Management Science 461 Lecture 8 – Vehicle Routing November 4, 2008
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
7 2 5 6 12 5 2 Vehicle Capacity =20 Route length = 8 hrs
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
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?
Savings Savings = d(Depot,1) +d(2,Depot) - d(2,1) Cust 2 Cust 2 Depot Cust 1 Depot Cust 1
cai + cia +caj + cja cai + cja + cij i i j j a a Savings vs. sij = cia + caj - cij
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
Interior customers Cust 2 Cust 3 Cust 1 Customer 2 is interior to the route
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.
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)
Comparison of Heuristics 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.