1. Management Science 461 Lecture 8 – Vehicle Routing November 4, 2008

2. 2 Basic Vehicle Routing Problem Extend the TSP Given customer and depot locations, demands, vehicle capacity Find a set of tours that minimize the total cost  Many potential constraints on tours… Two tasks: Assign customers to tours, optimize tours

3. 3 5 7 2 6 12 2 5 Vehicle Capacity =20 Route length = 8 hrs

4. 4 Cluster-Route

5. 5 Finding Clusters Seeding – choose some nodes, “grow” each cluster from the node Sweep – like a radar screen Grid – Overlay a grid, cluster based on the grid

6. 6 Route-Cluster (eg Sweep)

7. 7 Clarke-Wright Savings “Savings heuristic” Assume that each node served by a single truck For each pair, calculate the savings incurred by merging the two trips together Rank savings, keep merging Is this a greedy (myopic) heuristic?

8. 8 Savings Depot Cust 2 Cust 1 Depot Cust 2 Cust 1 Savings = d(Depot,1) + d(2,Depot) - d(2,1)

9. 9 Savings s ij = c ia + c aj - c ij c ai + c ia +c aj + c ja i j a c ai + c ja + c ij i j a vs.

10. 10 Savings Continued Rank savings from largest to smallest Run through the list and merge routes represented by the two nodes as long as:  combined route length < MAX length  combined weight < MAX weight  other constraints as necessary  nodes are not already on same route  neither node is interior

11. 11 Interior customers Cust 2 Cust 1 Cust 3 Customer 2 is interior to the route

12. 12 An Optimization-Based Approach to Vehicle Routing Bramel, J. and D. Simchi-Levi, 1995, A Location Based Heuristic for General Routing Problems, Operations Research, 43, 649-660. Fisher, M. L. and R. Jaikumar, 1981, A Generalized Assignment Heuristic for Vehicle Routing, Networks, 11, 109-124.

13. 13 Comparison of Heuristics Accuracy (how close to optimal) Speed (computation time) Simplicity (ease of understanding and implementation) Flexibility (ease of adding other constraints – e.g., time windows, multiple depots)

14. 14 Comparison of Heuristics AccuracySpeedSimplicityFlexibility SavingsLowVery highLow SweepLowMedium- high HighMedium B&S-LMediumLow Meta- heuristics High to very high Medium High Cordeau, J.-F., M. Gendreau, G. Laporte, J.-Y. Potvin, F. Semet, 2002, “A Guide to Vehicle Routing Heuristics,” Journal of the Operational Research Society, 53, pp. 512-522.