solving real-world vehicle scheduling and routing problems

Solving Real-WorldVehicle Scheduling andRouting Problems

Jens Gottlieb

SAP AGWalldorf, [email protected]

sample for a picture

in the title slide

mailto:[email protected]

© SAP 2008 / Solving Real-World Vehicle Scheduling and Routing Problems, Jens Gottlieb, VIP 2008, Oslo, 12-14 June 2008,

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


1. The vehicle scheduling and routing problem2. Solution approach3. Selected scenarios4. Conclusion

Agenda


in the divider slide


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


Example 1:Orders in classical CVRP scenario


Example 2:Orders in selected customer scenario


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

[ ][ ]


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)


Example:Schedule for a selected customer scenario


The vehicle scheduling and routing problem:Trailers and compartments (1)

C1 C2 C3 C4

Vehicle

C5 C6 C7 C8

Trailer

Vehicle Combination


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


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


Example:Selected customer scenario involving 5 hubs


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


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)



Agenda




Solution approach:Evolutionary local search

Population

Initialization

Selection

VariationSelection


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


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



Agenda




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.


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



Agenda




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


Thank you!


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solving real-world vehicle scheduling and routing problems

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