An iterative route construction and improvement algorithm for the vehicle routing problem with soft time windows

The solution of routing problems with soft time windows has valuable practical applications. Soft time window solutions 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 (c) the dispatcher has qualitative information regarding the relative importance of hard time-window constraints across customers. This paper proposes a new iterative route construction and improvement algorithm to solve vehicle routing problems with soft time windows. Due to its modular and hierarchical design, the solution algorithm is intuitive and able to accommodate general cost and penalty functions. Experimental results indicate that the average run time performance is of order O(n). The solution quality and computational time of the new algorithm has been compared against existing results on benchmark problems. The presented algorithm has improved thirty benchmark problem solutions for the vehicle routing problems with soft time windows. 2009 Elsevier Ltd. All rights reserved.