service network design: applications in transportation and logistics professor cynthia barnhart...

Service Network Design: Applications in Transportation

and Logistics

Professor Cynthia BarnhartProfessor Cynthia Barnhart

Center for Transportation and LogisticsCenter for Transportation and Logistics

Operations Research CenterOperations Research Center

Massachusetts Institute of TechnologyMassachusetts Institute of Technology

September 8, 2002September 8, 2002

Institute for Mathematics and its Applications

2

Problem Definition Service network design problems in transportation Service network design problems in transportation

and logistics, subject to limited resources and and logistics, subject to limited resources and variable service demandsvariable service demands Determine the cost minimizing or profit Determine the cost minimizing or profit

maximizing set of services and their schedulesmaximizing set of services and their schedules What is the best location and size of terminals such What is the best location and size of terminals such

that overall costs are minimized? that overall costs are minimized? What is the best fleet composition and size such that What is the best fleet composition and size such that

service requirements are met and profits are service requirements are met and profits are maximized?maximized?


3

Service Network Design Applications ExamplesExamples

Determining the set of flights and their Determining the set of flights and their schedules for an airlineschedules for an airline

Determining the routing and scheduling of Determining the routing and scheduling of tractors and trailers in a trucking operationtractors and trailers in a trucking operation

Jointly determining the aircraft flights, ground Jointly determining the aircraft flights, ground vehicle and package routes and schedules for vehicle and package routes and schedules for time-sensitive package deliverytime-sensitive package delivery


4

Research on Service Network Design Rich history of research on network design applicationsRich history of research on network design applications

Network DesignNetwork Design Balakrishnan et al (1996); Desaulniers, et al (1994); Gendron, Crainic Balakrishnan et al (1996); Desaulniers, et al (1994); Gendron, Crainic

and Frangioni (1999); Gendron and Crainic (1995); Kim and Barnhart and Frangioni (1999); Gendron and Crainic (1995); Kim and Barnhart (1999); Magnanti (1981); Magnanti and Wong (1984); Minoux (1989)(1999); Magnanti (1981); Magnanti and Wong (1984); Minoux (1989)

Freight Transportation Service Network DesignFreight Transportation Service Network Design Armacost, Barnhart and Ware (2002); Crainic and Rousseau (1986); Armacost, Barnhart and Ware (2002); Crainic and Rousseau (1986);

Crainic (2000); Farvolden and Powell (1994); Lamar, Sheffi and Crainic (2000); Farvolden and Powell (1994); Lamar, Sheffi and Powell (1990); Newton (1996); Ziarati, et al (1995) Powell (1990); Newton (1996); Ziarati, et al (1995)

Fleet Routing and SchedulingFleet Routing and Scheduling Appelgren (1969, 1971); Desaulniers, et al (1997); Desrosiers, et al Appelgren (1969, 1971); Desaulniers, et al (1997); Desrosiers, et al

(1995); Dumas, Desrosiers, Soumis (1991); Leung, Magnanti and (1995); Dumas, Desrosiers, Soumis (1991); Leung, Magnanti and Singhal (1990); Ribeiro and Soumis (1994) Singhal (1990); Ribeiro and Soumis (1994)


5

Challenges Service network design problems in transportation and Service network design problems in transportation and

logistics are characterized bylogistics are characterized by Costly resources, tightly constrainedCostly resources, tightly constrained Many highly inter-connected decisionsMany highly inter-connected decisions Large-scale networks involving time Large-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

Huge Huge mathematical programsmathematical programs Notoriously weak linear programming relaxationsNotoriously weak linear programming relaxations

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


6

Designing Service Networks for Time-Definite Parcel Delivery

Problem Description and BackgroundProblem Description and Background Designing the Air NetworkDesigning the Air Network

Optimization-based approachOptimization-based approach Case StudyCase Study

Research conducted jointly with Prof. Andrew Armacost, USAFA


7

Problem Overview

Gateway

HubGround centers

Pickup Route

Delivery RouteH

pickup linkdelivery linkfeeder/ground link

2

1

3


8

UPS Air Network Overview

AircraftAircraft 168 available for Next-Day Air operations168 available for Next-Day Air operations 727, 747, 757, 767, DC8, A300727, 747, 757, 767, DC8, A300

