Management Science 461 Lecture 8 Vehicle Routing November

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

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

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

Cluster-Route 4

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

Route-Cluster (eg Sweep) 6

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

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

Savings cai + cia +caj + cja i cai + cja + cij i j j vs. a a sij = cia + caj - cij 9

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

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

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. n Fisher, M. L. and R. Jaikumar, 1981, A Generalized Assignment Heuristic for Vehicle Routing, Networks, 11, 109 -124. n 12

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

Comparison of Heuristics Accuracy Speed Simplicity Flexibility Savings Low Very high Low Sweep Low Mediumhigh High Medium B&S-L Medium Low Low Metaheuristics 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. 14