time windows solutions as a lower bound for hard time window problems. Despite its simplicity and flexibility, the algorithm performs well in terms of solution quality and speed in instances with soft and hard time windows.