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

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

Vehicle Capacity =20 Route length = 8 hrs

4 Cluster-Route

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 Route-Cluster (eg Sweep)

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

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

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, Fisher, M. L. and R. Jaikumar, 1981, A Generalized Assignment Heuristic for Vehicle Routing, Networks, 11,

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 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