SERVICE NETWORK DESIGN: APPLICATIONS IN …ebusiness.mit.edu/.../Barnhart_Service-Network-Design.pdf · 2007-03-21 · 3/21/2007 Barnhart - Service Network Design 55 Challenges Service

SERVICE NETWORK DESIGN: SERVICE NETWORK DESIGN: APPLICATIONS IN APPLICATIONS IN

TRANSPORTATION AND TRANSPORTATION AND LOGISTICSLOGISTICS

Professor Cynthia BarnhartProfessor Cynthia BarnhartMassachusetts Institute of TechnologyMassachusetts Institute of Technology

Cambridge, Massachusetts USACambridge, Massachusetts USA

March 21, 2007March 21, 2007

3/21/20073/21/2007 Barnhart Barnhart -- Service Network Design Service Network Design 22

OutlineOutline

Service network design Service network design –– TimeTime--definite parcel deliverydefinite parcel deliveryRobust, Dynamic SchedulingRobust, Dynamic Scheduling–– Airline schedule designAirline schedule design


Service Network Design Service Network Design Problem DefinitionProblem Definition

–– Determine the cost minimizing or profit Determine the cost minimizing or profit maximizing set of services and their maximizing set of services and their schedulesschedules

Satisfy service requirementsSatisfy service requirementsOptimize the use of resourcesOptimize the use of resources


Service Network Design Service Network Design ProblemsProblems

Examples:Examples:1.1. Jointly determining the aircraft flights, Jointly determining the aircraft flights,

ground vehicle and package routes and ground vehicle and package routes and schedules for timeschedules for time--sensitive package sensitive package deliverydelivery

2.2. Determining an airlineDetermining an airline’’s flight network, its s flight network, its schedule and the assigned fleetsschedule and the assigned fleets

3.3. Determining the locations of warehouses Determining the locations of warehouses and inventory in a service parts logistics and inventory in a service parts logistics operationoperation


ChallengesChallengesService network design problems in Service network design problems in transportation and logistics are characterized transportation and logistics are characterized byby–– Costly resources, tightly constrainedCostly resources, tightly constrained–– Many highly interMany highly inter--connected decisionsconnected decisions–– LargeLarge--scale networks involving time scale networks involving time and and spacespace–– Integrality requirementsIntegrality requirements–– Fixed costsFixed costs

Associated with sets of design decisions, not a single Associated with sets of design decisions, not a single design decisiondesign decision

LargeLarge--scale scale mathematical programsmathematical programsNotoriously weak linear programming Notoriously weak linear programming relaxationsrelaxations

Both models and algorithms are Both models and algorithms are critical to tractabilitycritical to tractability


Designing Service Networks for Designing Service Networks for TimeTime--Definite Parcel DeliveryDefinite Parcel Delivery

Problem Description and BackgroundProblem Description and BackgroundDesigning the Air NetworkDesigning the Air Network–– OptimizationOptimization--based approachbased approachCase StudyCase Study

Research conducted jointly with Prof. Andrew Armacost, USAFA


Problem OverviewProblem Overview

GatewayHub

Ground centers

Pickup Route

Delivery RouteH

pickup linkdelivery linkfeeder/ground link

2

1

3


UPS Air Network OverviewUPS Air Network Overview

AircraftAircraft–– 168 available for Next168 available for Next--Day Air operationsDay Air operations–– 727, 747, 757, 767, DC8, A300727, 747, 757, 767, DC8, A300101 domestic air 101 domestic air ““gatewaysgateways””7 hubs (Ontario, DFW, Rockford, Louisville, 7 hubs (Ontario, DFW, Rockford, Louisville, Columbia, Philadelphia, Hartford)Columbia, Philadelphia, Hartford)Over one million packages nightlyOver one million packages nightly


Research QuestionResearch QuestionWhat aircraft routes and schedules What aircraft routes and schedules provide onprovide on--time service for all packages time service for all packages while minimizing total costs?while minimizing total costs?


UPS Air Network OverviewUPS Air Network Overview

Delivery Routes

Pickup Routes


Problem FormulationProblem Formulation

Select the minimum cost routes, fleet Select the minimum cost routes, fleet assignments, and package flowsassignments, and package flowsSubject to:Subject to:–– Fleet size restrictionsFleet size restrictions–– Landing restrictionsLanding restrictions–– Hub sort capacitiesHub sort capacities–– Aircraft capacitiesAircraft capacities–– Aircraft balance at all locationsAircraft balance at all locations–– Pickup and delivery time requirementsPickup and delivery time requirements


