Vehicle Routing in Practice - SINTEF · The Vehicle Routing Problem (VRP) Given a fleet of vehicles...

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Vehicle Routing in Practice

Geir HasleSINTEF ICT, Oslo, Norway

XVIII EWGLANaples, Italy April 28-30 2010

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Outline

Background and ContextThe Vehicle Routing ProblemIndustrial AspectsSpider - A Generic VRP SolverSpecific casesOngoing and Further Research

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Technology for a better society

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Norway

Oslo

Trondheim

An Independent Multi-DisciplinaryContract R&D OrganisationEstablished in 1950Among the Largest CRO in Europe

Vision:Technology for a better Society

Business Concept:To meet the needs for Research-Based Innovation and Development for the Private and Public Sectors

450 employees in Oslo

1.300 employees in Trondheim

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SINTEF - A Norwegian Contract Research InstituteScience and engineering – social sciences, health careConnected with

The Norwegian University of Science and Technology, TrondheimThe University of Oslo, Faculty of mathematics and natural sciences

> 90 % of turnover from industry and public sector contractsAnnual turnover ~ 200 M€Activities

Strategic, long term, basic researchContract ResearchConsultancyCommercialization and spin-offs

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The SINTEF GroupRe

sear

ch D

ivisio

ns

SINTEFHealth Research

SINTEFTechnology and

SocietySINTEF

ICTSINTEF

Materials and Chemistry

SINTEF Building and Infrastructure

SINTEF Petroleum and Energy

SINTEF Petroleum ResearchSINTEF Energy Research

SINTEFHolding

PresidentExecutive

Vice President

SINTEF’s CouncilSINTEF’s Board

Corporate Staff

SINTEF MarineMarintek

SINTEF Fisheries and Aquaculture

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Outline

Background and ContextThe Vehicle Routing ProblemIndustrial AspectsSPIDER - A Generic VRP SolverSpecific casesOngoing and Further Research

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The Vehicle Routing Problem (VRP)

Given a fleet of vehicles and a set of transportation orders, find a minimum cost routing plan. That is: allocate each order to a

vehicle, and for each vehicle, sequence the stops.

The VRP central to efficient transportation managementApplications

Distribution or pick-up of goodsDial-a-rideMunicipal servicesRepairman problemNewspaper distributionWaste managementGritting, snow clearing

Very hard, discrete optimization problem

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The Capacitated VRP (CVRP)Graph G=(N,A)

N={0,…,n} Nodes0 Depot, i≠0 Customers A={(i,j): i,j∈N} Arcscij >0 Arc cost

Demand di for each Customer ieither all pickups or all deliveries

V set of (identical) Vehicles, each with Capacity qGoal

Construct a set of minimum cost Routes that start and finish at the Depot.Each Customer shall be visited once (no order splitting)Total Demand for all Customers serviced less than Capacity qCost: Total Arc cost (also # Routes in richer VRP variants)

DVRP – constraint on route lengthVRPTW – VRP with time windowsVRPB – VRP with backhauling (deliveries first, then pickups)PDP – pickup and delivery without going through the depot

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Mathematical formulation of VRPTW (vehicle flow formulation)

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capacity

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k routes into depot (redundant)

start of service and driving time

start of service within TWarc (i,j) driven by k

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The VRP is very hard, computationally

Belongs to class of strongly NP-hard optimization problemsComputing time for all VRP optimization algorithms grows”exponentially” with the number of nodes (probably ... )Exact methods are ”easy” to design, may take foreverCurrently, exact methods for the C/DVRP can consistentlysolve instances with some 70 customers only to optimalitywithin a few minutesFor generic industrial VRP tools, we must give up the questfor optimality and resort to some form of approximationWhat is the optimal plan, anyway?

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VRP in Operations Research

since 1959thousands of papersmostly generic work on idealized VRP modelsstill, one of the successes of ORa tool industry has emerged, based on research resultstremendous increase in ability to ”solve” VRP variants

general increase of available computing powermethodological improvement

still much to do, VRP research has never been more activeshort road from research results to industrial benefits

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VRP in Operations ResearchGeneral, idealized formulationsExtensions studied in isolation

time windowsmultiple depotsinventory constraints....

