Solving Real-World Vehicle Scheduling and Routing Problems ...© SAP 2008 / Solving Real-World...
Transcript of Solving Real-World Vehicle Scheduling and Routing Problems ...© SAP 2008 / Solving Real-World...
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Solving Real-WorldVehicle Scheduling andRouting Problems
Jens Gottlieb
SAP AGWalldorf, [email protected]
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mailto:[email protected]
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 2
Vehicle Routing @ SAP
SAP offers two products covering transportation planning functionality:Since 2001: SAP Supply Chain Management, APO TP/VS(Advanced Planner and Optimizer, Transportation Planning / Vehicle Scheduling)Since 2007: SAP Transportation Management
SAP offers one product for service management and technician scheduling:SAP Multi Resource Scheduling
Since 2001, SAP has developed and continuously improved an optimization algorithm for thevehicle scheduling and routing problem, which is the planning engine in above products
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 3
1. The vehicle scheduling and routing problem2. Solution approach3. Selected scenarios4. Conclusion
Agenda
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 4
The vehicle scheduling and routing problem:Orders
Order-based modelSource and destination location per order
Priority (Non-delivery costs)Loading dimensions (weight, volume, ...)Characteristics (hazardous goods, frozen, ...)Loading/unloading durations (depending on vehicle)
Order 4
Order 3
Order 2Order 1
6
24
1
3
5 Order 5
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 5
Example 1:Orders in classical CVRP scenario
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Example 2:Orders in selected customer scenario
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 7
Time windows per order (hard and soft) for loading and unloading
Loading requires outbound handling resource at source locationBusiness hoursCapacities
Unloading requires inbound handling resource at destination locationBusiness hoursCapacities
The vehicle scheduling and routing problem:Time restrictions per order
time
costs
lateloading
earlyloading
[ ][ ]late
unloadingearly
unloading
[ ][ ]
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 8
The vehicle scheduling and routing problem:Vehicles
Travel capabilities (duration, distance, distance cost per lane)
Characteristics (cooled, available for hazardous goods, …)
Break calendar
Constraints:Start location, end locationDurationDistanceNumber of stopsLoad capacity (weight, volume, …), may depend on number of stops
Costs:Fixed costsDurationDistanceNumber of stopsQuantity costs (distance x load)
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 9
Example:Schedule for a selected customer scenario
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 10
The vehicle scheduling and routing problem:Trailers and compartments (1)
C1 C2 C3 C4
Vehicle
C5 C6 C7 C8
Trailer
Vehicle Combination
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 11
The vehicle scheduling and routing problem:Trailers and compartments (2)
Trailers cannot move without vehicle
Coupling/uncoupling activities
Constraints for trailers like for vehiclesStart location, end locationDuration, distance, number of stops, load (weight, volume, …)
Costs for trailers like for vehiclesFixed costs, duration, distance, number of stopsQuantity costs (distance x load)
Constraint for vehicle combinations: load (weight, volume, …)
CompartmentsEach vehicle/trailer has fixed number of compartmentsLoad capacity per compartment (weight, volume, …)Fixed versus flexible load capacity
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 12
Hub locations (= transshipment locations):Indirect shipment via hub(s) versus direct shipment
Minimum and maximum waiting time at hub
The Vehicle Scheduling and Routing Problem:Hubs
H1 2
1 H2
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 13
Example:Selected customer scenario involving 5 hubs
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 14
Incompatibility constraints:Between order characteristicsBetween vehicle characteristics and order characteristicsBetween trailer characteristics and order characteristicsBetween compartment characteristics and order characteristicsBetween vehicle characteristics and trailer characteristicsBetween order characteristics and hubsBetween vehicle characteristics and hubsBetween trailer characteristics and hubs
Schedule vehicles:Route is fixed a prioriSchedule is fixed a priori
The vehicle scheduling and routing problem:Incompatibilities and schedule vehicles
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 15
The vehicle scheduling and routing problem:Summary
Goal:Determine transportation plan that minimizes total costs and satisfies all constraints.
A transportation plan is characterized by the following decisions:per order: deliver or not?per delivered order: select legs (= path through hub network)per selected leg: select vehicle/trailer and compartmentper vehicle/trailer:– select relative ordering of activities (= routing)– assign start time to each activity (= scheduling)
Total costs = weighted sum of costs fororders (non-delivery, earliness, lateness), andvehicles and trailers (fixed, duration, distance, stops, quantity)
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 16
1. The vehicle scheduling and routing problem2. Solution approach3. Selected scenarios4. Conclusion
Agenda
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Solution approach:Evolutionary local search
Population
Initialization
Selection
VariationSelection
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 18
Solution approach:Ingredients of evolutionary local search
InitializationGreedy insertion heuristics + local search
VariationUses > 20 different atomic variation operators, grouped into:
Assignment moves (e.g. insert an order, delete an order, delete a vehicle)Routing moves (e.g. 2-opt, variants of Or-opt, 3-opt, 4-opt)Scheduling moves
Moves are applied subsequently and with certain probabilities, using the following concepts:Local searchRandomnessIterated local searchVariable neighbourhood searchTabu search
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 19
Solution approach:Key features
Direct solution representation
Only feasible solutions
Local search
Small population
Many specialized atomic move operators
Orchestration of atomic moves in the variation step
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 20
1. The vehicle scheduling and routing problem2. Solution approach3. Selected scenarios4. Conclusion
Agenda
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 21
Using the optimizer
Input data specified by selection profile
Different operating modesBatch versus interactive startLong runs at night versus short runs during the dayFrom scratch versus incrementallyPlanning horizon ranges from a few hours to several weeks
Run-time limits vary from a few minutes to several hours
Human transportation planner processes the optimizer‘s result:reviewing it,manipulating it interactively if needed, andreleasing it to transportation execution
Side-effect of optimizer: Check input dataUnexpected results typically indicate that input data are not clean.
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 22
Characteristics of selected customerscenarios
Scenario 1 2 3 4 5 6 7 8 9
Orders 75 255 662 778 804 1177 2029 7040 13569
Loading dimensions 1 1 2 1 3 2 5 4 3
Locations 30 199 55 8 32 565 128 1873 14
Hubs 9 5
Sources 9 5 11 1 1 1 1 1 1
Destinations 14 194 46 7 31 559 127 1872 13
Vehicle types 4 38 9 7 3 10 10 2
Vehicles 58 93 301 281 680 2701 2011 100
Schedule vehicle types 1 6
Schedule vehicles 38 11
Business hours 2 196 1 29 64
Capacitive resources 54 32
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 23
1. The vehicle scheduling and routing problem2. Solution approach3. Selected scenarios4. Conclusion
Agenda
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 24
Conclusion
SummaryReal-world problems are complexHeterogeneous instances of the same abstract problemOne algorithm for the abstract problem, applicable to arbitrary special instances of ourcustomersMetaheuristics work well in practice
OutlookContinuous extension of functionalityHub networks with several „parallel“ hubs and more than 2 „sequential“ hubsDifferent variants of trailer scenarios, depending on frequency of coupling and uncoupling
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 25
Thank you!
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© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008, Page 26
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