Tradeoffs among Planned vs Performed Activity Patterns, In press by Transpometrica B:Transport Dynamics

Tradeoffs among Planned vs. Performed Activity Patterns Mahdieh Allahviranloo1, Will Recker2, Harry J.P. Timmermans3 ‘1

Department of Civil Engineering, The City College of New York – CUNY Steinman Hall 134, 160 Convent Avenue, New York, NY 10031, USA

2

Department of Civil and Environmental Engineering, Institute of Transportation Studies University of California, Irvine, Irvine, CA 92697-3600, USA 3

Urban Planning Group, Eindhoven University of Technology P.O. Box 513, Vertigo 8.18, 5600 MB, Eindhoven, Netherlands

1

Abstract This paper focuses on the development of a methodology to identify the latent factors leading to changes in the planned itineraries of travelers that result in their actual activity patterns. Specifically, we propose a way to utilize patterns of activities established by individuals across multiple days to generate possible alternative actions by these individuals when faced with conditions that produce a discrepancy between performed and planned patterns on a particular day. The choice alternatives, which are unobserved, are inferred by rules applied to comprehensive multiday data collected in Belgium, consisting of information regarding planned activity itineraries, performed activity/travel diaries, and demographics of travelers. These data are utilized to analyze and explore the underlying reasons preventing individuals from performing their planned activities on a given day, and to identify the influential parameters that lead individuals to trade their planned patterns with those actually performed. Using multiday data, we generate all possible combinations of categories of activities—mandatory, maintenance, discretionary, and pickup/drop off activities—that can form patterns for individuals. Under the assumption that the performed patterns have the closest utility to the planned patterns, we estimate the latent factors that influence travelers’ time use behavior using a multinomial probit choice structure in which the covariance structure of the choice alternatives is specified in terms of the overlap in activities. We further identify the “costs’ associated with making changes in planned agenda (replacing, inserting or deleting an activity). These penalty values are estimated using ‘Parallel Genetic Algorithm’, where the fitness function is the likelihood function estimated under the multinomial choice model structure. The results show that individuals’ mobility decisions related to mandatory activities are more robust than those associated with their nonmandatory counterparts. Keywords: Activity trade off, pattern robustness, agenda reliability, parallel genetic algorithm

1. Introduction Humans, as intelligent agents, routinely participate in activities and, for the most part, schedule them based on a plan that they have in their minds prior to the start of the day, whether it be going to work in the morning, or visiting a friend in late afternoon, or just staying at home for the entire day and relaxing. Addressing such questions as: are travelers willing to reschedule their departure time to work because sharing a ride with a friend would benefit their out-of-pocket cost or would they rather start working early and pay more by driving alone?; or, is the disutility of eliminating a social activity from the agenda equivalent to that of eliminating a grocery shopping activity? can disclose many latent parameters influencing the mobility decisions of travelers, and ultimately assist decision makers in selecting more effective tools to improve system operation. The shuffling of travel and activity participation decisions in response either to unforeseen personal preferences and constraints, or to policy-driven, environmental constraints is manifest in the activity/travel scheduling decisions that are a product of the elasticity of choices of travelers to the set of parameters influencing their perceived utility gained from participating in a set of activities and the travel required to access those activities. This paper quantifies the decision process that results in the adaptation of activity participation behavior of a population in response to changes in the circumstances of planned activities. Modeling human scheduling decisions that result in daily activity-travel patterns poses a complex problem that is influenced by multiple factors. Such factors as physical barriers, institutional constraints, family responsibilities, personal preferences, etc., may force an individual to pursue a distinctively different 2