Very fruitful for understanding VRP variantsdeveloping highly targeted algorithms

Not always relevant to real-life problemsSome application specific workRecently: More holistic approach: ”Rich VRPs”

General model, many aspects of industrial problemsRobust algorithms

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Extensions in the VRP-literatureLocation Routing LRPFleet Size and Mix FSMVRPVRP With Time Windows VRPTWGeneral Pickup and Delivery GPDPDial-A-Ride DARPPeriodic VRP PVRPInventory Routing IRPDynamic VRP DVRPCapacitated Arc Routing Problem CARP

All kinds of algorithmic approachesexactapproximation methods

based on systematic, exact methodsmetaheuristics

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Outline


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Industrial aspects – VRP toolAdequate model of the applicationsWide range of applicationsHigh quality information

addressesdistances, times, costsordersfleet and driver information

Manual planning, user interfaceEase of useSoftware issues

Integration with ERP etc.ExtendabilityMaintainabilityDocumentation

High quality solution in short time – powerful VRP solver

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Industry needs rich VRP modelsType of service and operation

multiple depots, no depotdifferent order types (delivery, pickup, direct, service, ...)order splitting, flexible order volumesnode routing, arc routing, mixedmultiple tours per dayperiodic problemsconnection to inventory and manufacturing

Constraintscapacity, several dimensions, hard and softtime windows, multiple, hard and softprecedences(in)compatibilities

Realistic distances, times, costs Cost components

multiple criteriasoft constraints and penalties

Uncertainty and Dynamics

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Research on Rich VRPs & related problems at SINTEFIndustrial Contracts since 1995Strategic Research

European Commission FP III, IV, V (e.g., GreenTrip 1996-1999)Norwegian Research Council (RCN)Internal Projects, students

Generic VRP Solver - Spider (1995→)Commercialization from 1999GreenTrip AS → Spider Solutions AS

TOP Programme 2001-2004 (RCN) http://www.top.sintef.no/Basic Research on Rich VRP and related problemsVRPTWShortest Path Problem in Dynamic Road Topologies

Innovation Projects supported by Research Council of Norway“I Rute” (2001 – 2004) Bulk transportation“DOiT” (2004 – 2007) Stochastic and Dynamic Routing“EDGE” (2005 – 2008) Large Scale Routing“Effekt” (2008 – 2011) Media Product Distribution Routing

Ship routingTurboRouter 1995 ->SINTEF Internal Strategic Project (2005-2008)LNGShipping

http://www.top.sintef.no/

ProductionProduction portport

ConsumptionConsumption portport

ProductProduct 11

ProductProduct 22 KjKjøøpsvikpsvik

BrevikBrevik

AltaAlta

Mo i RanaMo i Rana

TrondheimTrondheim

KarmKarmøøyy

ÅÅrdalrdal

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Invent – solving maritime routing problems

Invent is a software library that can model and solve a wide class of maritime routing problems. This includes both traditional tramp shipping and industrial shipping problems with inventory management.

Vessels can be modeled at tank level with the possibility of detailed tank stowage and cleaning operations.

Inventories can have a time varying production or consumption profile together with an upper and lower limit on the inventory level.

The inventories can be combined with traditional orders with laycan and quantity intervals for a pair of pickup and delivery locations.

It is also possible to include contracts with details on required pickup or delivery in given periods, and time varying price curves for income and cost.

Problem instances are described in a general XML format that can be used as input for the automatic planning process.

Invent generates optimized plans for the problems based on advanced heuristic methods that are able to provide high quality solutions in short time.

Invent

xmlC++ API

User application

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TurboRouter

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Maritime Transport Optimization AN OCEAN OF OPPORTUNITIES

ORMS Today, Special International Issue, Vol 36 No 2 pp 28-31, April 2009.

http://viewer.zmags.com/publication/1368b369#/1368b369/28

http://viewer.zmags.com/publication/1368b369#/1368b369/28

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Outline


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Spider - A Generic VRP Solver

Designed to be widely applicableBased on generic, rich modelPredictive route planningPlan repair, reactive planningDynamic planning with stochastic model

Framework for VRP research

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SPIDER - Generalisations of CVRPHeterogeneous fleet

CapacitiesEquipmentArbitrary tour start/end locationsTime windowsCost structure

Linked tours with precedencesMixture of order typesMultiple time windows, soft time windowsCapacity in multiple dimensions, soft capacityAlternative locations, tours and ordersArc locations, for arc routing, mixed problems and aggregation of node ordersAlternative time periodsNon-Euclidean, asymmetric, time-varying travel timesCompatibility constraintsA variety of cost components and soft constraints

driving time restrictionsvisual beauty of routing plan, non-overlapping routeslevelling

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Transportation OrderDifferent types:

DeliveryPickupDirect (P&D)Service

Plan structuretasktask sequencetourplan

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Tour

Time windows and locations given by start/stop tasksSelected vehicle and driver (alternative equipages)Linked tours

(may have different vehicles)

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Vehicle and Driver

CapacityTravelling attributes

Speed profileHeight, weight, lengthObey one-way restrictions?