The Size ChallengeThe Size Challenge

Conventional modelConventional model–– Number of variables exceeds one Number of variables exceeds one

billionbillion–– Number of constraints exceeds Number of constraints exceeds

200,000200,000


Column and Cut GenerationColumn and Cut Generation

Constraint MatrixConstraint Matrix

variables in thevariables in theoptimal solutionoptimal solution

variables not consideredvariables not considered

billions of variablesbillions of variables

Hun

dred

s of

H

undr

eds

of

thou

sand

sth

ousa

nds

of

of

cons

trai

nts

cons

trai

nts

additionalconstraints added

constraints not considered

additionaladditionalvariablesvariablesconsideredconsidered


ARM vs UPS PlannersARM vs UPS PlannersMinimizing Operating Cost for UPSMinimizing Operating Cost for UPS

Improvement (reduction)Improvement (reduction)–– Operating cost: 6.96 %Operating cost: 6.96 %–– Number of Aircraft: 10.74 %Number of Aircraft: 10.74 %–– Aircraft ownership cost: 29.24 %Aircraft ownership cost: 29.24 %–– Total Cost: 24.45 %Total Cost: 24.45 %Running timeRunning time–– Under 2 hoursUnder 2 hours


Planners’ Solution

ARM vs. PlannersARM vs. PlannersRoutes for One Fleet TypeRoutes for One Fleet Type

Pickup Routes Delivery Routes

ARM Solution


ARM SolutionARM SolutionNonNon--intuitive doubleintuitive double--leg routesleg routes

Model takes advantage of timing requirements, especially in Model takes advantage of timing requirements, especially in case of Acase of A--33--1, which exploits time zone changes1, which exploits time zone changes

Model takes advantage of ramp transfers at gateways 4 and 5Model takes advantage of ramp transfers at gateways 4 and 5

1

2

A

4

36

5

B


Robust, Dynamic SchedulingRobust, Dynamic Scheduling

An approach to improve airline schedule An approach to improve airline schedule profitabilityprofitability–– Dynamic scheduling and passenger routing Dynamic scheduling and passenger routing

(revenue maximizing)(revenue maximizing)–– Hub deHub de--banking (cost minimizing)banking (cost minimizing)–– Robust (flexible) schedulingRobust (flexible) scheduling


Flight Scheduling and DemandsFlight Scheduling and DemandsFlight schedules and fleet assignments are Flight schedules and fleet assignments are developed based on deterministic, static passenger developed based on deterministic, static passenger demand forecasts (made months or longer in demand forecasts (made months or longer in advance)advance)–– Air travel demand is highly variableAir travel demand is highly variable–– Each daily demand is differentEach daily demand is different

Significant mismatch exists between supply and Significant mismatch exists between supply and demanddemand–– Even with sophisticated revenue management systems Even with sophisticated revenue management systems

Idea: Dynamically adjust airline networks in the Idea: Dynamically adjust airline networks in the booking process to match supply with demandbooking process to match supply with demand


Dynamic Airline SchedulingDynamic Airline SchedulingAdjust the schedule during the booking period to match Adjust the schedule during the booking period to match capacity to demand for each individual datecapacity to demand for each individual date

Consider:Consider:–– The set of flight legs scheduled for day The set of flight legs scheduled for day d d –– The associated current booking data on day The associated current booking data on day d d –– t t for each of these flight legs, for each of these flight legs,

say with say with t = t = 21 days prior to day 21 days prior to day dd–– The forecasted demand for each of these flight legs, updated on The forecasted demand for each of these flight legs, updated on dd--2121(Extend earlier research to integrate both re(Extend earlier research to integrate both re--timing and retiming and re--fleeting decisions (Berge and fleeting decisions (Berge and

HopperstadHopperstad (1993), (1993), BishBish (2004), (2004), SheraliSherali et al. (2005))et al. (2005))


Dynamic Airline SchedulingDynamic Airline SchedulingDynamic scheduling ideaDynamic scheduling idea–– Adjust the capacity (supply) in various markets Adjust the capacity (supply) in various markets

so as to satisfy more exactly emerging demand so as to satisfy more exactly emerging demand by:by:

Retiming flights Retiming flights –– Creating new itineraries and eliminating itineraries only if no Creating new itineraries and eliminating itineraries only if no

bookings to datebookings to date

““SwappingSwapping”” aircraftaircraft–– ReRe--assigning aircraft within the same fleet familyassigning aircraft within the same fleet family

Maintaining crew feasibilityMaintaining crew feasibilityMaintaining conservation of flow (or balance) by fleet Maintaining conservation of flow (or balance) by fleet typetypeMaintaining satisfaction of maintenance constraintsMaintaining satisfaction of maintenance constraints


““Matching Capacity and DemandMatching Capacity and Demand””

Assign new aircraft with different numbers of seats to the Assign new aircraft with different numbers of seats to the flight legsflight legsReRe--time flight legs and create a new itinerarytime flight legs and create a new itinerary–– Potentially many opportunities in a dePotentially many opportunities in a de--peaked peaked hubhub--andand--spoke spoke

networknetwork

MinCT25min

HUB

Time


DeDe--banked (or Debanked (or De--peaked) Hubspeaked) HubsDepature/arrival activities

