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VRP. Vehicle Routing Problem. What is VRP. Objective Minimize routing costs. Variations. No. of vehicles No. of depots Time windows Returned goods Combinations. Motivation. Deliveries Airlines Cargo Ships. Solutions techniques. Route first, Partition later
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VRP Vehicle Routing Problem
What is VRP • Objective • Minimize routing costs.
Variations • No. of vehicles • No. of depots • Time windows • Returned goods • Combinations
Motivation • Deliveries • Airlines • Cargo Ships
Solutions techniques • Route first, Partition later • Partition first, Route later
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.
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.
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.
TSP vs. SWEEP • Which is better ???
??? Thank you!