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
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5 Cases

Conclusion
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
2
General Concepts

Activity Problem
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“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
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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
Starchild, HAPP and PDPTW

Starchild Model
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Best previous model
Problems:
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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
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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
Starchild, HAPP and PDPTW

PDPTW – Pickup and Delivery Problem with Time
Windows
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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
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
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
HAPP - Input
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
6
HAPP - Input
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
7
HAPP - Input
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
8
HAPP – Case 1
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Case 1
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Each member of the household has exclusive
unrestricted use of a vehicle
Any activity can be completed by any member of the
household
PDPTW
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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
HAPP – Case 1
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
10
HAPP – Case 1
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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
HAPP – Case 1
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Constraint Functions
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Disutility Function
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If u is an activity location, then there is a trip from u to
some w
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There are the same number of trips as back trips
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
12
HAPP – Case 1
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Constraint Functions
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Vehicle v will travel to at least 1 activity
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Vehicle v will return home
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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
HAPP – Case 1
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Constraint Functions
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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
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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
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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
HAPP – Case 1
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Constraint Functions
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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
HAPP – Case 1

Constraint Functions

The finish time for vehicle v is within bounds
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Moving onto another activity costs demand
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Returning from an activity relieves demand
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
16
HAPP – Case 1
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Constraint Functions
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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
HAPP – Case 1

Constraint Functions
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The total cost of all trips can not be more than the
budgeted cost
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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
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
HAPP – Case 1

Summary:
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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
HAPP – Case 1
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Example
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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
HAPP – Case 1

Example
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Disutility function
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Minimize the cost + delay + extent of the travel day
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
22
HAPP – Case 1
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
23
HAPP – Case 2
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Case 1
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Unrealistic
Only certain people can perform some activities
Case 2
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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
HAPP – Case 2
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Constraint Functions
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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
HAPP – Case 2

Example

Same as Example 1 with the following added
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
26
HAPP – Case 2
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
27
HAPP – Case 3
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Case 2
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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
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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
HAPP – Case 3

Constraint Functions
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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
HAPP – Case 3
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Example
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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
HAPP – Case 3
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
31
HAPP – Case 4
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Case 3
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Not everyone has unrestricted access to a vehicle
Case 4
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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
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
HAPP – Case 4

Constraint Functions
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
34
HAPP – Case 4

Constraint Functions
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
35
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
HAPP – Case 4

Example a

Same as Example 3 with the following added
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
37
HAPP – Case 4
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
38
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
HAPP – Case 4
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
40
HAPP – Case 5
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Case 5
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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
HAPP – Case 5
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Adding Ridesharing
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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
HAPP – Case 5

New Terms
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
43
HAPP – Case 5

Definitions of Terms
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
44
HAPP – Case 5
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Categories of Constraint Functions
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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
HAPP – Case 5

Vehicle Temporal
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
46
HAPP – Case 5

Household Member Temporal
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
47
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
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
HAPP – Case 5

Spatial Connectivity Constraints on Vehicles
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
50
HAPP – Case 5

Spatial Connectivity Constraints on Household
Members
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
51
HAPP – Case 5

Capacity, Budget and Participation Constraints
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
52
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
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
53
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
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
54
HAPP – Case 5
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
55
HAPP

Runtime
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Cases 1 – 4 were run using a commercially available
software program GAMS ZOOM.
Case 5 was solved using GAMS ZOOM on the nonridesharing 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.
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
56
Conclusion

Utility Maximization

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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
Jeremiah Jilk
University of California, Irvine
ICS 280, Spring 2004
57