VRP

1. 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 • VRPis 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!