101 domestic air “gateways”101 domestic air “gateways” 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


9

Research Question

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


10

UPS Air Network Overview

Delivery Routes

Pickup Routes


11

Problem Formulation

Select the minimum cost routes, fleet assignments, Select the minimum cost routes, fleet assignments, and package flowsand package flows

Subject 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


12

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

Express Shipment ServiceNetwork Design Problem

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6

minX

k2K

X

(i;j )2A

ckij x

kij +

X

f 2F

X

r2R f

dfr yf

r

subject to:

X

k2K

xkij ·

X

f 2F

X

r2R f

±f rij uf

r yfr (i; j ) 2 A (5)

X

j :(i;j )2A

xkij ¡

X

j :(j ;i)2A

xkj i =

8>>><

>>>:

bk if i = O(k)

¡ bk if i = D(k)

0 otherwise

i 2 N; k 2 K (6)

X

k2K

X

(i;j )2A

±hij x

kij · eh h 2 H (7)

X

r2R f

¯ ri y

fr = 0 i 2 N; f 2 F (8)

X

r2R f

yfr · nf f 2 F (9)

X

f 2F

X

r2R f

±rhyf

r · ah h 2 H (10)

xkij ¸ 0 (i; j ) 2 A; k 2 K (11)

yfr 2 Z+ r 2 Rf ; f 2 F (12)

6


13

The 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


14

Column and Cut Generation

Constraint MatrixConstraint Matrix

variables in thevariables in theoptimal solutionoptimal solution

variables not consideredvariables not considered

billions of variablesbillions of variables

Hu

nd

red

s o

f H

un

dre

ds

of

tho

usa

nd

sth

ou

san

ds

of

o

f

co

nst

rain

ts c

on

stra

ints

additionalconstraints added

constraints not considered

additionaladditionalvariablesvariablesconsideredconsidered


15

Algorithms for Huge Integer Programs: Branch-and-Price-and-Cut

Determines Optimal Solutions to Huge Integer Determines Optimal Solutions to Huge Integer ProgramsPrograms Combines Branch-and-Bound with Column Combines Branch-and-Bound with Column

Generation and Cut Generation to solve the Generation and Cut Generation to solve the LP’sLP’s

x1 = 1 x1 = 1 x1=0x1=0

x2=1x2=1 x2=0x2=0 x3=1x3=1 x3=0x3=0

x4=1x4=1 x4=0x4=0


16

The Integrality Challenge

Initial feasible solution about triple Initial feasible solution about triple the best boundthe best bound Multiple day runtimes to achieve Multiple day runtimes to achieve

first feasible solutionfirst feasible solution


17

Resolution of Challenges

Algorithms are not enoughAlgorithms are not enough Key to successful solution of these Key to successful solution of these

very large-scale problems are the very large-scale problems are the models themselvesmodels themselves


18

Alternative Formulations

A given problem may have different A given problem may have different formulations that are all logically equivalent formulations that are all logically equivalent yet differ significantly from a yet differ significantly from a computational point of viewcomputational point of view

This has motivated the study of systematic This has motivated the study of systematic

procedures for generating and solving procedures for generating and solving alternativealternative formulations formulations


19

Reformulation: Key IdeasAircraft Route VariablesAircraft Route Variables

3000y1 + 8000y2 6000

Capacity-demand:

Cover:

g hdemand =6000

capacity =3000

capacity =8000

Cover:

Composite Variables

g hdemand =6000

capacity =6000

capacity =8000

y1 + y2 1y3+ y2 1


20

Strength Results: Single Hub Example

ESSND ARMRows 53 34Cols 67 42NZ 274 255LP Solution 10663 28474IP Solution 28474 28474B&B Nodes 781 1LP-IP Gap 167% 0%

