1. Dynamic Traveling Salesman Problem Jan Fábry University of Economics Prague _____________________________________________________________________________________ MME 2006, Pilsen 1

2. Standard TSP (Static) _____________________________________________________________________________________ MME 2006, Pilsen 2 All customers are known before start of travel Dynamic TSP Some requirements arrive after start of travel

3. Static TSP _____________________________________________________________________________________ MME 2006, Pilsen 3 (Miler-Tucker-Zemlin) minimize subject to

4. Static TSP Static TSP _____________________________________________________________________________________ MME 2006, Pilsen 4 Example1 4 2 3 5 6Depot Optimal Route

5. Dynamic TSP Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 5 Example1 4 2 3 5 6Depot7 New customer

6. Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 6 A new customer Re-optimization of the route Insertion algorithm

7. Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 7 Re-optimization of the route minimize subject to Set of locations to be visited

8. Dynamic TSP Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 8 Example1 4 2 3 5 6Depot7 New customer

9. Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 9 Insertion algorithm Sequence of locations to be visited i k+1 ik ik ik ik r r r r

10. TSP with Time Windows _____________________________________________________________________________________ MME 2006, Pilsen 10 minimize subject to

11. TSP with Time Windows _____________________________________________________________________________________ MME 2006, Pilsen 11 minimize Waiting times included Change of the model:

12. Dynamic TSP with Time Windows _____________________________________________________________________________________ MME 2006, Pilsen 12 A new customer Re-optimization of the route Insertion algorithm

13. _____________________________________________________________________________________ MME 2006, Pilsen 13 Re-optimization of the route minimize subject to Dynamic TSP with Time Windows (to be continued…)

14. _____________________________________________________________________________________ MME 2006, Pilsen 14 Re-optimization of the route Dynamic TSP with Time Windows

15. _____________________________________________________________________________________ MME 2006, Pilsen 15 Insertion algorithm Dynamic TSP with Time Windows Sequence of customers to be visited

16. _____________________________________________________________________________________ MME 2006, Pilsen 16 Insertion algorithm Dynamic TSP with Time Windows

17. _____________________________________________________________________________________ MME 2006, Pilsen 17 Hard windowsHard windows TSP with Time Windows Soft windows Penalties minimize