Driving time regulations

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Cost elements

Travel cost (distance, time, tolls)Tour usage cost

Cost for starting a tourCost per order on tour

Cost for unserviced orderWaiting time costCost for alternative locationsCost for same/different locationCost for breaking work regulationsCost for “ugly”, overlapping routes

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Constraints

ConsistencyComplete orderPickup/delivery (Direct orders) same tour and precedence

TimeTravel time, DurationTime windows, multiple, hard and soft

Vehicle capacities, multiple dimensions, hard and softTotal capacities over a set of tours

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Constraints

Compatibility vehicle/order vehicle/location product/compartmentOrders on same tourCorresponding locations (when alternatives)

Order: Choose corresponding locations for pickup and delivery taskTour: Choose corresponding locations for start/stop tasks

Corresponding time periods for sets of ordersE.g. Delivery day 1,3,5 or day 2,4,6

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Locks

Prevent optimiser changing part of planTask: Time lockTour: Lock whole or initial part of tourOrder: Lock (un)assignment

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Uniform Algorithmic ApproachGoals

Reach a good local optimum fastExplore interesting parts of search space efficiently

3 phasesConstructionIterative Improvement: Iterated Variable Neighborhood DescentTour Depletion

Based onIterated Local Search (Martin, Lourenço et al)Variable Neighborhood Descent (Hansen & Mladenovic)Diversification when VND reaches local optimum

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Construction of Initial Solution

Various Sequential Construction HeuristicsExtended to cover Richer Model

Several types of orderNon-standard constraintsNon-homogeneous fleetMultiple DepotsMultiple Tours per Vehicle

New ConstructorInhomogeneous problemsMultiple depotsMultiple tours per vehicleMore search

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Variable Neighborhood Descent - Operators

InsertRemove2-optOr-opt3-optRelocateCross (2-opt*)Exchange (Cross-Exchange)Tour DepletionChange alternative locationChange alternative time periodChange vehicle...

Variety, efficiency, sequence?

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Illustration: ExchangeInter-tour operatorFull neighborhood is typically largeRemedy: Limit on maximum segment lengthAlternative: Focus on promising cut points

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Iterated Local Search (Martin, Lourenço et al)

Goal: Efficient search in new basins of attractionWhen VND reaches local optimum: diversifyRandom restartAlternative initial solutionPath relinkingNoising: perturb problem dataChange objectiveLNS, VLNS

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Take away a substantial number of commitmentsrandomly“similar” commitments

Reconstruct with fast insertion methodCheapest insertionRegret-based insertion

Accept new solution ifbetter, diverseThreshold AcceptanceSimulated Annealing

IterateAlternative modifications

Limited Local SearchFull VND MachineryDistance Metrics

Large Neighborhood Search (Shaw)

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Computational Experiments

Standard test problems in literature for most VRP variants”World championship” in Vehicle RoutingFor most instances, the optimal solution is not knownTesting against the best methods reported in the literature”Unfair” comparison: competing with solvers optimized for solving a specific, idealized problemNice to know how well you perform ...

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Experimental studies PDPTW http://www.sintef.no/top

Author 100 200 400 600 800 1000 TotalLi & Lim 41 14 6 2 0 0 63Spider 13 11 5 4 9 4 46BVH 2 8 6 3 4 1 24TS 0 1 2 0 0 2 5SR 0 26 41 51 47 51 216

Total 56 60 60 60 60 58 354

354 standard test problems Li & Lim: 100 – 1.000 orders

BVH: Bent & Van Hentenryck: Two-stage, Hybrid Local Search1. Minimize # tours by SA, modified objective2. Minimize Distance with Large Neighborhood Search

TS: Tetrasoft, Danish tool vendor, Method unknownSR: Stefan Röpke, Univ. Copenhagen

Adaptive Large Neighborhood Search

http://www.sintef.no/top

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Results on CVRP - Rounded distances (1)

Augerat et al 74 instances, 15-100 customers, limit on # vehicles A (27): 0.15% from optimum, 19 optimal, 0-541 s, average 100 sB (23): 0.11% from optimum, 17 optimal, 1-582 s, average 95 sP (24): 0.23% from optimum, 15 optimal, 0-450 s, average 99 s

