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Household Activity Pattern Problem

Household Activity Pattern Problem. Paper by: W. W. Recker. Presented by: Jeremiah Jilk May 26, 2004. Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004. Overview. General Concepts Starchild, HAPP and PDPTW 5 Cases Conclusion. Jeremiah Jilk

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Household Activity Pattern Problem

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  1. Household Activity Pattern Problem Paper by: W. W. Recker. Presented by: Jeremiah Jilk May 26, 2004 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

  2. Overview • General Concepts • Starchild, HAPP and PDPTW • 5 Cases • Conclusion Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 2

  3. General Concepts • Activity Problem • “There is a general consensus that the demand for travel is derived from a need or desire to participate in activities that are spatially distributed over the geographic landscape.” • In other words, we travel because we need or want to do things that are not all in the same place. • Spatial and Temporal • Travel and Activities can be represented by a continuous path in the spatial and temporal dimensions. • This is a simple concept, but is very difficult to implement operationally. Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 3

  4. Starchild, HAPP and PDPTW • Starchild Model • Best previous model • Problems: • Model members of the household separately • Exhaustive enumeration and evaluation of all possible solutions • Discretizes temporal decisions • Does not consider vehicle or activity allocation • HAPP – Household Activity Pattern Problem • The Goal of HAPP is to create a travel schedule of a household that accomplishes a set of activities. • Avoid the problems of Starchild. Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 4

  5. Starchild, HAPP and PDPTW • PDPTW – Pickup and Delivery Problem with Time Windows • Well known Problem of scheduling pickups and deliveries. • Optimizes a utility function to get a set of interrelated paths for pickup and deliveries though the time and space continuum. • HAPP – Household Activity Pattern Problem • HAPP can be viewed as a modified version of PDPTW and can use the same algorithms for solving. • Optimize a utility function to get interrelated paths through the time and space continuum of a series of household members with a prescribed activity agenda and a stable of vehicles and ridesharing options. Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 5

  6. HAPP - Input Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 6

  7. HAPP - Input Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 7

  8. HAPP - Input Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 8

  9. HAPP – Case 1 • Case 1 • Each member of the household has exclusive unrestricted use of a vehicle • Any activity can be completed by any member of the household • PDPTW • The demand function and vehicle capacity are important to PDPTW. They are unimportant to HAPP, but can redefined as follows: Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 9

  10. HAPP – Case 1 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 10

  11. HAPP – Case 1 • Disutility function (Z) • By minimizing the disutility function, we are optimizing the schedule. There are many disutility functions to choose from. The basic components of the disutility function are: Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 11

  12. HAPP – Case 1 • Constraint Functions • Disutility Function • If u is an activity location, then there is a trip from u to some w • There are the same number of trips as back trips Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 12

  13. HAPP – Case 1 • Constraint Functions • Vehicle v will travel to at least 1 activity • Vehicle v will return home • If v travels from w to u it will also travel to the return destination of u Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 13

  14. HAPP – Case 1 • Constraint Functions • The time u starts + the time it takes to do activity u + the time it takes to get from u back home ≤ the time v gets home • If v goes from u to w, then the time u starts + the time it takes to do activity u + the time it takes to get from u to w ≤ the start time of w • If u is the first stop for vehicle v, then the start time + the time it takes to get from home to u ≤ the start time of u Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 14

  15. HAPP – Case 1 • Constraint Functions • If v goes from u to the end, then the start time of u + the time it takes to do activity u + the time to travel from u to home ≤ the end time • The start time of u is within bounds • The start time for v is within bounds Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 15

  16. HAPP – Case 1 • Constraint Functions • The finish time for vehicle v is within bounds • Moving onto another activity costs demand • Returning from an activity relieves demand Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 16

  17. HAPP – Case 1 • Constraint Functions • Moving from home to an activity costs demand • Demand starts at 0 can not be less than 0 and can not be more than D • Vehicle v either goes from u to w or not Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 17

  18. HAPP – Case 1 • Constraint Functions • The total cost of all trips can not be more than the budgeted cost • The total time vehicle v is on trips can not be more than the budgeted time • Vehicle v can not go from the beginning directly to the end Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 18

  19. HAPP – Case 1 • Constraint Functions • Vehicle v can not go from an activity u to the beginning • If u is an activity, vehicle v can not be finished after u • If v is finished, it can not go to another activity Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 19

  20. HAPP – Case 1 • Summary: • Disutility Function • Functions handling trip restrictions • Functions handling time restrictions • Functions handling demand restrictions • Functions handling overall cost and time • Functions handling start and stop positions Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 20

