1

On Activity-Based Network Design ProblemsJEE EU N ( JA MIE) K ANG, JOSEPH Y. J . CH OW, AND W ILL W. RECK ER

20 T H INTERNATIONA L SYMPOSIU M ON TRANSP ORTATION A ND TRAFF IC THEORY

7/17 /2013

2

Motivation

Network Design Problem has been negligent of travel demand dynamics.

Transportation Planning in general had been negligent of travel demand dynamics.

Activity-Based Travel Demand Models are maturing

3

Motivation “dinner” activity following “work”

Departure time adjustment Mode choice Destination choice Activity participation Sequence of activities

Aggregate time-dependent activity-based traffic assignment (Lam and Yin, 2001)

No NDP with individual traveler’s travel demand dynamics Work ends 6pm

Dinner at 7 pm

Free Flow Travel Time: 30 minutes

4

Network LOS Influences HHs on daily itinerary Departure time adjustmentActivity sequence adjustment

Motivating Examples

H

Work:Start at 9For 8 hr

Return before 22

Grocery Shopping:Start [5,20]

For 1 hrReturn before 22

2 1 0min ( )v vn

v V

Z T T

19:00

8:00

Work9:00

18:30

Grocery Shopping

17:30

17:00

19:00

8:18

Work9:00

18:30

Grocery Shopping

17:30

17:00

17:42

7:00

Grocery Shopping

7:30

17:30

Work

9:00

8:30

5

Network LOSParadoxical cases link investment that generates traffic

without any increase in activity participation

Improvement result in higher disutility

H

Work:Start at 9For 8 hr

Return before 22

Social Activity:Start at 18.25

For 1 hrReturn before 22

min ( )vT uw uw C u n u

v V w u u

Z t X T T

N N N

1, 1T C 1, 1.514.25

T W

Z

1, 1.5

16.625T W

Z

2 1 0min ( ) ( )v v vT W uw uw W n

v V w u v V

Z t X T T

N N

Motivating Examples 19:50

8:00

Work9:00

19:25

Social18:25

17:0017:30

Waiting time

19:50

8:00

Work9:00

19:25Social 18:25

17:0017:42

Home17:45

19:50

8:00

Work9:00

19:25

Social18:25

17:0017:30

Waiting time

19:50

8:00

Work9:00

19:25

Social18:25

17:00 17:15

Waiting time

0.25

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Network Design Problem (NDP)Strategic or tactical planning of resources to manage a networkRoadway Network Design Problems

“Optimal decision on expansion of a street and highway system in response to a growing demand for travel” (Yang and Bell, 1998)

Congestion effect Route choice: “selfish traveler” Bi-level structure Upper Level: NDP Lower Level: Traffic Assignment

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Location Routing Problem (LRP)Facility Location decisions are influenced by possible routing

Facility Location Strategy Vehicle Routing Problem (VRP)

One central decision maker

Depot

Depot

Depot

Depot

Depot

Depot

Primary Facility

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Network Design Problem – Household Activity Pattern Problem

Inspired by Location Routing ProblemActivity-based Network Design ProblemBi-level formulationUpper Level: NDP Lower Level: Household Activity Pattern Problem (HAPP)

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Household Activity Pattern Problem (HAPP)

Full day activity-based travel demand model

Formulation of continuous path in time, space dimension restricted by temporal, spatial constraints (Hagerstrand, 1970)

Network-Based Mixed Integer Linear Programming Base Case: Pickup and Delivery Problem with Time Windows (PDPTW)

Simultaneous Travel Decisions Activity, vehicle allocation between HH members Sequence of activities Departure (activity) times Some level of mode choice

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Conservation of Flow

Precedence ConstraintsTime windows

Tour Length Constraints

𝑴𝒊𝒏𝒊𝒎𝒊𝒛𝒆 𝒁=𝑻𝒓𝒂𝒗𝒆𝒍 𝑫𝒊𝒔𝒖𝒕𝒊𝒍𝒊𝒕𝒚

11

Location Selection Problem for HAPP

Generalized VRP (Ghiani and Improta, 2000)

