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 2 Jeremiah Jilk University of California, Irvine ICS 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. 3 Jeremiah Jilk University of California, Irvine ICS 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. 4 Jeremiah Jilk University of California, Irvine ICS 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. 5 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

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

HAPP - Input 8 Jeremiah Jilk University of California, Irvine ICS 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: 9 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 1 10 Jeremiah Jilk University of California, Irvine ICS 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: 11 Jeremiah Jilk University of California, Irvine ICS 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 12 Jeremiah Jilk University of California, Irvine ICS 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 13 Jeremiah Jilk University of California, Irvine ICS 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 14 Jeremiah Jilk University of California, Irvine ICS 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 15 Jeremiah Jilk University of California, Irvine ICS 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 16 Jeremiah Jilk University of California, Irvine ICS 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 17 Jeremiah Jilk University of California, Irvine ICS 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 18 Jeremiah Jilk University of California, Irvine ICS 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 19 Jeremiah Jilk University of California, Irvine ICS 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 20 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

Example 2 Person / Vehicle S = [8, 1, 2] Durations [a i,b i ] = [8, 8.5; 10, 20; 12, 13] [a n+i, b n+i ] = [17, 19; 10, 21; 12, 21] [a 0,b 0 ] = [6, 20] [a 2n+1,b 2n+1 ] = [6, 21] B c = 8 B t = 3.5 D s = 4 Time & Cost Matrixes from activity to activity HAPP – Case 1 21 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

HAPP – Case 1 23 Jeremiah Jilk University of California, Irvine ICS 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 24 Jeremiah Jilk University of California, Irvine ICS 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 25 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

HAPP – Case 2 27 Jeremiah Jilk University of California, Irvine ICS 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 28 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 3 29 Jeremiah Jilk University of California, Irvine ICS 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} [a i,b i ] = [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 30 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 3 31 Jeremiah Jilk University of California, Irvine ICS 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 32 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

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

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

HAPP – Case 4 36 Jeremiah Jilk University of California, Irvine ICS 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 37 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 4 38 Jeremiah Jilk University of California, Irvine ICS 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 39 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 4 40 Jeremiah Jilk University of California, Irvine ICS 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 41 Jeremiah Jilk University of California, Irvine ICS 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) 42 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

HAPP – Case 5 Definitions of Terms 44 Jeremiah Jilk University of California, Irvine ICS 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 45 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

HAPP – Case 5 Household Member Temporal 47 Jeremiah Jilk University of California, Irvine ICS 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 48 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

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

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

HAPP – Case 5 Spatial Connectivity Constraints on Household Members 51 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 5 Capacity, Budget and Participation Constraints 52 Jeremiah Jilk University of California, Irvine ICS 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 53 Jeremiah Jilk University of California, Irvine ICS 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 54 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004

HAPP – Case 5 55 Jeremiah Jilk University of California, Irvine ICS 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. 56 Jeremiah Jilk University of California, Irvine ICS 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 57 Jeremiah Jilk University of California, Irvine ICS 280, Spring 2004