1ICT

eVITA Scientific MeetingGeilo, Norway January 28, 2010

Geir Hasle, SINTEF ICT

Optimization-based decision support within healthcare and transportation

2ICT

Acknowledgment

Henrik Andersson, NTNUMarielle Christiansen, NTNUArild Hoff, Høgskolen i MoldeArne Løkketangen, Høgskolen i MoldeTomas Nordlander, SINTEFAtle Riise, SINTEFMartin Stølevik, SINTEF

3ICT

Outline

Motivation – relevance to practice and eVitaDiscrete optimizationChallengesSummary and conclusion

4ICT

Messages

Discrete optimization problems central to better performancehard

Strong need for more powerful methodsSeveral challenges and promising research avenuesShort road from theoretical to practical improvementsImportant part of eScience

5ICT

Healthcare Need for better coordination

Increasing demandsPatient focus: high quality treatment Resource focus: Need to curb cost increase

Design, planningCrucial to performanceToo complex for manual decision-makingTime consuming and repetitive

Need for decision support systemsAutomated planningObjectives and constraintsComputationally complex Discrete Optimization Problems

Need for models and effective solution algorithms

5

”Det er mye god omsorg i effektivitet” P. Syrstad presentasjon på Ringerikskonferansen 2008.

6ICT 6

Coordination challenges in healthcare

Funksjonsfordeling

Turnusplanlegging

Ambulanseallokering

Operasjonsplanlegging

Lagerbeholdning

Optimized Patient Transports in Hospitals

SimulereSimulere

VisualisereVisualisere

Pasientforløp

OptimereOptimere

Planning

SimulereSimulere

VisualisereVisualisere

OptimereOptimere

OptimeringBlodbankBlodbank

Supply chain optimisation

Blodbank Organer …

Sykehusplanleggingog -design

SimulereSimulere VisualisereVisualisereOptimereOptimere

BehandlingsmixBehandlingsmix

Hvilken behandlingHvilken behandling

InntaksplanleggingInntaksplanlegging

UkeplanleggingUkeplanlegging

DagsplanleggingDagsplanleggingBlock scheduleBlock schedule

Open scheduleOpen schedule

Surgical mixSurgical mix

StillingsprosenterStillingsprosenter

Master Surgery ScheduleMaster Surgery Schedule

BemanningsbehovBemanningsbehov

Simulere beholdningSimulere beholdning

Optimere beholdningOptimere beholdning

LagerdesignLagerdesignSimulereSimulereVisualisereVisualisere OptimereOptimere

WorkforceTraining

”What if” Scenario”What if” Scenario

LagerdesignLagerdesign FunksjonsfordelingFunksjonsfordeling

TurnusplanleggingTurnusplanlegging

AmbulanseallokeringAmbulanseallokering

OperasjonsplanleggingOperasjonsplanlegging

LagerbeholdningLagerbeholdning

Optimized Patient Transports in Hospitals

Optimized Patient Transports in Hospitals

SimulereSimulere

VisualisereVisualisere

Pasientforløp

OptimereOptimere

Planning

SimulereSimulere

VisualisereVisualisere

OptimereOptimere

OptimeringBlodbankBlodbank

Supply chain optimisation

BlodbankBlodbank OrganerOrganer ……

Sykehusplanleggingog -design

Sykehusplanleggingog -design

SimulereSimulere VisualisereVisualisereOptimereOptimere

BehandlingsmixBehandlingsmix

Hvilken behandlingHvilken behandling

InntaksplanleggingInntaksplanlegging

UkeplanleggingUkeplanlegging

DagsplanleggingDagsplanleggingBlock scheduleBlock schedule

Open scheduleOpen schedule

Surgical mixSurgical mix

StillingsprosenterStillingsprosenter

Master Surgery ScheduleMaster Surgery Schedule

BemanningsbehovBemanningsbehov

Simulere beholdningSimulere beholdning

Optimere beholdningOptimere beholdning

LagerdesignLagerdesignSimulereSimulereVisualisereVisualisere OptimereOptimere

WorkforceTraining

WorkforceTraining

”What if” Scenario”What if” Scenario

LagerdesignLagerdesign

7ICT

• Enterprise Models• Information• High quality data• OR models• Solution algorithms• Computing power

