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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
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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
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3 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Delivery Problem Troubles Diversity of Problems NP-hardness
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4 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Standard Formulation Vehicle Capacity Demand
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5 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Miler-Tucker-Zemlin minimize subject to
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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
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7 Split Delivery Problem ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Several Routes for Some Vertices Split even if
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8 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example 234 23 10 8 84 1 Depot Destinations Demand Distance
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9 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example – w/o Split 234 23 10 8 84 1 3 Routes: (1-2-1); (1-3-1); (1-4-1) Total Distance = 60
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10 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Split Delivery Problem Example – Split 234 23 10 8 84 1 2 Routes: (1-2-3-1); (1-3-4-1) Total Distance = 45
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11 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové minimize subject to Split Delivery Problem
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12 ____________________________________________________________________________ ____________________________________________________________________________ Split Delivery Problem MME 2005, Hradec Králové Vehicle Routing Problem Split Delivery Problem vs. SDP Each solution of VRP is solution of SDP
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