Household Activity Pattern Problem Paper by: W. W. Recker. Presented by: Jeremiah Jilk May 26, 2004...
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Transcript of Household Activity Pattern Problem Paper by: W. W. Recker. Presented by: Jeremiah Jilk May 26, 2004...
Household Activity Pattern Problem
Paper by:W. W. Recker.
Presented by:Jeremiah Jilk
May 26, 2004
Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Overview
General Concepts
Starchild, HAPP and PDPTW
5 Cases
Conclusion
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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.
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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.
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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.
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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:
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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:
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Constraint Functions
The finish time for vehicle v is within bounds
Moving onto another activity costs demand
Returning from an activity relieves demand
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Example Disutility function
Minimize the cost + delay + extent of the travel day
HAPP – Case 1
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 2
Example Same as Example 1 with the following added
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 3
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Constraint Functions Recall:
Vehicle v will travel to at least 1 activity
Vehicle v will return home
Replace with:
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 4
Decoupling Household Members and Vehicles Simply need to add household members and their
constraints
Household Members
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 4
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Constraint Functions
HAPP – Case 4
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Constraint Functions
HAPP – Case 4
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
HAPP – Case 4
Example a Same as Example 3 with the following added
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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)
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Definitions of Terms
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Household Member Temporal
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
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
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Spatial Connectivity Constraints on Vehicles
Passengers may not perform passenger serve activities
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Spatial Connectivity Constraints on Vehicles
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Spatial Connectivity Constraints on Household Members
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Capacity, Budget and Participation Constraints
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Vehicle and Household Member Coupling Constraints
Only one person can travel to any activity in a particular seat
Drivers and passengers can be transferred at home
The departure time of a household member must coincide with the departure of the vehicle they are in
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP – Case 5
Example Same as example 4b with an increase in duration of
activity 2 to allow for a viable ridesharing window Capacity of vehicles is sufficient
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
HAPP
Runtime Cases 1 – 4 were run using a commercially available
software program GAMS ZOOM. Case 5 was solved using GAMS ZOOM on the non-
ridesharing problem (Case 4) and then that solution was used to generate viable ridesharing options. These options were then optimized temporally. The best of these was then selected.
Case 5 example took 3.5 minutes on a 50 Mhz machine.
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004
Conclusion
Utility Maximization It is assumed that activities are chosen and
scheduled base on a principle utility maximization HAPP provides a mathematical framework similar to
the well studied PDPTW problem. The disutility function can be customized to fit specific
needs and will allow for different solutions This framework may contain redundancy and/or
hidden inconsistency that may need to be worked out This paper is an initial attempt to provide direction for
further research
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Jeremiah JilkUniversity of California, IrvineICS 280, Spring 2004