activity pattern from what had been planned at the beginning of the day (or, even earlier). The rich literature on activity-based and tour-based models ranges from using complex econometric models to capture human behavior as a function of demographics and the built environment—works of Bhat (Bhat et al., 2015, 2004; Paleti et al., 2009) and Ben-Akiva (Ben-Akiva and Bowman, 1998) are good examples of these studies— to comprehensive simulation models—e.g., TRANSIM (Smith et al., 1995), FAMOS (Pendyala et al., 2005), ALBATROSS (Arentze et al., 2000), ADAPTS (Auld and Mohammadian, 2012), CUSTOM (Habib et al., 2016), etc.—to constrained optimization models—HAPP (Recker, 1995) and its extensions. Significant research effort has been devoted to estimating the types of activities forming an individual’s travel/activity agenda. SCHEDULER, as one of the early models in this area, is an activity generator model (Garling et al., 1994). In the SCHEDULER framework, it is assumed that individuals have a mental calendar of the daily activities; activities are added to the agenda based on their priority and duration; additionally, spatiotemporal constraints of activities are stored in cognitive maps. If a conflict exists in the mental map of activities of individuals, either the sequence of activity participation is changed or the activity is replaced with a lower priority activity. Kitamura and his colleagues used a sequential approach to generate synthetic household daily activities (Kitamura et al., 1997). Considering the record of activity generation until time ‘T’, activities are added one-by-one to the agenda. Accordingly, the daily activity pattern of the individual is comprised of series of trips and activities where, at each step in the sequence, the individual first selects activity type, and then decides about the activity duration and location. In their analysis, Monte Carlo simulation is used to generate activity patterns of individuals (Kitamura et al., 2000). Meister and Axhausen use a genetic algorithm to generate daily activities (Meister et al., 2005), where the fitness function includes utilities at both individual- and household-levels. The utility at the individual-level is defined as the number and the duration of individual activities, whereas the utility at the household level is specified as the utility of joint activities. It is assumed that each individual has a mental map and that there exists an activity repertoire about the daily activity pattern that includes all performed activities and their locations. Normally, the mental map has more activities than does the repertoire. The model chooses activities and inserts them into the agenda. In the genetic algorithm, feasible household schedules with a constant population size are generated. Then, crossover and mutation operations are applied to the schedules with high utility to search for the optimum. The CHASE (Computerized Household Activity Scheduling Elicitor) Survey program, developed by Doherty and Miller (Doherty and Miller, 2000), was used as a survey instrument to elicit relationships between planned and performed activity patterns of households. Individuals were asked to enter into computers both their planned activities and their actual activities over the course of a week. Activity duration, scheduling, travel patterns and time horizon in individuals’ decisions are the main outputs of the program. The results of the CHASE survey have been used by a number of researchers. For example, Auld used the CHASE database to propose different strategies to resolve conflicts in a rule-based scheduling process (Auld et al., 2009). The strategies include moving, modifying or deleting original or conflicting activities in the CHASE scheduling process database for Toronto 2002-2003. REACT!, developed by Lee and McNally, automated CHASE’s recording of an individual’s travel diary (Lee and McNally, 2003). Using REACT! respondents document their activities in three steps: initial interview, pre-travel interview and post-travel interview. Study results showed that individuals tend to schedule their daily activities sequentially rather than simultaneously. Also, they found that shorter activities are more likely to be opportunistically added to a schedule while longer activities are normally planned in advance. The TASHA (Travel Activity Scheduler for Household Agents) micro-simulator is an operational computational process 3

