This paper presents the results of a comparison study of three solution strategies for integrating a routing and a control model for a fleet of vehicles planned to visit a number of customer locations. The three strategies considered are: (i) shortest route followed by a constant speed model, (ii) shortest route followed by an optimal control model, and (iii) optimal control-based route. The objective is to compare and contrast optimized costs, a combination of vehicles’ travel time and control cost (or energy consumption), following these different strategies. The routing problem considers a capacitated multi-vehicle routing without time windows but with capacity and customer demand requirements. The control problem considers a continuous-time optimal control problem. Using the data from a benchmark multi-vehicle routing problem, as an example, it is shown that when compared with using a commonly used constant speed model for all vehicles, the optimized cost can be reduced by incorporating optimal control strategies. To the best of our knowledge, this is the first study in the literature that compares solution strategies for control-based vehicle routing, and in particular, formulates and explores continuous time optimal control combined with capacitated multi-vehicle routing. Furthermore, the effect of existence of wind on the vehicle dynamic equations is considered, and optimal results of the routing problem with different wind directions are compared.

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