  21. HAPP – Case 1 • Example • 2 Person / Vehicle • S = [8, 1, 2] Durations • [ai,bi] = [8, 8.5; 10, 20; 12, 13] • [an+i, bn+i] = [17, 19; 10, 21; 12, 21] • [a0,b0] = [6, 20] • [a2n+1,b2n+1] = [6, 21] • Bc = 8 • Bt = 3.5 • Ds = 4 • Time & Cost Matrixes from activity to activity Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 21

  22. HAPP – Case 1 • Example • Disutility function • Minimize the cost + delay + extent of the travel day Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 22

  23. HAPP – Case 1 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 23

  24. HAPP – Case 2 • Case 1 • Unrealistic • Only certain people can perform some activities • Case 2 • Each member of the household has exclusive unrestricted use of a vehicle • Some activities can be completed by any member of the household • The remaining activities can be completed by a subset of the household members Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 24

  25. HAPP – Case 2 • Constraint Functions • This new constraint can be added with new vectors of what activities can not be performed by individual members • Thus only one constraint function need be added • If a member of the household can not perform w then there is no trip to w Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 25

  26. HAPP – Case 2 • Example • Same as Example 1 with the following added Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 26

  27. HAPP – Case 2 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 27

  28. HAPP – Case 3 • Case 2 • Better, but still unrealistic • Some members of the household should be allowed to stay home. • The disutility function should reflect the cost of leaving the house • Case 3 • Each member of the household has exclusive unrestricted use of a vehicle • Some activities can be completed by any member of the household • The remaining activities can be completed by a subset of the household members • A member of the household may perform no activities Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 28

  29. HAPP – Case 3 • Constraint Functions • Recall: • Vehicle v will travel to at least 1 activity • Vehicle v will return home • Replace with: Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 29

  30. HAPP – Case 3 • Example • Same as Example 1 with the following added • Ω = {null} • [ai,bi] = [8, 8.5; 6, 20; 12, 22] • Add 1 more term to the disutility function • Where K is the cost associated with leaving the house, in this case 100 was used Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 30

  31. HAPP – Case 3 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 31

  32. HAPP – Case 4 • Case 3 • Not everyone has unrestricted access to a vehicle • Case 4 • Each member of the household has access to a stable of vehicles • Some vehicles can be used by any member of te household • The remaining vehicles may be used by a subset of members • Some activities can be completed by any member of the household • The remaining activities can be completed by a subset of the household members • Some members of the household may perform no activities • Some vehicles may not be used Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 32

  33. HAPP – Case 4 • Decoupling Household Members and Vehicles • Simply need to add household members and their constraints • Household Members Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 33

  34. HAPP – Case 4 • Constraint Functions Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 34

  35. HAPP – Case 4 • Constraint Functions Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 35

  36. HAPP – Case 4 • Constraint Functions • If a household member goes from activity u to activity w then they take a vehicle • A household member must leave home in a vehicle Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 36

  37. HAPP – Case 4 • Example a • Same as Example 3 with the following added Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 37

  38. HAPP – Case 4 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 38

  39. HAPP – Case 4 • Example b • Same as example 4a with the following changed restrictions on who can perform activities and what vehicles can perform what activities Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 39

  40. HAPP – Case 4 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 40

  41. HAPP – Case 5 • Case 5 • General HAPP Case • Add Ridesharing • Each member of the household has access to a stable of vehicles • Some vehicles can be used by any member of te household • The remaining vehicles may be used by a subset of members • Some activities can be completed by any member of the household • The remaining activities can be completed by a subset of the household members • Some members of the household may perform no activities • Some vehicles may not be used Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 41

  42. HAPP – Case 5 • Adding Ridesharing • Ridesharing significantly changes the problem • The basic formulation (constraints) no longer applies • However, the structure remains the same and similar constraint functions can be used • All vehicles now must have passenger seats • Need to include picking up passengers (discretionary) and dropping off passengers (mandatory) Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 42

  43. HAPP – Case 5 • New Terms Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 43

  44. HAPP – Case 5 • Definitions of Terms Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 44

  45. HAPP – Case 5 • Categories of Constraint Functions • Vehicle Temporal • Household Member Temporal • Spatial Connectivity Constraints on Vehicles • Spatial Connectivity Constraints on Household Members • Capacity, Budget and Participation Constraints • Vehicle and Household Member Coupling Constraints Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 45

  46. HAPP – Case 5 • Vehicle Temporal Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 46

  47. HAPP – Case 5 • Household Member Temporal Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 47

  48. HAPP – Case 5 • Spatial Connectivity Constraints on Vehicles • Activities are performed by either the driver or a passenger • Drivers can perform passenger service activities • Passenger activities are performed on a passenger serve trip Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 48

  49. HAPP – Case 5 • Spatial Connectivity Constraints on Vehicles • Passengers may not perform passenger serve activities Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 49

  50. HAPP – Case 5 • Spatial Connectivity Constraints on Vehicles Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004 50

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