model that generates, schedules, and executes activities at both the household and individual levels (Miller and Roorda, 2003). The model generates activities in nine categories (business work, primary work, secondary work, return home from work, school, joint and individual shopping, and joint and individual other activities). There are certain rules available for activity scheduling in the TASHA software, such as: add, delete, and shift for new activities. In a practical application, Roorda used TASHA to study the effects of the number of vehicles on activity patterns of household members (Roorda et al., 2009). Not surprisingly, the results indicate that with fewer vehicles in the household more scheduling conflicts arise. Kang and Scott, use the first phase of the Toronto Travel-Activity Panel Survey (TTAPS), collected using CHASE survey, to assess the variability in day to day activity patterns and the impact of joint and solo activities in the formation of activity patterns(Kang and Scott, 2010). In ADAPTS (Auld and Mohammadian, 2012), activities of household members are generated and scheduled using simulation methods. Arentze and Timmermans use a different approach to deal with activity-based models (Arentze and Timmermans, 2009). Their basic concept is that individuals participate in activities in order to fulfill needs accumulated over time. In their procedure, a threshold value for the “utility-of-time” is introduced, in which activities are added to the agenda if the resultant utility is greater than the threshold. Activities can have either positive or negative effects on corresponding needs for other activities—some activities can fulfill the needs for other activities, or can create additional needs. Based on the duration of activities and the need for the activity—at either household level or individual level—the frequency of different activities in a multi-day agenda is calculated. Constrained by a time budget, individuals compete to fulfill the household needs and to improve the total utility. Dharmowijoyo et al, conduct a comprehensive survey to study travel behavior, activity participation, physical activity habits and quality of life in Bandung Metropolitan Area of Indonesia. The study evaluates the impacts of beliefs, emotions, gender, socioeconomic factors and access to motorized transportation on travel behavior or participants in the study(Dharmowijoyo et al., 2015). A study conducted by Schwanen et al.., in Ohio, USA, shows the fixity and flexibility of different types of activities in the agenda of men and women. The authors, collect activity data with detailed information on the type of activity and frequency of the activities. The result indicate the correlation in the degree of fixity of activities and attributes of the activities (duration, location, companion, etc.) and demographics of individuals, (Schwanen et al., 2008). Meloni et al., use N-tobit model to assess the impacts of the exogenous variables and demographics of travelers on time allocation to discretionary activities, the results indicates that the number of trips and the duration of mandatory trips are influential in allocation of time to discretionary trips (Meloni et al., 2004). Keeping in mind the broad scope of literature in the field, the main focus of this paper is to investigate the latent factors leading to changes in the planned itineraries of travelers that result in their actual activity patterns, therefore the literature presented here on the subject of activitybased model is not an exhaustive list. Specifically, in this paper, we analyze the underlying reasons creating the discrepancy between performed and planned patterns. Comprehensive multiday data were collected in Belgium, consisting of information regarding planned activity itineraries, performed activity/travel diaries, and demographics of travelers. The processed dataset comprises activity patterns of 1,605 individuals over multiple days, adding up to total of 9,759 patterns. Using this rich dataset, this paper addresses three main objectives: 1- Analyze and explore the underlying reasons preventing individuals from performing their planned activities on a given day; this objective is addressed by integrating, querying and analyzing the survey data.

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2- Identify the influential parameters that lead individuals to trade their planned patterns with those actually performed. Using multiday data, we generate all possible combinations of categories of activities—mandatory, maintenance, discretionary, and pickup/drop off activities—that can form patterns for individuals. Under the assumption that the performed patterns have the closest utility to the planned patterns, we estimate the latent factors that influence travelers’ time use behavior. 3- Identify the ‘penalties’1 associated with replacing a planned activity in the agenda with the one actually performed, inserting an unplanned activity in the agenda, or deleting a planned activity from the agenda using ‘Sequence Alignment Technique’ and measuring the dissimilarity between planned and performed patterns. These penalty values are estimated using ‘Parallel Genetic Algorithm’, where the fitness function is the likelihood function estimated under the multinomial choice model structure. The current paper presents a methodology to quantify the penalty values associated with making adjustments in the planned activity itineraries in response to many influencing factors. Such adjustments are restricted to: 1) changes in the duration or start time of the activity, 2) its possible elimination, and 3) addition of different types of activities. Despite the importance of the concept from a travel behavior and regional planning perspective, to the best of authors’ knowledge, this is the first methodological paper focused on this subject. The paper is outlined as follows: section 2 describes the empirical data utilized in this study, in section 3, we discuss about the assumptions and procedure that we follow to generate possible combinations of activity patterns. Section 4 explains the methodology used to compute the tradeoffs between planed and performed patterns, followed by section 5, which specifically looks at the penalty values associated with insertion, deletion, or substitution of an activity in the agenda with other activities. Finally, section 6 concludes the paper by discussing the outcomes and stating the closing remarks.

2. Empirical Data In a comprehensive survey conducted during 2009 in Belgium, respondents were asked to report detailed information about: their personal and household characteristics, job status, residential information, vehicle/motor/bike ownership, public transportation membership and benefits and etc. The share of male participants in the survey is 48%, and 54% of the participants are employed. Weekdays account for 73% of the data and 27% belong to weekends. The share of students and participants in the age range of [6 to 18] were 5% and 3%, respectively, in the final dataset. Number of days that people have participated in survey varies in the range of 1 to 10 days, TABLE1 shows the share of surveyed days across in the dataset. TABLE1. Percentage of Number of Surveyed Days

# of days

1

2

3

4

5

6

7

8

9

10

Percentage

4.92

3.68

3.99

4.30

6.67

15.08

50.59

9.41

1.06

0.31

FIGURE 1 provides information regarding age, income level, and household size of participants.