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departure arrival

American deAmerican de--peaked peaked ORD (2002), DFW ORD (2002), DFW (2002), MIA(2004)(2002), MIA(2004)

Continental deContinental de--peaked peaked EWREWR

United deUnited de--peaked ORD peaked ORD (2004), LAX (2005), (2004), LAX (2005),

SFO (2006)SFO (2006)

Delta deDelta de--peaked ATL peaked ATL (2005)(2005)

Lufthansa deLufthansa de--peaked peaked FRA (2004)FRA (2004)


HubHub--andand--Spoke NetworksSpoke Networks

1.1. Improve aircraft and crew productivityImprove aircraft and crew productivity•• Shorter turn timesShorter turn times

2.2. Reduce maximum demand for gates, ground Reduce maximum demand for gates, ground personnel and equipment, runway capacity, personnel and equipment, runway capacity, etc.etc.

3.3. Improve schedule reliabilityImprove schedule reliability4.4. Eliminate passenger connectionsEliminate passenger connections

•• Extend/ reduce duration of passenger connectionsExtend/ reduce duration of passenger connections


Opportunity in a DeOpportunity in a De--Banked Banked ScheduleSchedule

MaxCT

MinCT

HUB

Flight reFlight re--timing creates new itineraries, timing creates new itineraries, adjusts market supply adjusts market supply


DeDe--Peaking Hub OperationsPeaking Hub OperationsFind flight schedule and associated fleet Find flight schedule and associated fleet assignment that maximizes profitability assignment that maximizes profitability and limits the number of departures + and limits the number of departures + arrivals to 5 in any 10arrivals to 5 in any 10--minute intervalminute interval

Depature/arrival activities

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Flight Cover ConstraintsServe Passenger Demand

Capacity Constraints

Aircraft Balance ConstraintsAircraft Count Constraints

Departure/Arrival Activities Constraints(For De-peaking)

Separate Mainline & Express Network

Maximize Profit


0

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25 40 55 70 85 100 115 130 145 160 175

Connection Time (min)

Num

of P

ax

Original Debank

DeDe--Banking ResultsBanking ResultsLoad factor and schedule profitability essentially Load factor and schedule profitability essentially unchangedunchanged

Set of flight legs unchangedSet of flight legs unchangedFlight schedule execution requires one fewer aircraft Flight schedule execution requires one fewer aircraft (A320)(A320)Average passenger connection times increase by 8 Average passenger connection times increase by 8 minutes after deminutes after de--peaking (from 73 minutes to 81 minutes)peaking (from 73 minutes to 81 minutes)


The Dynamic CaseThe Dynamic Case

Itineraries to bePreserved in

Period 2

Period 2 Pax Demand

Forecast

Re-optimize fleet& flight timing

Seats TakenOn Each Leg

New schedule

# of AircraftOvernighted

At Each StationFor Each Fleet

Departuredate21 days prior

to departure

Period 1 pax demand

Period 2 pax demand

PassengerMix

Model

Period 1Pax Assignment

PassengerMix

Model

RemainingLeg capacity

BookingLimit

Output

New schedule guarantees:• All connecting itineraries sold in Period 1 remain feasible• # of aircraft for each fleet overnighted at each station is the same as originally planned


ReRe--optimization Formulationoptimization Formulation

Flight Cover

Serve Pax

Capacity

Balance

Count

Max Profit


ReRe--optimization Formulationoptimization Formulation

Overnight AircraftCount

Restrict departure and arrivalactivities

Protect Itineraries

Enable Re-fleeting


Case StudyCase StudyMajor US AirlineMajor US Airline–– 832 flights daily832 flights daily–– 7 aircraft types7 aircraft types–– 50,000 passengers50,000 passengers–– 302 inbound and 302 outbound flights at hub daily302 inbound and 302 outbound flights at hub daily

Banked hub operationsBanked hub operations–– must demust de--bankbankReRe--timetime–– +/+/-- 15 minutes 15 minutes

ReRe--fleetfleet–– A320 & A319A320 & A319–– CRJ & CR9CRJ & CR9

One week in August, with daily total demand:One week in August, with daily total demand:–– higher than average (Aug 1)higher than average (Aug 1)–– average (Aug 2)average (Aug 2)–– lower than average (Aug 3)lower than average (Aug 3)

Protect all connecting itineraries sold in Period up to Protect all connecting itineraries sold in Period up to dd--tt–– t t =21 or 28 days=21 or 28 days

Two scenarios concerning forecast demandTwo scenarios concerning forecast demand–– Perfect informationPerfect information–– Historical average demandHistorical average demand