Christofides & Eilon (1969)13 instances, 12-100 customers, limit on # vehiclesE (13): 0.32% from optimum, 2 optimal, 7 - 487 s, average 178 s

Fisher3 instances, 44 - 134 customers, limit on # vehiclesF (3): 0.27% from optimum, 7 optimal, 0-289 s, average 103 s

Gillett & Johnson, 1 instance: G-n262-k25best known, -7.09% from previous best known (5685)

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G-n262-k25: 5685 vs. 6119

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Results on CVRP - Rounded distances (2)

Christofides, Mingozzi & Toth (1979)5 CVRP instances, 100-199 customers, limit on # vehicles0.99 % from optimum, 21-1255 s, average 404s1 optimal1 new best known -1.6 %1 worse by 2.7 %1 worse by 2.9 %M-n200-k16: no feasible solution previously knownFeasible solution found

after 533s: distance 1371

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M-n200-k16: First known feasible solution

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Computational tests - NEARP

Prins & Bouchenoua CBMix (23 instances)No lower bounds, no proven optima, only one competitorUB error 0.94%8 best known solutions (6 new)

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Comparison with Prins & Bouchenoua

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Products - architecture

Guider(topology)

Planner(VRP solver, COM)

Designer

SPIDER Solutions AS

Distribution Innovation AS

Geomatikk AS

Web-server (Servlet, C++/Java)

Web solution

Guider(topology)

Spider Server

Guider(topology)


DI web solution

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Spider Designer - ApplicationsDistribution of bread (Bakers)Mail collection and distribution (Posten Norge)Local pickup and delivery (Schenker)Newspaper distribution, 1st tier (Aftenposten, Dagbladet)Newspaper distribution, last mile (Aftenposten, Stavanger Aftenblad)Collection of milk from farms (TINE)Distribution of fodder to farms (Landbruksdistribusjon)Distribution of fuel oil (Hydro Texaco)Location analyses, depot (obnoxious facility location, Norsk Gjenvinning AS)Distribution of blood (Ullevål sykehus)Distribution of groceries (REMA 1000)Distribution of magazines (Bladcentralen)Distribution of ice cream (Diplom Is; Hennig Olsen)Dial-a-ride, elderly, hospital patients (Nor-Link)

Savings 2-35%, depending on application

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Challenges for Routing Technology

Industrial awarenessRange of applicationsInformation availability and qualityUser interfacesModel adequacy and flexibilitySoftware engineeringRobustness of solution methodSolution quality for large-size and complex problems

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Challenges for Spider

Electronic road network - GISInstance robustness

all kinds of instancesScalability

very large size problemsExtendability

new operators, new VND sequence

Exploiting modern commodity computersmulti-core, heterogeneous, GPUs

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Outline


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Scalability – Solving ”Huge” VRPsFaster VRP solver

heuristic investigation of neighborhoodsclever sequencing of constraint and objective component evaluationmore powerful metaheuristicshybrid methods, even combining exact methods and heuristics

Problem Decompositiongeographicallytemporallybased on productclustering methods will be usefulsubproblem

Abstraction and Aggregationclustering methods will be useful

Exploit modern parallel and heterogeneous computer architecturesMulti-level search and collaborative solvers

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Outline


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Products - architecture

Guider(topology)


Designer

SPIDER Solutions AS

Distribution Innovation AS

Geomatikk AS

Web-server (Servlet, C++/Java)

Web solution

Guider(topology)

Spider Server

Guider(topology)


DI web solution

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NewspaperdistributionCity of Oslo500k inhabitants200k households35k modules

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Problem description

Last mile part of two-echelon distribution(Open) DVRP with extensionsObjectives

total durationroute balancingclustering, route separation, ”visual beauty”

Constraintsroute duration# routes

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Additional niceties

Determination of vehicle type (pedestrian, car)Combined routesLinks that may be used by one route only...

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Extended problem

Integrated problemDistribution from print shop to subscriberLocation routing: Determination of pickup points

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Demand aggregation based on road topology, proximity

Distance/time, capacity thresholdIssues on traversal possibilities, constraintsTypical reduction factor of 5-20Needs extention to arc model (Node Edge Arc Routing Problem, NEARP)

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Case: Oslo data from Aftenposten33.200 orders reduced to 5600 aggregates

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Decomposition approaches

GeographicalCluster-first route second

Capacitated Clustering Problem – with balancingRouting

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Outline


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Important trends in VRP research

Richer models, larger instancesExact methodsSelf-adaptationHybrid and collaborative methodsParallel and heterogeneous computing