Candidate Locations for activity

Activities with Pre-Selected Locations

12

Supernetwork approach Infrastructure networkActivity network

dHAPP

dNDP

Network design decisionsFlow assignment

Network Level of Service

Individual HH travel decisions

OD Flow

H1H2

HNDP-HAPP Model

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NDP-HAPP: dNDP( , ) ( , )

min ( , )

, , ( , )

, , ( , ) ,

=0, , , , ( , )

,

dNDP ij ij ij iji j i j

uw uw uwji il

j l

uw uw uwij li

j l

uw uwji ij

j j

uw uwij ij

z f F z c f

f f D i u u w

f f D i u u w

f f i i u i w u w

f D z

E E

N N

N N

N N

N K

N K

N K

,

( , ) , ( , )

(0,1), ( , )

where

, , ( , )h

ij

uw v huw

h v V

i j u w

z i j

D X w i u w

H

E K

E

N K

Modified from Unconstrained Multicommodity Formulation(Magnanti and Wong, 1984)

Aggregate individual HH itinerary into OD flow

Each OD pair is treated as one commodity type

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NDP-HAPP: dHAPP, , , ,

2 1 0

,,

,( , )

min ( , ) ( )

;

, , , , , , ,

where

( ) ,

hh h

h h

h h T v h v h C v h v hdHAPP h n h uw uw

h h u wv V v V

h

h hh

h

h v h h h h hu w h h u h u h

uw ij uw iji j

X T T T c X

X u w v T u Y u

t z t

H H Q Q

E

XA bT

Y

X N V T P Y P

, ,,

( , )

,

, ,

( ) , ,

0 0, ( , ) , ( , ) , ,

1 otherwise

h

v h v huw ij uw ij h

i j

uwij

uw ij h

u w h

c z c u w

fi j u w v V h

E

Q H

Q

E K H

Update Network LOS

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NDP-HAPPSolution AlgorithmDecomposition Blocks of decision

making rationale Location Routing

Problems (Perl and Daskin, 1985)

Iterative Optimization Assignment (Friesz and Harker, 1985)

Network Initializationall links are available

dNDPmin ( , )dNDP f z

dHAPP

1min ( )hdHAPP X

min ( )hdHAPP X⋮

Terminate

no

No changes in variables and

Obj. value

yes

No changes in variables and

Obj. value

yesTerminate

no

Shortest Path Problem for Initialization

,0 01 otherwise

( , ) , ( , ) , ,

uwij

uw ij

h

f

i j u w v V h

E K H

, , , ( , )h

uw v huw

h v V

D X w i u w

H

N K

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Illustrative ExampleNDP-GHAPP

0 1 2

3 4 5

6 7 8

H1

Work:Start [9, 9.5]

For 8 hrReturn before 22

Work:Start [8.5,9]

For 8 hrReturn before 22

Grocery Shopping Start [5,20]

For 1 hrReturn before 22Node 1, Node 5

H2

General Shopping Start [5,21]

For 1 hrReturn before 22Node 3, Node 8

( , ) ( , )

min ( , ) 3 0.5dNDP ij iji j i j

z f z f

E E

, ,min ( )h

h h

h v h v hdHAPP uw uw

u w v V

X c X

Q Q

Network Objective:

2 HHs: 1 HH member with 1 vehicle Objective: A(HH1) = {work, grocery shopping} A(HH2) = {work, general shopping}

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Iteration 1 Iteration 2 Iteration 3 Iteration 4

dHAPP1Home (0) → grocery shopping (1) → work (2) → home (0)Objective Value: 2

Home (0) → work (2) → grocery shopping (1) → home (0)Objective Value: 2

Home (0) → grocery shopping (5) → work (2) → home (0)Objective Value: 4

Home (0) → grocery shopping (5) → work (2) → home (0)Objective Value: 3

dHAPP2

Home (5) → work (6) → general shopping (8) → home (5)Objective Value: 3

Home (5) → work (6) → general shopping (8) → home (5)Objective Value: 3

Home (5) → work (6) → general shopping (3) → home (5)Objective Value: 4

Home (5) → work (6) → general shopping (3) → home (5)Objective Value: 4

dNDP

Network Design Decisions: Z01, Z10, Z12, Z21, Z58, Z67, Z76, Z78, Z85, Z87dNDP objective value: 35 HH1 Paths link Flows: (0) → (1) → (2) → (1) → (0) HH2 Paths link Flows: (5) → (8) → (7) → (6) → (7) → (8) → (5) Update each dHAPP objective values: HH1: 2, HH2: 3

