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

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

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

Static TSP Static TSP _____________________________________________________________________________________ MME 2006, Pilsen 4 Example Depot Optimal Route

Dynamic TSP Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 5 Example Depot7 New customer

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

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

Dynamic TSP Dynamic TSP _____________________________________________________________________________________ MME 2006, Pilsen 8 Example Depot7 New customer

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

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

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

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

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

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

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

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

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