A Set-Partitioning-Based Model and Solution Procedure for the SVRP

1
A Set-Partitioning-Based Model and Solution
Procedure for the SVRP

• Rosemary Berger, Jeff Linderoth, Clara Novoa and
  Bob Storer
• Department of Industrial and Systems Engineering
• Lehigh University
• October 21, 2004

2
(Classical) Vehicle Routing Problem
distance, travel time or travel cost
Depot
m identical vehicles
3
(Classical) Vehicle Routing Problem

• Construct a set of vehicle routes of minimum
  total cost
• starting and ending at the depot
• visiting each customer exactly once
• satisfying any side constraints (capacity,
  duration, time windows)

4
Stochastic Vehicle Routing Problem

• some elements are random
• stochastic demands
• stochastic travel times
• stochastic customers
• demand revealed when vehicle arrives at customer
• planned vehicle route fails at a customer
  whenever demand exceeds current vehicle capacity
• recourse action must be taken at extra cost

5
Previous Work on SVRP

• Markov Decision Process with Approximate Dynamic
  Programming
• wait and see
• Chance-Constrained Programming
• first stage solution for which probability of
  failure is constrained to be below a certain
  threshold
• Stochastic Programming with Recourse
• first stage solution that minimizes expected cost
  of second stage solution