Network Design Decisions: Z03, Z10, Z21, Z36, Z52, Z67, Z78, Z85dNDP objective value: 32

HH1 Paths link Flows: (0) → (3) → (6) → (7) → (8) → (5) → (2) → (1) → (0) HH2 Paths link Flows: (5) → (2) → (1) → (0) → (3) → (7) → (8) → (5)

Update each dHAPP objective values: HH1: 4, HH2: 4

Network Design Decisions: Z03, Z10, Z21, Z34, Z36, Z45, Z52, Z63dNDP objective value: 31

HH1 Paths link Flows: (0) → (3) → (4) → (5) → (2) → (1) → (0) HH2 Paths link Flows: (5) → (2) → (1) → (0) → (3) → (6) → (3) → (4) → (5) Update each dHAPP objective values: HH1: 3, HH2: 4

NA3

Objective 40 40 38 38

Changes in activity sequences, destination choice, departure times

Changes in network investment decisions

Shortest path, Link flow changes

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Illustrative ExampleNDP-GHAPPNDP-GHAPPOptimal

NDP-HAPP 5% Optimality

gap

Flexibility in dHAPP allows more options to be searched

0 1 2

3 4 5

6 7 8

Grocery shopping@ Node 5H1

H2

General shopping@ Node 3

17:00

6:00

9:008:30

7:30

18:00

Work

17:00

7:00

Work8:30

16:30

18:0019:00

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Large scale case studyLink improvement decision SR39, SR68, SR55,

SR55, SR22, SR261, SR 241

dNDP:

SR 73

I 405

SR 39

SR 14

I 5

SR 134 I 210

I 210

I 210I 210 I 210

SR 57

SR 57

SR 57

SR 57

SR 55SR 57

SR 55

SR 55

SR 71

SR 71SR 142

SR 71

SR 90

SR 91SR 91

SR 241

SR 241

SR 241

SR 261

SR 133

SR 133

SR 133

SR 55

I 5

SR 74

I 5

I 5

I 5

I 5

I 5I 5

I 5

I 5

I 5

SR 22SR 22I 405SR 22

I 405 I 405

I 405

I 405

I 405

I 405

SR 1

SR 1

SR 1

SR 1

SR 1

SR 91

SR 91 SR 91SR 91 SR 91SR 91

I 405

SR 91

SR 1SR 1

SR 1

SR 1

SR 1

I 10

I 105

SR 110

I 10 I 10 I 10 I 10

SR 60

SR 60SR 60

SR 60 SR 60

I 5

I 5

US 101

US 101

US 170

SR 134US 101

I 405

I 405

SR 91

I 105 I 105SR 90I 105

I 105

SR 90

I 10

SR 2

SR 110

SR 110

SR 110

SR 110

I 405SR 110

SR 107

SR 42

SR 110SR 42

SR 42

SR 1

SR 42

I 710

I 710

I 710

I 10

I 710

I 710

I 710

SR 19

SR 19I 5

SR 19

SR 19

SR 19

SR 19

SR 19

I 605

I 605

I 605

I 605

SR 19

I 605

I 605

SR 72

SR 39

SR 39

SR 39

SR 39

SR 73

SR 73

I 405

0

1

12

11

10

3 45

8

17 18

23

38

39

5049

48

62

75

77

76

74

73

66

71

72

69

64

65

70

68

67

63

60

37

4647

5958

67

45

53

575654

40

31

41

3334

55

42 43

52

2

13

19 20

1516

30

3635

44

32

21 22

28 29

24

2725

14

26

61

9

51

78

79

80

8182

8384

85 86

87

88

89

91

9092

9394

95

96

97Link Improvement

( , )

min ( , )dNDP ij jii j

z f t f

E

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California Statewide Household Travel Survey CalTrans, 2001 Departure and arrival times, trip/activity durations, geo-coded

locations 60HHs HAPP case1: no interaction between HH members Time Windows generated similar to Recker and Parimi (1999) Individually estimated objective weights (Chow and Recker, 2012) dHAPP:

