household activity pattern problem

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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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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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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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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HAPP - Input

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HAPP - Input

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HAPP - Input

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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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HAPP – Case 1

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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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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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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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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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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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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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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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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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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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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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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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Example Disutility function

Minimize the cost + delay + extent of the travel day

HAPP – Case 1

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HAPP – Case 1

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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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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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HAPP – Case 2

Example Same as Example 1 with the following added

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HAPP – Case 2

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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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HAPP – Case 3

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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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HAPP – Case 3

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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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HAPP – Case 4

Decoupling Household Members and Vehicles Simply need to add household members and their

constraints

Household Members

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HAPP – Case 4

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HAPP – Case 4

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HAPP – Case 4

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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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HAPP – Case 4

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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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HAPP – Case 4

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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

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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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HAPP – Case 5

New Terms

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HAPP – Case 5

Definitions of Terms

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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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HAPP – Case 5

Vehicle Temporal

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HAPP – Case 5

Household Member Temporal

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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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HAPP – Case 5


Passengers may not perform passenger serve activities

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HAPP – Case 5


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HAPP – Case 5

Spatial Connectivity Constraints on Household Members

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HAPP – Case 5

Capacity, Budget and Participation Constraints

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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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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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HAPP – Case 5

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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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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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household activity pattern problem

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