1

The main assumption in the paper is that individuals try to hold on to their planned activity pattern as much as possible, under all the environmental or personal constraints that might impact their choices. We assume individuals penalize any small disruption in their agenda. However these penalties depending on the type of the activity, duration and start time of the activity vary. The penalty of replacing a work activity with a shopping activity is different form penalty of replacing a work activity with in-home activity. Later in the paper we discuss this concept more in depth.

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FIGURE 1. Boxplots illustrating income, household size, and age in the sample population

During the survey, any future events that might change residential status or employment status of participants were also questioned. In this survey, very detailed information regarding individuals’ daily activity patterns, e.g., whether or not an activity was planned before it was executed, if it was performed jointly with other individuals—including such information about the companionship as age, gender and relation—is provided in the diary. In the case of failure to perform the activity as it was planned, or adding an unplanned activity in the agenda, users were asked to indicate the reason (from the list of available reasons provided in the survey. The set of 10 reasons for participation in activities without prior planning and 13 reasons for elimination of a planned activity from the agenda were listed in the survey (TABLE2). TABLE2. Reasons to Modify Activity Agenda Why was the activity carried out, but not planned? P1: Activity scheduled that day without prior planning P2: This was an impulsive activity P3: Weather conditions (ex: going to mall because of heavy rain) P4: Change in duration of other activities, previous activities were shorter than what it was expected P5: Arrived too early to the activity P6: Activity was added as the influence of other household members P7: Activity was added as the influence of other people not in the household P8: Other reasons P10: Activity was planned but the respondents forgot to mention the activity in the planned agenda

Why activity was planned but not carried out? U1: Not feeling the obligation to participate in the activity U2: Miscalculation in closing hours of the activity U3: Weather conditions U4: Vehicle malfunction U5: Delays in trip, unexpected stops in the trips U6: Forgot to perform the activity U7: Activity was performed by someone else U8: Previous activity lasted longer than expected U9: Unexpected important activities were added to the agenda U10: Activity was eliminated as the influence of other household members U11: Activity was eliminated as the influence of others not household members U12: Other reasons U13: Error in planning

As indicated in TABLE2, activities can be added to or deleted from the agenda without prior planning due to many reasons such as impulse, weather conditions, influence of activity patterns of other people, miscalculation in the trip duration or operating hours of the destination, situational factors, or simply lack 6

of motivation to participate in the activity. Such additions/deletions create disparity between planned and performed activity patterns. While it is well beyond the scope of this research to offer substantive analysis regarding the likelihood of such random events, we argue that, regardless of the nature of the situational (or impulsive) factors that precipitate a change in plans that leads to an insertion/deletion of activities, the reaction/adjustment of the individual is to try, as much as possible, to maintain the essential features of the planned activity pattern; i.e.., the beginning and end of the travel day, durations of activities, and the total time spent traveling. Specifically, in the following sections, we develop models to predict the preferred “global” responses to such events based on the patterns exhibited by the individual on other days in the sampling period, and/or by other individuals in the sample. In order to address the particular trade-offs between the various potential adjustments to the planned activity patterns, these models are followed by a detailed analysis of the “local” adaptations to the schedule based on adjustments (insertions/deletions/substitutions of activities) over 15-minute time segments that are required in order to adapt to these unanticipated events. As in the latter models, the underlying assumption is that, subject to the adjustments required, the executed pattern is as close as possible to that planned. However, in this case, rather than using the Euclidean distance metric applied to a series of global activity pattern parameters as the basis for proximity, we use sequence alignment operations based on 15-minute segmentations of the candidate patterns. These results help to clarify the importance of the various trade-offs relative both to type of activity and between activity duration and travel. For analysis purposes in this paper, out-of-home activities were classified into 4 general categories as: “mandatory”, “maintenance”, “discretionary”, and “pickup/drop off”. TABLE3 states the details of different activity categories used in this paper, together with their share of out-of-home activities pursued by respondents during the day. The definition of activities groups and the classification of activities to different groups, and the number of classes in the literature normally depend on the nature of the analysis, for example, Akar et al, categorize activities to three groups of subsistence (work-related) activities, maintenance activities (performed to satisfy the household and personal or biological needs) and leisure activities (performed to fulfill cultural and psychological needs) to study the location choice for discretionary activities (Akar et al., 2011). TABLE3. Descriptions of different activity categories Categories