Large scale case study

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BudgetNDP-HAPP Conventional NDP

# iter

Link Construction Decision

dNDP obj

dHAPP obj

# trips(# intra)

# HHs affected Time (sec) Link Construction

DecisionNDP obj

Before NA NA 27.02 616.49 199(76) NA NA NA 27.02

1000 2 8988, 7875, 7578 25.99 609.58 199(76) 5/60 306 8988, 7875, 7578 25.99

2000 28988, 7875, 7578, 7937, 8660, 6786,

888725.30 606.51 199

(76) 13/60 2948988, 7875, 7578, 7937, 8660, 6786,

888725.30

3000 2

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667,

8889

24.88 604.49 199(76) 14/60 326

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667,

8889

24.88

4000 1

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589,

8765, 8788

24.79 604.12 199(76) 17/60 196

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589,

8765, 8788

24.79

5000 1

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788, 6261

24.79 604.11 199(76) 17/60 191

8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788, 6261

24.79

No limit 1 All 24.79 604.11 199(76) 17/60 215 All 24.79

0

1

2

3

4

5

6

7

8

9

10

number

of

trips

Time-of-Day

No Budget Limit Budget Limit 1000 Before Improvement

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NDP-HAPP SummaryOD is not a priori, subject of responses of individual HH decisions

Bi-level formulation Upper level: NDP Lower Level: HAPP Decomposition algorithm Reasonable in accuracy, running time

Incorporated OD changes, TOD changesFuture Research More sophisticated network strategies Integration of congestion effect: Infrastructure layer Demand Capacity: Activity layer

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Thank youQuestions or comments?

jekang@uci.edu

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Illustrative exampleNDP-HAPP

Network◦ Objective:

2 HHs: 1 HH member with 1 vehicle

◦ Objective:

◦ A(HH1) = {work, grocery shopping}

◦ A(HH2) ={work, general shopping}

0 1 2

3 4 5

6 7 8H1

Work:Start [9, 9.5]

For 8 hrReturn before 22

Work:Start [8.5,9]

For 8 hrReturn before 22

H2

( , ) ( , )

min ( , ) 3 0.5dNDP ij iji j i j

z f z f

E E

, ,min ( )h

h h

h v h v hdHAPP uw uw

u w v V

X c X

Q Q

Grocery Shopping Start [5,20]

For 1 hrReturn before 22

General Shopping Start [5,21]

For 1 hrReturn before 22

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Illustrative exampleNDP-HAPP Iteration 1 Iteration 2

dHAPP1Home (0) → work (2) → grocery shopping (5) → home (0)Objective Value: 3

Home (0) → work (2) → grocery shopping (5) → home (0)Objective Value: 3

dHAPP2Home (5) → work (6) → general shopping (8) → home (5)Objective Value: 3

Home (5) → work (6) → general shopping (8) → home (5)Objective Value: 3

dNDP

Network Design Decisions: Z01, Z12, Z25, Z30, Z36, Z43, Z54, Z36, Z78, Z85dNDP objective value: 36 HH1 Paths link Flows: Home (0) → (2) → (5) → (4) → (3) → (0) HH2 Paths link Flows: (5) → (4) → (3) → (6) → (7) → (8) → (5) Update each dHAPP objective values:HH1: 3, HH2: 3

NA

Final Objective 42 42

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Illustrative exampleNDP-HAPP

0 1 2

3 4 5

6 7 8

Grocery shopping

Work

Work

General shopping

H1

H2

8:30

17:30

17:30

9:00

0 1 2

3 4 5

6 7 8

Grocery shopping

Work

Work

General shopping

H1

H2

8:30

6:30

17:30

9:00

NDP-HAPP 5% Optimality gap