• Enterprise Models• Information• High quality data• OR models• Solution algorithms• Computing power

Vision: An optimized healthcare systemVision: An optimized healthcare system

8ICT

Two cases in point

Nurse rosteringSolved manually by experienced nursesTimetabling problemComputationally hard discrete optimization problem

Surgery schedulingSolved manually by experienced nursesLong-term, mid-term, short termCritical resources: operation theaters, surgeonsVariants of the Job-Shop Scheduling ProblemComputationally hard discrete optimization problem

9ICT

10ICT

Discrete optimization (1) Central to real-life problems across many application areas

routingschedulingplanningdesign

resources, time, activitieseconomy, environmental effects

Healthcare, transportation, manufacturing, oil & gas, finance, sportsComputationally hard

Physics, chemistry, biology, electronics, statistics, geometry, ...

11ICT

Discrete optimization (2) Two basic types of methodExact, mathematical programming

guarantees to find the optimal solutionresponse time problematicmay be interrupted for feasible solutionlow quality, but upper bound on error

Approximative (typically heuristics)greedylocal searchmetaheuristicsgood solutions in limited timeno useful error bound

12ICT

Standard test instance G-n262-k25 (Gillett & Johnson 1976)

13ICT

"The world record" for G-n262-k25: 5685 vs. 6119 (SINTEF 2003)

14ICT

15ICT

16ICT

17ICT

18ICT

Discrete optimization – main challenges More powerful methods – exact and approximative

better solutions in shorter timenew applications

Combining the strengths of exact methods and heuristics Decomposition and aggregationMulti-level solvers, different levels of abstractionStochastic modelsParallelization

fine grained, e.g. to exploit the architecture of modern commodity computersmulti-core and heterogeneous computing coarse grained, e.g. cooperative hybrid solvers, multi-level solvers

Self-adaptive methods

Better benchmarks

19ICT

Norwegian University of Science and Technology (NTNU), Molde University College (HiM)

and SINTEF ICT

DOMinantDiscrete Optimization Methods

In Maritime and Road-based Transportation

20ICT

Main objective

More efficient methods for rich, industrial variants of computationally hard discrete optimization problemsin maritime and road-based transportation

Two types of problemsInventory routingFleet composition

21ICT

Classical VRP(TW)

Deliveries from a single depotGiven customer demandHomogeneous fleetSizes/capacitiesMinimize total transportation cost(Single time windows)

More than 1000 references

22ICT

VRP with Capacity Constraints (CVRP) Graph G=(N,A)

N={0,…,n+1} Nodes0 Depot, i≠0 Customers A={(i,j): i,j∈N} Arcscij >0 Transportation Costs

Demand di for each Customer iV set of identical Vehicles each with Capacity qGoal

Design a set of Routes that start and finish at the Depot - with minimal Cost.Each Customer to be visited only once (no order splitting)Total Demand for all Customers not to exceed CapacityCost: weighted sum of Driving Cost and # Routes

DVRP – distance/time constraint on each routeVRPTW – VRP with time windowsPickup and Delivery

Backhaul – VRPB(TW)Pickup and delivery VRPPD(TW)PDP

23ICT

kijx ji

24ICT

A mathematical model for VRPTW (Network Flow Formulation)

( , )

0

, 1

minimize (1)

subject to:1, (2)

, (3)

1, (4)

0, , (5)

1, (6)

( ) 0, ( , ) , (7)

∈ ∈

∈ ∈

∈ ∈

∈

∈ ∈

+∈

= ∀ ∈

≤ ∀ ∈

= ∀ ∈

− = ∀ ∈ ∀ ∈

= ∀ ∈

+ − ≤ ∀ ∈ ∀ ∈

∑ ∑

∑∑

∑ ∑

∑

∑ ∑

∑

kij ij

k V i j A

kij

k V j Nk

i iji C j N

kj

j Nk kih hj

i N j Nki n

i Nk k kij i ij j

i

c x

x i C

d x q k V

x k V

x x h C k V

x k V

x s t s i j A k Va , , (8)

