1. Vehicle Routing Problem
VRP
Vehicle Routing Problem

2. What is VRP
Objective
Minimize routing costs.

3. Variations No. of vehicles No. of depots Time windows Returned goods
Combinations

4. Motivation
Deliveries
Airlines
Cargo Ships

5. Solutions techniques Route first, Partition later
Partition first, Route later

6. Route first, Partition later
Finding a short path through the set of customers sites first.
Equivalent to TSP
Partition customers into subsets s.t:
For each subset Si, vehicle V:
Tdemand (Si) <= capacity (V)
Choose the one which minimizes the total cost.

8. Partition first, Route later
Computes the polar coordinates of each customer with respect to the depot.
The sites are then sorted by increasing polar angle.
Start from arbitrary customer and sweep through consecutive customers.
For each Ci in customers
Add customer to subset Si while
Capacity(Si)+Capacity(Ci)<=Capacity(V)
Compute TSP for all subsets.

9. α

10. Equivalence to TSP
VRP is a generalization of the Traveling Salesperson.
TSP = VRP with one vehicle with no limits, no depot, customers with no demand.
Therefore is NP-Hard.

11. Demo

16. Sweep radius

17. Improvements

19. TSP vs. SWEEP
Which is better ???

20. ???
Thank you!