Improvement In ProfitabilityImprovement In ProfitabilityConsistent improvement Consistent improvement in profitability in profitability –– Forecast AForecast A

44--8% improvement in profit8% improvement in profit6060--140k daily 140k daily

–– Forecast BForecast B22--4% improvement in profit4% improvement in profit3030--80k daily80k dailyBenefits remain significant Benefits remain significant when using Forecast Bwhen using Forecast B-- a a lower boundlower bound

–– not including benefit not including benefit from aircraft savings, from aircraft savings, reduced gates and reduced gates and personnel personnel ……

4.35%5.09%

7.63%

6.52%

4.43%4.84%

6.70%

2.55%1.97%

4.91%

2.02% 1.99%2.64%

4.01%

0%

2%

4%

6%

8%

10%

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7

Incr

ease

in P

rofit

Dynamic scheduling under Forecast A Dynamic scheduling under Forecast B


Comparison: ReComparison: Re--Time & ReTime & Re--FleetFleet

The two mechanisms are synergisticThe two mechanisms are synergistic–– PPAA(Dynamic(Dynamic scheduling) scheduling) > > PPAA(re(re--fleeting)+Pfleeting)+PAA(re(re--timingtiming))–– PPBB(Dynamic(Dynamic scheduling) scheduling) > > PPBB(re(re--fleeting)+Pfleeting)+PBB(re(re--timingtiming))

ReRe--timing is less affected by deterioration of forecast timing is less affected by deterioration of forecast qualityquality–– Larger PLarger PBB/P/PAA ratiosratios

ReRe--timing contributes more than flight retiming contributes more than flight re--fleetingfleeting–– PPAA(re(re--fleeting) fleeting) < < PPAA(re(re--timing)timing)–– PPBB(re(re--fleeting) fleeting) < < PPBB(re(re--timing)timing)

Average daily profitability results ($)Forecast A Forecast B PB/PA

Dynamic Scheduling 99,541 49,991 50.22%Re-fleeting Only 28,031 7,542 26.91%Re-timing Only 44,297 37,800 85.33%


Other StatisticsOther StatisticsSystem load factors went up 0.5System load factors went up 0.5--1%1%Aircraft savingsAircraft savings

Schedule changesSchedule changes–– About 100 fleet changesAbout 100 fleet changes–– 8585--90% flights are retimed90% flights are retimed

Average retiming of 8 minutes Average retiming of 8 minutes

perfect + retime + swap average + retime + swap1-Aug 1 A320 1 A3202-Aug 1 A320 1 CR9 1 A320 1 CR93-Aug 1 A320 2 CR9 1 A320

0

-5

-10

-15

+5

+10

+15


Flexible PlanningFlexible Planning

ReRe--optimization decisions constrained by optimization decisions constrained by original scheduleoriginal schedule–– Can we design our original schedule to facilitate Can we design our original schedule to facilitate

dynamic scheduling?dynamic scheduling?

GoalGoal–– Maximize the number of Maximize the number of connectionsconnections that can be that can be

created to accommodate unexpected demandscreated to accommodate unexpected demandsObjective function value within 0.0% of original scheduleObjective function value within 0.0% of original schedule


A A FlexibleFlexible Formulation (1)Formulation (1)Max sum of

connection variables

Fleet assignment, Passenger flows

de-peaked operations


A A FlexibleFlexible Formulation (2)Formulation (2)Profitability bound

Constraints on Wp


Preliminary ResultsPreliminary ResultsUnder Forecast A, Under Forecast A, improvement is not improvement is not significantsignificant–– When forecast is perfect, When forecast is perfect,

dynamic scheduling can dynamic scheduling can always make good decisions always make good decisions to respondto respond

Under Forecast B, Under Forecast B, improvements obtainableimprovements obtainable–– When forecast is imperfect, When forecast is imperfect,

an improved schedule can be an improved schedule can be constructed by accounting for constructed by accounting for dynamic scheduling dynamic scheduling opportunitiesopportunities

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7Prof

it in

crea

se c

ompa

ring

to o

rdin

ary

de-p

eak

mod

elpefect average


Summary and ContributionsSummary and Contributions

Solving largeSolving large--scale service network scale service network design problemsdesign problems–– Blend art and scienceBlend art and science–– Model selection key to achievingModel selection key to achieving

TractabilityTractabilityExtendibilityExtendibility

Dynamic and robust scheduling form core Dynamic and robust scheduling form core of nextof next--generation optimization generation optimization approachesapproaches


Questions?Questions?

Documents

SERVICE NETWORK DESIGN: APPLICATIONS IN …ebusiness.mit.edu/.../Barnhart_Service-Network-Design.pdf · 2007-03-21 · 3/21/2007 Barnhart - Service Network Design 55 Challenges Service