{0,1}, ( , ) , (9)≤ ≤ ∀ ∈ ∀ ∈∈ ∀ ∈ ∀ ∈

ki i

kij

s b i N k Vx i j A k V

minimize cost

each customer 1 time

Capacity

k routes out of depot

flow balance for each customer

k routes into depot (redundant)

sequence and driving time

arrival time in time windowarc (i,j) driven by vehicle k

Arc Decisionvariables

Variables-arrival time

25ICT

VRP Research in general

Since 1959Much harder than the TSPThousands of papersMore popular than everImportant vehicle for development of generic methodsOne of the great successes of Operations ResearchIndustry of tools for transportation optimizationQuick dissemination and exploitation of scientific advancesThe road is short from scientific to practical improvements

26ICT

Inventory routing problem (IRP)

Inventories with capacitiesProduction/consumption rateHeterogeneous fleetDesign routes that minimize the transportation cost without interrupting production and consumption of the products

No pickup and delivery pairsQuantity loaded unknownNumber of visits unknown

Inventory level, production

TimeLB

UB

ProductionProduction portport

ConsumptionConsumption portport

ProductProduct 11

ProductProduct 22 KjKjøøpsvikpsvik

BrevikBrevik

AltaAlta

Mo i RanaMo i Rana

TrondheimTrondheim

KarmKarmøøyy

ÅÅrdalrdal

28ICT

Practical applications - IRP Both road-based and maritime transportation

One/multiple productsVRP and PDP structure (with and without depot)Variable production/consumption rateStochastic demand/productionCombining inventory routing with other planning aspects (production, allocation,..)

Industry casesAmmonia – YaraLNG - Suez Energy International, StatoilHydro, RasGas, QuatarGasCement - NorcemFuel oil - Hydro TexacoAnimal fodder - Landbruksdistribusjon, Felleskjøpet

29ICT

Daily charter rate USD 60,000Shipload of LNG worth USD 10,000,000Purchase price LNG tanker USD 150,000,000

30ICT

Fleet composition

VRP, PDP (or IRP) structure

Variable heterogeneous vehicle fleet

capacities acquisition costs….

Objective: find a fleet composition and a corresponding routing plan that minimizes the sum of routing and vehicle acquisition/depreciation/ rental costs

G-n262-k25: 5685 vs. 6119, 5767 CPU s

31ICT

Practical applications – Fleet compositionBoth road-based and maritime transportation

Strategic and tactical fleet dimensioningOne/multiple productsVRP and PDP structure (with and without depot)Stochastic demand and price/cost structure

Industry casesCars - Høegh AutolinersLNG – Statoil Dairy products - Tine Midt-NorgeNewspapers - Aftenposten, DagbladetIce cream - Henning Olsen, Diplom is local distribution - LinjegodsChemicals – Broström Tankes (now Maersk)Cement – NorcemAnimals Norsk Kjøtt, Gilde

32ICT

Research approachMathematical formulations for industrially relevant variants of inventory routing and fleet composition problems

AnalysisSolution methods

Exact methods (Column generation and Lagrangian relaxation)Bounds, relaxations and reductionsApproximative methods (heuristic column generation, metaheuristics)Hybrid methods (combining exact methods and metaheuristics)

Prototype solvers

Computational experiments on instances from literature and industry

33ICT

Relevance to eScienceMathematics

mathematical modellingpolyhedral theorymathematical programming methods

Computing science, informaticsconceptual modellingsearch methodsdecision support systems

ApplicationsNumericsHigh-performance computing

computational experimentsautomated code generation for metaheuristics

34ICT

SummaryChallenges in industry and the public sector

coordinationactivities, time, resourcesplanning, design

Computationally hard DOPs often at the core There is a strong need for more powerful methodsMany challenges, promising research avenuesApplication oriented and scientifically challengingeScienceNorway has a strong position

good scientistsgood access to application casesgood infrastructure good funding opportunities

The road is short from scientific to practical improvements

35ICT

Conclusion

Applied research in discrete optimization deserves further funding in eVITA

36ICT

eVITA Scientific MeetingGeilo, Norway January 28, 2010

Geir Hasle, SINTEF ICT

Optimization-based decision support within healthcare and transportation