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Parallel computing Some tasks in EA and LS are embarassingly parallel”Simple” parallelization through multi-threading

fine-grained to medium level granularityvery interesting for routing technologynot so interesting for VRP research, no literature

More interesting parallelizationCoarse-grained, asynchronousMulti-searchCollaborative searchParallel multi-level

Recent review by Crainic, 80 referencesAdditional 30 papersHeterogeneous computing not really investigated

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Parallel and heterogeneous computing

CPU Clock frequency has stagnated(The Beach Law does not hold anymore ...)Moore’s Law still validMulti-core and heterogeneous commodity computersFine-grained and coarse-grained parallelism

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The Collab project

”Iteration level” parallelization of Spider Experimental VRP Solverhttp://www.sintef.no/Projectweb/Collab/

Special session ”Metaheuristics on graphics hardware”under the META’10 conference in Djerba Island, October28-30 2010, deadline May 15 http://www2.lifl.fr/META10/

http://www.sintef.no/Projectweb/Collab/http://www2.lifl.fr/META10/index.php?n=Main.InfoMGHhttp://www2.lifl.fr/META10/

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SummaryThe Vehicle Routing Problem is a key to efficient transportationThe VRP is a very hard optimization problemThousands of VRP papers, mostly generic, idealizedOR success story, tool industryIndustry needs rich models, powerful algorithmsStill challenges, VRP research has never been more activeGeneric VRP Solver SPIDER

rich, generic modelresolution algorithm based on metaheuristicsresults

Still a lot of work to be done ...

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Geir Hasle and Oddvar Kloster: Industrial Vehicle Routing.Chapter (pp 397-435) in

Hasle, Geir; Lie, Knut-Andreas; Quak, Ewald (Eds.) Geometric Modelling, Numerical Simulation, and Optimization:

Applied Mathematics at SINTEF2007, XI, 558 p. 162 illus., 59 in color., Hardcover. ISBN: 978-3-540-68782-5

http://www.springer.com/

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Special Issue Transportation Science

Advances in Vehicle RoutingTRISTAN VII, Tromsø, Norway June 20-25 2010Guest editors

Marielle ChristiansenArne LøkketangenGeir Hasle

Deadline October 15, 2010

See May issue of Transportation Science for call

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Geir HasleSINTEF ICT, Oslo, Norway

XVIII EWGLANaples, Italy April 28-30 2010

Vehicle Routing in PracticeOutlineSlide Number 3Slide Number 4SINTEF - A Norwegian Contract Research Institute�The SINTEF GroupOutlineThe Vehicle Routing Problem (VRP)The Capacitated VRP (CVRP)Mathematical formulation of VRPTW�(vehicle flow formulation)The VRP is very hard, computationallyVRP in Operations ResearchVRP in Operations ResearchExtensions in the VRP-literatureOutlineIndustrial aspects – VRP toolIndustry needs rich VRP modelsResearch on Rich VRPs & related problems at SINTEF Slide Number 19Invent –�solving maritime routing problemsTurboRouterMaritime Transport Optimization�AN OCEAN OF OPPORTUNITIESOutlineSpider - A Generic VRP SolverSPIDER - Generalisations of CVRPTransportation OrderTourVehicle and DriverCost elementsConstraintsConstraintsLocksUniform Algorithmic ApproachConstruction of Initial SolutionVariable Neighborhood Descent - OperatorsIllustration: ExchangeIterated Local Search �(Martin, Lourenço et al)Slide Number 38Computational ExperimentsExperimental studies PDPTW�http://www.sintef.no/topResults on CVRP�- Rounded distances (1)Slide Number 42Results on CVRP�- Rounded distances (2)Slide Number 44Computational tests - NEARPSlide Number 46Products - architectureSlide Number 48Spider Designer - ApplicationsChallenges for Routing TechnologyChallenges for SpiderOutlineScalability – Solving ”Huge” VRPsOutlineProducts - architectureSlide Number 56Vehicle Routing in PracticeSlide Number 58Slide Number 59Slide Number 60Slide Number 61Slide Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number 66Problem descriptionAdditional nicetiesExtended problemDemand aggregation based on road topology, proximityCase: Oslo data from AftenpostenSlide Number 72Decomposition approachesOutlineImportant trends in VRP researchParallel computing Parallel and heterogeneous computingSlide Number 78Slide Number 79Slide Number 80The Collab projectSummarySlide Number 83Special Issue Transportation ScienceVehicle Routing in Practice

Vehicle Routing in Practice - SINTEF · The Vehicle Routing Problem (VRP) Given a fleet of vehicles...

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