1 Split Delivery Problem Jan Pelikán, Jan Fábry, Václav Kořenář University of Economics Prague Split Delivery Problem Jan Pelikán, Jan Fábry, Václav Kořenář University of Economics Prague ___________________________________________________________________________ ___________________________________________________________________________ MME 2005, Hradec Králové

2 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Delivery Problem Standard Problem of OR Fuel & Time Consumption Savings Number of Used Vehicles * * * * * * * * * * * * * * * * * * * * * * Using Optimum Repeatedly Any Improving Solution Impact on the Environment } } WHAT HOW

3 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Delivery Problem Troubles Diversity of Problems NP-hardness

4 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Standard Formulation Vehicle Capacity Demand

5 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Miler-Tucker-Zemlin minimize subject to

6 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Vehicles with Different Capacities minimize subject to Each vertex lies exactly on 1 route

7 Split Delivery Problem ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Several Routes for Some Vertices Split even if

8 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example Depot Destinations Demand Distance

9 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example – w/o Split Routes: (1-2-1); (1-3-1); (1-4-1) Total Distance = 60

10 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example – Split Routes: ( ); ( ) Total Distance = 45

11 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové minimize subject to Split Delivery Problem

12 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Split Delivery Problem vs. SDP Each solution of VRP is solution of SDP