1. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Carl Bro a|s International consulting engineering company 2100 employees worldwide 80 offices Specializes in multi- disciplinary solutions

2. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems

3. Center of Expertise Logistics & Planning Tenna Kellberg Larsen, M.Sc. Anette Vainer, M.Sc. Graduates from the Dept. of Operational Research University of Copenhagen Working fields: vehicle routing localization work flow analysis demand specification project planning

4. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Theory vs. Practice The issue in designing algorithms for real life routing problems: Usability Flexibility Consistency to (certain) changes in problem Generalizing

5. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Exact algorithms often focuses on the structure Heuristics often give a framework to a variety of problems –For example when the demand can not be met Theory vs. Practice

6. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems 1. Ordering the customers/orders after importance Solving iterative problems Make a solution meeting the demand of all costumers with importance 1. If there is more capacity add costumers with importance 2 and so on Theory vs. Practice Relaxing the demand

7. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems 2. Ordering after geographical areas Solving iterative problems Make a solution meeting the demand of all costumers in geographic area 1. If there is more capacity add costumers in geographic area 2... In this way you have a flexible algorithm. Both according to the nature of the problem and the problem size / computing time. Theory vs. Practice Relaxing the demand

8. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Theory vs. Practice Ordering after geographical areas

9. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Case Presentation The client is a major Danish company delivering goods of own production as well as other goods. The demand for one day can often not be met. The client have a variety of staff policies. The client is divided into sections, that have different distribution pattern. Their customers are evenly distributed over the country

10. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Case Presentation Plants Depot Customer

11. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems There are two types of orders: high priority and low priority There are three types of areas: have to be visited, can be visited and areas, that are not taken into consideration. Some orders must be placed in the beginning of the trip There can be several trips in one route. The vehicles are previously assigned to depots. Orders are assigned to plants in the ERP-system Case Presentation

12. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems The solution must be feasible according to: Time windows Working hour restrictions Driving and resting rules Capacity Vehicle characteristics Availability of the vehicle Opening hours at the depots Case Presentation

13. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Case algorithm Four step algorithm 1.Assign orders to depots 2.Make plan for each depot in the ”have to visit” area 3.Swap orders between depots 4.After having completed planning for the ”have to visit” area, the algorithm tries to add orders from the ”can visit” area with an insertion algorithm

14. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Assigning orders to depots: The orders are assigned to the one of the three nearest depots, that generates the lowest transportation costs Case algorithm

15. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Use a heuristic to create as many routes as there is vehicles assigned to the depot. The routes may contain of more than one trip. High-priority orders first Step 1. Select a vehicle. Randomly select an order to the trip. Repeat step 1 until all vehicles have a trip Step 2. Search all the trips. Add the order, that renders the lowest cost and that does not violate the constraints. The cost is defined as the minimum distance from any order on the trip (or the depot itself) to any order not on the trip Case algorithm Solving the problem for each depot using a parallel nearest customer algorithm:

16. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Create N different initial solutions. Use a r-opt based heuristic to improve the initial solutions. The arcs, that joins the orders within the trip is being swapped Case algorithm

17. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Improving the trip: Swapping 2 arcs Case algorithm The 2-opt heuristic

18. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems A r,p-opt based Tabu Search heuristic is used to improve the N 1  N best solutions by swapping r orders from one trip with p orders from another trip. Both trips from the same depot. A r,p-opt based Tabu Search heuristic is used to improve the N 2  N 1 best solutions by swapping orders between the depots to minimize the load costs. Case algorithm

19. Carl Bro a|s - Route 2000 Solving real life vehicle routing problems Conclusions The academic research in exact algorithms for the VRP is hard to take advantage of in the kind of consulting areas, where problem changes constantly The growing amount of research done within the heuristic algorithms gives a good framework for creating tools suitable to solve many different kinds of planning problems