Descriptions

Mandatory

Work and work related out of home activities School activity: education and training activity Grocery shopping, home chores and maintenance 2 Personal: Visiting family/friends, doctor visit, workout and sports, shopping for clothing and non-maintenance items, bank and administrative visits, pharmacy visit. Recreational: Social activity, leisure activity, walking, sightseeing, dine out. Other activity: Picking up someone, dropping someone off

Maintenance Discretionary

Pickup-drop off

Share of activity category pursued by respondents in population (%) 25 12 52

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For each activity category, a thorough analysis of the reasons for agenda modification was performed and the results are stated in TABLE4 and TABLE5. According to the information provided in these tables, across all activity types more than 78% of the activities were performed as they were planned, and for the 2

In this study, maintenance category represents set of activities that serve household and can be executed by any household me mber. Maintenance activities have higher priority compared to discretionary activities. Such activities as grocery shopping, refilling tank of the vehicle, etc. are categorized as maintenance. Discretionary activities are more flexible in time and location even they can be rescheduled; however, discretionary activities are more personal and normally are pursued by specific individuals. Such activities as socializing, or physical activity belong to this category.

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unperformed activities, virtually no resourceful information is provided. Most of the inconsistencies between performed and planned activities are caused by adding a new activity to the agenda. As stated in TABLE5, 44% of the maintenance activities, 41% of discretionary activities, and 33% of pickup/drop off activities were added to the agenda without previous planning, indicating that the number of performed activities exceeds the number of those actually planned for completion. Noteworthy that the definition and categorization of the activities impacts the outcomes of the analysis. The results presented in this paper are valid for this dataset under the assumptions made in this paper. However, as the main goal of the current work is to present a methodology to quantify the penalties associated with adjusting planned activity patterns in response to a variety of stimuli, the categorizations used in this paper represent only a single application of the methodology, and is intended to demonstrate the method.

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TABLE4. Share of different reasons for not performing a preplanned activity Planned Activity Mandatory

Performance Percentage of performed activities which were planned Percentage of activities deleted from the agenda categorized according to different reasons

Maintenance

Percentage of activities deleted from the agenda categorized without mentioning the reason Percentage of performed activities which were planned Percentage of activities deleted from the agenda categorized according to different reasons

Discretionary

Percentage of activities deleted from the agenda categorized without mentioning the reason Percentage of performed activities which were planned Percentage of activities deleted from the agenda categorized according to different reasons

Pickup/drop off

Percentage of activities deleted from the agenda categorized without mentioning the reason Percentage of performed activities which were planned Percentage of activities deleted from the agenda categorized according to different reasons

Percentage of activities deleted from the agenda categorized without mentioning the reason

9

Percentage 83.29 U1 0.16 U2 0.02 U3 0.14 U4 0.03 U5 0.06 U6 0.02 U7 0.21 U8 0.50 U9 0.50 U10 0.06 U11 0.19 U12 0.89 U13 0.14 13.79 78.07 U1 0.70 U2 0.13 U3 0.38 U4 0.19 U5 0.00 U6 0.19 U7 1.60 U8 1.15 U9 0.45 U10 0.45 U11 0.26 U12 1.60 U13 1.02 13.81 79.68 U1 1.01 U2 0.13 U3 1.05 U4 0.02 U5 0.03 U6 0.10 U7 0.35 U8 0.73 U9 0.78 U10 0.27 U11 0.62 U12 1.94 U13 0.35 12.94 82.80 U1 0.08 U2 0.04 U3 0.15 U4 0.00 U5 0.04 U6 0.00 U7 2.67 U8 0.39 U9 0.50 U10 0.31 U11 0.31 U12 1.02 U13 0.15 11.54

TABLE5. Share of different reasons for performing an unplanned activity Performed activity Mandatory

Maintenance

Flexible (Discretionary)

Pickup/drop off

Performance Percentage of performed activities which were planned Percentage of performed activities that were not previously planned according to different reasons

Percentage of performed activities that were not previously planned without mentioning the reason Percentage of performed activities which were planned Percentage of performed activities that were not previously planned according to different reasons

Percentage of performed activities that were not previously planned without mentioning the reason Percentage of performed activities which were planned Percentage of performed activities that were not previously planned according to different reasons

