Visualization of a Capacitated Vehicle Routing Problem with Time Window

The video shows side by side comparison of a capacitated multi-vehicle problem (L.H.S) with the goal of optimizing distance, and a capacitated vehicle time-window problem with the goal of optimizing both distance and time (R.H.S).
The Vehicle Routing Problem (VRP) is a combinatorial optimization problem of the NP-hard category. It is a broad generalization of the better known Traveling Salesman Problem (TSP). There is a huge concern in the logistics and transportation industry where the goal of a given company is to transport goods and services to their customers in the most efficient way. This efficiency can be measured by a wide variety of metrics for example minimising the total distance taken, time taken for journey, fuel costs, number of riders or maximizing the amount of customers serviced by one rider etc.
There are many variants of the vehicle routing problem where different objective functions are optimized based on particular needs. For instance, the most basic form of VRP is Capacitated VRP (CVRP) where the constraint is applied on the capacity of the vehicle while making sure that maximum customers are served at minimum cost. Similarly, in Distance Constraint VRP (DCVRP), there is a constraint on the distance that can be covered by the vehicle. Another category is VRP with Time Window (VRP-TW) where only limited time is allowed to make the delivery and return back to the depot.

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