6

2

1

5

3

4

6

2

1

5

3

4

6

Time-Space Representation of Plane/Package Movements


21

ARM vs UPS PlannersMinimizing 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


22

Planners’ Solution

ARM vs. PlannersRoutes for One Fleet Type

Pickup Routes Delivery Routes

ARM Solution


23

ARM SolutionNon-intuitive double-leg routes

Model takes advantage of timing requirements, especially in case of Model takes advantage of timing requirements, especially in case of A-3-1, which exploits time zone changesA-3-1, 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

3

6

5

B


24

Conclusions

Solving large-scale service network Solving large-scale service network design problemsdesign problemsBlend art and scienceBlend art and scienceComposite variable modeling can Composite variable modeling can

often facilitateoften facilitateTractabilityTractabilityExtendibilityExtendibility


25

Research conducted jointly with Stephane Bratu

Service Network Design and Passenger Service in the Airline Industry

Problem Description and BackgroundProblem Description and Background AnalysisAnalysis Some Research FindingsSome Research Findings


26

Route individual aircraft honoringmaintenance restrictions

Assign aircraft types to flight legs such that contribution is maximized

Airline Schedule Planning

Schedule Design

Fleet Assignment

Aircraft Routing

Crew Scheduling

Select optimal set of flight legs in a schedule

Assign crew (pilots and/or flight attendants) to flight legs


27

Some Simple Statistics …


28

30%

40%

50%

60%

70%

1995 1996 1997 1998 1999 200032000003300000340000035000003600000370000038000003900000400000041000004200000

% of flights arriving later thanscheduled

Total number of flights operated

Number and Percentage of Delayed Flights


29

Average Delay Duration of Operated Flights

0

5

10

15

20

25

1995 1996 1997 1998 1999 2000

(Min

utes

)


30

15-minute On-Time Performance

50%

60%

70%

80%

90%

100%

1995 1996 1997 1998 1999 2000


32

Number of Delayed Flights

The delay distribution has shifted from short to long delays

Factor 1: Shift to Longer Flight Delays

Total Delay Minutes


33

Factor 2: Hub-and-Spoke and Connecting Passengers

-5

0

5

10

15

20

25

30

35

(min

utes

)

Average Delay

Local

Connecting

Flight Delay

Flight delays underestimate passenger delays Key explanation lies in the connecting passengers

Average Passenger and Flight Delays


34

Factor 3: Number of Canceled Flights and Cancellation Rates

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

1995 1996 1997 1998 1999 2000

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

Number of CanceledFlights

Cancellation Rate

Delay statistics do not consider cancellations


35

Cancellation Rate: Southwest and the Other Majors Airlines

0%

2%

4%

6%

8%

10%

12%

1995 1996 1997 1998 1999 2000

Maximum Others

Average Others

Minimum Others

Southwest

Southwest has a lower cancellation rate than any other Major from 1995 to 2000 due in part to increases in cancellation rates at some congested hubs


36

Hub Cancellation Rates

0%

1%

2%

3%

4%

5%

6%

7%

8%

ORDAA

ORDUA

EWRCO

DFWAA

SFOUA

ATLDL

EWRCO

MSPNW

1995

2000


37

Research Findings: Service Network Design and Passenger Service DOT 15 minute on-time-performance is inadequateDOT 15 minute on-time-performance is inadequate There are a number of alternative “flight schedules” with There are a number of alternative “flight schedules” with

similar associated costs and profitability, but vastly similar associated costs and profitability, but vastly different associated passenger delaysdifferent associated passenger delays ServiceService network design needs to incorporate network design needs to incorporate service service

considerationsconsiderations Flight cancellations can reduce overall passenger delayFlight cancellations can reduce overall passenger delay

High load factors together with flight delays can result High load factors together with flight delays can result in excessive passenger delaysin excessive passenger delays

De-banking can result in much longer planned connection De-banking can result in much longer planned connection times, but only slightly longer connection times in actualitytimes, but only slightly longer connection times in actuality

service network design: applications in transportation and logistics professor cynthia barnhart...

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