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VRP with Time Windows (VRPTW)

The VRPTW is the same problem that VRP with the additional restriction that in VRPTW a time window is associated with each customer , defining an interval wherein the customer has to be supplied. The interval at the depot is called the scheduling horizon. Here is a formal description of the problem:

In the figure below we can see a graph representing an instance for solving with VRPTW. There, blue and white bars are representing the time window (i.e. business hours), where white area represents when we can make a delivery at that customer. By other side, the red line shows when is the delivery made for this particular solution.


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