The use of public bicycle systems has gained great importance in European countries and around the globe; this has led to the need to seek advanced techniques to help decision making. A public bicycle system consists of a set of points where you can pick up and deliver bicycles; a headquarters where a group of vehicles taking leftover bikes and transported to the points where a deficit (the demand exceeds supply) exists. One of the major problems that arise in systems of public bike is balanced, which involves sending bikes from the point where an offer (bicycles left over) to the point where there is a demand (bikes missing) occurs. The way to model this problem is with an adaptation of the vehicle routing problem with pickup and delivery (VRPPD), allowing each route make partial deliveries to customers and limiting the number of customers to visit by each route. In this paper an integer linear programming model is introduced and a metaheuristic based on granular tabu search to find a local optimum. Instances from 15 to 500 customers adapted from the literature are used. The computational results show that the proposed algorithm finds solutions in short computational time.
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