No information provided Percentage of performed activities which were planned Percentage of performed activities that were not previously planned according to different reasons

Percentage of performed activities that were not previously planned without mentioning the reason

Percentage 74.97 P1 2.53 P2 0.49 P3 0.29 P4 0.63 P5 0.12 P6 0.26 P7 0.73 P8 2.50 P10 1.89 15.59 56.00 P1 P2 P3 P4 P5 P6 P7 P8 P10 18.52 58.93 P1 P2 P3 P4 P5 P6 P7 P8 P10 18.65 67.47 P1 P2 P3 P4 P5 P6 P7 P8 P10

11.09 2.32 0.40 0.84 0.13 2.38 0.86 4.90 2.56

6.51 4.08 0.68 0.83 0.12 0.81 1.53 5.66 2.21

4.44 1.01 0.69 0.72 0.12 2.89 2.71 3.66 3.00

13.28

Based on the 4 categories of out-of-home activities, as well as a general category for in-home activities (de facto, all patterns must include time spent at home), we generate 16 possible combinations of patterns of activities comprising the agenda that conceivably could reflect the individuals’ participation in these distinct activity groupings, as illustrated in TABLE6.3

3

Note that the order of the activity sequences in each of these possible patterns is arbitrary, as shown, and that other factors required to establish each activity pattern (e.g., sequencing, start time, duration, etc.) associated with each agenda are determined by further analyses using the multiday data.

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TABLE6. Descriptions of Sixteen Categories of Activity Patterns Pattern Type of Out of home activities 1. H* No out of home activity 2. H,M Only mandatory activities 3. H,N Only maintenance activities 4. H,D Only discretionary activities 5. H,K Only pickup/drop off activities 6. H,M,N Both mandatory and maintenance activities 7. H,M,D Both mandatory and discretionary activities 8. H,M,K Both mandatory and pickup/drop off activities 9. H,N,D Both maintenance and discretionary activities 10. H,N,K Both maintenance and pickup/drop off activities 11. H,D,K Both discretionary and pickup/drop off activities 12. H,M,N,D Mandatory, maintenance and discretionary activities 13. H,M,N,K Mandatory, maintenance and pickup/ drop off activities 14. H,M,D,K Mandatory, discretionary and pickup/ drop off activities 15. H,D,K,N Discretionary, maintenance and pickup/ drop off activities 16. H,M,N,D,K Mandatory, maintenance, discretionary and pickup/ drop off activities *H: represents in-home activity, M: represents mandatory activity, N: represents maintenance activity, F: represents flexible activity, K: represents pickup/drop off activity

A confusion matrix between planned and performed activity agenda is presented in TABLE7. According to this table, 56.22% of activity patterns were performed as they were planned. The highest share of the planned patterns in the data set belongs to pattern 3 (31%), which includes only one or more maintenance activities in the agenda. In the observed patterns, pattern type 3, 16 and 6 have the highest shares, which respectively correspond to inclusion of {maintenance}, {mandatory, maintenance, discretionary, and pickup/drop off}, and {maintenance, mandatory} activities in the agenda. TABLE7. Confusion matrix on planned and performed activity inclusions in the agenda (%)

