A sequential insertion heuristic for the vehicle routing problem with time windows with relatively few customers per route

In this paper we study the performance of Solomon’s (1987) sequential insertion heuristic |1, for Vehicle Routing Problems with Time Windows (VRPTWs) in which the number of customers per rout is small with respect to the customers’ time windows and the scheduling horizon. Solomon’s (1987) time insertion c12 (i, u, j) underestimates the additional time needed of inserting a new customer u between the depot, i= i0 and the first customer j in the partially constructed rout (i0= I, i1=j,i1,…,im). This can cause the insertion criterion to select suboptimal insertion places for unrouted customers and the error in the corresponding insertion cost can cause the selection criterion to choose the wrong customer for intersection. Since the advance of the depot departure time is taken into account too cheaply, can have a larger schedule time than necessary. If, on the other hand, the number of custmoers per route is high, there is a high probability that the waiting time at the custmers, that were at position 1 during the construction of the route, can be used to insert other customers. An easy way to solve this problem and hence improve the quality of the heuristic for short-routed VRPTWs is suggested.