On ActivityBased Network Design Problems JEE EUN JAMIE
On Activity-Based Network Design Problems JEE EUN (JAMIE) KANG, JOSEPH Y. J. CHOW, AND WILL W. RECKER 20 TH INTERNATIONAL SYMPOSIUM ON TRANSPORTATION AND TRAFFIC THEORY 7/17/2013 1
Motivation Transportation Planning in general had been negligent of travel demand dynamics. Activity-Based Travel Demand Models are maturing Network Design Problem has been negligent of travel demand dynamics. 2
Motivation § “dinner” activity following “work” Dinner at 7 pm § Departure time adjustment § Mode choice § Destination choice § Activity participation Free Flow Travel Time: 30 minutes § 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 6 pm 3
Motivating Examples 17: 42 19: 00 Grocery Shopping §Network LOS § Influences HHs on daily itinerary § Departure time adjustment § Activity sequence adjustment 17: 00 H 17: 30 Work 9: 00 Work Grocery Shopping: Start [5, 20] For 1 hr Return before 22 18: 30 17: 30 9: 00 7: 00 8: 18 8: 30 Grocery Shopping 7: 30 Work: Start at 9 For 8 hr Return before 22 4
Motivating Examples 19: 50 §Network LOS 17: 45 § Paradoxical cases 17: 00 17: 42 § link investment that generates traffic 17: 00 without any increase in activity participation Work § Improvement result in higher 9: 00 disutility 19: 25 18: 25 Social Waiting time Home 17: 30 8: 00 H Social Activity: Start at 18. 25 For 1 hr Return before 22 Work: Start at 9 For 8 hr Return before 22 5
Network Design Problem (NDP) §Strategic or tactical planning of resources to manage a network §Roadway 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 6
Location Routing Problem (LRP) §Facility Location decisions are influenced by possible routing § Facility Location Strategy § Vehicle Routing Problem (VRP) §One central decision maker 7
Network Design Problem – Household Activity Pattern Problem §Inspired by Location Routing Problem §Activity-based Network Design Problem § Bi-level formulation § Upper Level: NDP § Lower Level: Household Activity Pattern Problem (HAPP) 8
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 9
Conservation of Flow Tour Length Constraints Precedence Constraints Time windows 10
Location Selection Problem for HAPP Activities with Pre-Selected Locations §Generalized VRP (Ghiani and Improta, 2000) 11
NDP-HAPP Model §Supernetwork approach § Infrastructure network § Activity network Network design decisions Flow assignment OD Flow d. NDP Network Level of Service Individual HH travel decisions d. HAPP 12
NDP-HAPP: d. NDP Modified from Unconstrained Multicommodity Formulation (Magnanti and Wong, 1984) Each OD pair is treated as one commodity type Aggregate individual HH itinerary into OD flow 13
NDP-HAPP: d. HAPP Update Network LOS 14
NDP-HAPP Solution Algorithm §Decomposition § Blocks of decision making rationale § Location Routing Problems (Perl and Daskin, 1985) § Iterative Optimization Assignment (Friesz and Harker, 1985) 15
Illustrative Example NDP-GHAPP § Network § Objective: Grocery Shopping Start [5, 20] For 1 hr Return before 22 Node 1, Node 5 H 1 Work: Start [9, 9. 5] For 8 hr Return before 22 § 2 HHs: 1 HH member with 1 vehicle H 2 § Objective: § A(HH 1) = {work, grocery shopping} § A(HH 2) = {work, general shopping} Work: Start [8. 5, 9] For 8 hr Return before 22 General Shopping Start [5, 21] For 1 hr Return before 22 Node 3, Node 8 16
