A New Heuristic for Vehicle Routing with Narrow Time Windows

This paper describes a new heuristic for vehicle routing problems with narrow time windows. The problem arises in the context of the delivery of groceries to restaurants. For most of the instances the given time window distribution does not allow solutions where no time restrictions are violated. The aim is to schedule most of the customers in time building regionally bounded tours. The few remaining customers have to be scheduled manually. If the disponent decides to serve one or more of the remaining customers in time, he has to allow out-of-time deliveries for some of the automatically planned stops. The algorithm is based on a clustering procedure where a tree with multiple node weights is divided into subtrees. Upper bounds restrict the sums of the weight functions in each subtree. This problem is NP-complete for trees with a restricted number of weight functions. A greedy algorithm is developed to determine the tree partition. For our application it is extended to a version which..