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In this paper, the authors introduced a real world new problem, the multi-trip vehicle routing problem with time windows and the possible use of a less-than-truckload carrier to satisfy customer demands. The purpose of this paper is to develop a heuristic algorithm to route the private trucks with time windows and to make a selection between truckload and less-than-truckload carriers by minimizing a total cost function.,Both mathematical model and heuristic algorithm are developed for routing the private trucks with time windows and for selecting of less-than-truckload carriers by minimizing the total cost function.,In all, 40 test problems were examined with the heuristics. Computational results show that the algorithm obtains the optimal or near-optimal solutions efficiently in terms of time and accuracy.,The research described in this paper differs from the previous one on fleet planning or vehicle routing, in that it modifies the Clarke and Wright method by shifting the performance measure from a distance to cost and also incorporates the fixed cost of different types of trucks into the model. In addition, the authors simultaneously consider the multiple trip vehicle routing problems with time windows and the selection of less-than-truckload carriers that is an integrated scenario of real-world application. To the best of the authors’ knowledge, this scenario has not been considered in the literature.

A heuristic algorithm for multiple trip vehicle routing problems with time window constraint and outside carrier selection