Changes in activity sequences, destination choice, departure times d. HAPP 1 d. HAPP 2 d. NDP Objective Iteration 1 Iteration 2 Iteration 3 Iteration 4 Home (0) → grocery shopping Home (0) → work (2) → grocery Home (0) → grocery shopping (5) → work (2) → (1) → work (2) → home (0) shopping (1) → home (0) (5) → work (2) → home (0) Objective Value: 2 Objective Value: 4 Objective Value: 3 Home (5) → work (6) → general shopping (3) → shopping (8) → home (5) shopping (3) → home (5) Objective Value: 3 Objective Value: 4 Network Design Decisions: Z 03, Network Design Decisions: Z 01, Z 10, Z 21, Z 34, Z 36, Z 45, Z 52, Z 10, Z 21, Z 36, Z 52, Z 67, Z 78, Z 10, Z 12, Z 21, Z 58, Z 67, Z 76, Z 63 Z 85 Z 78, Z 85, Z 87 d. NDP objective value: 31 d. NDP objective value: 32 d. NDP objective value: 35 Changes in network investment decisions HH 1 Paths link Flows: (0) → (3) → (6) → (7) → (8) → (0) → (3) → (4) → (5) (0) → (1) → (2) → (1) → (0) (5) → (2) → (1) → (0) NA 3 HH 2 Paths link Flows: (5) → (8) → (7) → (6) → (7) → (5) → (2) → (1) → (0) → (3) → (8) → (5) (6) → (3) → (4) → (5) (7) → (8) → (5) Shortest path, Link flow changes Update each d. HAPP objective values: HH 1: 2, HH 2: 3 HH 1: 3, HH 2: 4 HH 1: 4, HH 2: 4 40 40 38 38 17
Illustrative Example NDP-GHAPP § Optimal §NDP-HAPP § 5% Optimality gap §Flexibility in d. HAPP allows more options to be searched General shopping @ Node 3 18: 00 17: 00 19: 00 18: 00 9: 00 17: 00 8: 30 7: 30 16: 30 6: 00 Work 8: 30 Work H 1 Grocery shopping @ Node 5 7: 00 H 2 18
Large scale case study §Link improvement decision § SR 39, SR 68, SR 55, SR 22, SR 261, SR 241 §d. NDP: 19
Large scale case study §California Statewide Household Travel Survey § Cal. Trans, 2001 § Departure and arrival times, trip/activity durations, geo-coded locations § 60 HHs § HAPP case 1: no interaction between HH members § Time Windows generated similar to Recker and Parimi (1999) § Individually estimated objective weights (Chow and Recker, 2012) § d. HAPP: 20
NDP-HAPP d. NDP d. HAPP # trips obj (# intra) Budget # iter Link Construction Decision Before NA NA 27. 02 616. 49 1000 2 8988, 7875, 7578 25. 99 609. 58 2000 2 3000 2 4000 1 8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788 5000 1 8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788, 6261 No limit 1 All 199 (76) # HHs Time (sec) affected Conventional NDP Link Construction NDP Decision obj NA NA NA 27. 02 5/60 306 8988, 7875, 7578 25. 99 25. 30 606. 51 199 (76) 24. 88 604. 49 199 (76) 14/60 326 24. 79 604. 12 199 (76) 17/60 196 13/60 294 24. 79 604. 11 199 (76) 17/60 8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788 25. 30 24. 88 24. 79 191 8988, 7875, 7578, 7937, 8660, 6786, 8887, 6086, 8667, 8889, 6162, 6589, 8765, 8788, 6261 24. 79 215 All 24. 79 21
NDP-HAPP Summary §OD 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 changes §Future Research § More sophisticated network strategies § Integration of congestion effect: Infrastructure layer § Demand Capacity: Activity layer 22
Thank you Questions or comments? jekang@uci. edu 23
Network ◦ Objective: Work: Start [9, 9. 5] For 8 hr Return before 22 H 1 Illustrative example NDP-HAPP ◦ Objective: ◦ A(HH 1) = {work, grocery shopping} ◦ A(HH 2) = {work, general shopping} H 2 2 HHs: 1 HH member with 1 vehicle Grocery Shopping Start [5, 20] For 1 hr Return before 22 Work: Start [8. 5, 9] For 8 hr Return before 22 General Shopping Start [5, 21] For 1 hr Return before 22 24
Illustrative example NDP-HAPP d. HAPP 1 d. HAPP 2 d. NDP Final Objective Iteration 1 Home (0) → work (2) → grocery shopping (5) → home (0) Objective Value: 3 Home (5) → work (6) → general shopping (8) → home (5) Objective Value: 3 Network Design Decisions: Z 01, Z 12, Z 25, Z 30, Z 36, Z 43, Z 54, Z 36, Z 78, Z 85 d. NDP objective value: 36 HH 1 Paths link Flows: Home (0) → (2) → (5) → (4) → (3) → (0) HH 2 Paths link Flows: (5) → (4) → (3) → (6) → (7) → (8) → (5) Update each d. HAPP objective values: HH 1: 3, HH 2: 3 42 Iteration 2 Home (0) → work (2) → grocery shopping (5) → home (0) Objective Value: 3 Home (5) → work (6) → general shopping (8) → home (5) Objective Value: 3 NA 42 25
Illustrative example NDP-HAPP § 5% Optimality gap 26
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