Planned Patterns

Performed Patterns 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Sum

1

8.6

0.1

0.5

0.1

0.5

2.7

0.3

0.1

0.0

0.1

0.2

0.0

0.3

0.0

0.0

1.2

15

2

0.2

1.0

0.3

0.0

0.0

0.1

0.0

0.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.2

3

3

0.8

1.6

18.7

0.2

0.1

2.0

0.1

4.2

0.1

0.8

0.3

0.0

0.1

0.3

0.0

1.9

31

4

0.0

0.0

0.2

0.8

0.0

0.0

0.1

0.0

0.1

0.3

0.0

0.0

0.0

0.1

0.0

0.1

2

5

0.3

0.1

0.0

0.0

0.6

0.1

0.0

0.0

0.0

0.0

0.1

0.0

0.0

0.0

0.0

0.0

1

6

1.4

0.1

0.9

0.0

0.6

8.7

0.1

0.2

0.0

0.1

1.2

0.0

0.5

0.0

0.1

0.2

14

7

0.2

0.0

0.0

0.1

0.0

0.1

1.6

0.0

0.0

0.1

0.0

0.1

0.4

0.0

0.1

0.0

3

8

0.1

0.3

0.5

0.0

0.1

0.6

0.0

3.1

0.0

0.1

0.3

0.0

0.0

0.2

0.0

0.1

5

9

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.0

0.3

0.0

0.0

0.0

0.0

0.1

0.0

0.0

1

10

0.0

0.0

0.3

0.1

0.0

0.1

0.1

0.1

0.3

1.9

0.0

0.1

0.3

0.7

0.1

0.1

4

11

0.0

0.0

0.1

0.0

0.1

0.2

0.0

0.1

0.0

0.0

0.7

0.0

0.0

0.0

0.1

0.0

1

12

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.0

0.0

0.0

0.0

0.2

0.0

0.0

0.0

0.0

0

13

0.1

0.0

0.0

0.0

0.0

0.2

0.3

0.0

0.0

0.2

0.1

0.2

1.5

0.1

0.3

0.0

3

14

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.1

0.1

0.0

0.0

0.1

0.6

0.0

0.0

1

15

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.1

0.1

0.2

0.0

0

16

0.5

0.7

4.3

0.1

0.0

0.3

0.1

0.6

0.1

0.3

0.1

0.0

0.1

0.1

0.0

7.6

15

Sum

12

4

26

1

2

15

3

9

1

4

3

1

3

2

1

12

Although 54% of participants in this survey are employed, according to TABLE7, only 49% of performed patterns and 44% of planned patterns contain mandatory activities. This might be due two reasons: (1) in this analysis we are only considering out of home activities. Therefore, if a mandatory activity is being 11

conducted at home it will be considered as in-home activity; (2) Only 7114 out of 9759 patterns were recorded during weekdays, and the remaining 2645 patterns were recorded during weekends where most likely do not include mandatory activity. The trip/activity diary table was complemented with a planning table wherein detailed information regarding type of planned activities, activity duration, companionship, transportation mode, planned trip duration, and etc. are reported by the individuals. Prior to analysis, a preprocessing step, including cleaning both diary and planning data, is implemented. The details are as follows: 1- Consistency of activity location and activity type in dataset is checked. 2- Trips and activities with missing information are excluded from the analysis. 3- Activities longer than 24 hours are excluded from the data. 4- Simultaneous or logically infeasible activities are excluded from the diary data. 5- Only trip diaries with corresponding planning information for the same individual on the same day, are included in the dataset. 6- Trips of children younger than 6 years of age are excluded from dataset. The final dataset comprises 9,759 daily patterns of 1605 individuals, belonging to 1,528 households.

3. Generation of Alternative Patterns The key assumption throughout this paper is that the planned patterns are the most desirable (i.e., offer the greatest utility) patterns to travelers; however, due to some unpredictable events (not known or forecast at the time of the planning), individuals may alter their planned patterns leading to patterns actually performed. The question here is ‘what would be the other alternative patterns that individuals could have rationally chosen’? This question is being answered with the help of the multiday data and some rational assumptions. Using the reported multiday activity patterns for each individual, such pattern attributes as: activity order, duration and scheduling—all being key to specifying the activity patterns beyond the simple inclusion of the associated activities in the individual’s agenda—are constructed for each of the 16 possible patterns based on the following rules: Rule 1: If the pattern has been performed by the individual on other days, we use the attributes of the performed pattern, (e.g., person’s Monday pattern includes a work and recreational activity so we use the attributes of his/her revealed Monday pattern for pattern 7 in TABLE6). Rule 2: If a pattern combination has not been performed by the individual on any other day—for example, in none of the survey days did the person participate in all 4 activities (pattern 16 of TABLE6) —but we have data regarding the individual’s participation in each of these activities singularly, we use the attributes of each of these activities (arrival time, duration, and travel distance) and generate the most likely pattern based on an aggregation of the singular events. Rule 3: If, in the multiday data, the person has no record of participation in an activity associated with one of the sixteen possible combinations (e.g., the person has never performed pickup/drop off activities during survey days), we use population statistics to generate that pattern’s attributes.

12

FIGURE 2 illustrates the details of each step used to generate possible patterns and activity sequencing for each individual in the dataset. Generate all possible sequences of 4 out of home activity categories (total of 16 patterns)

Update the average duration of the activity, earliest departure time from home, latest return time to home and total time spent on travel using population data

Check if person has participated in specific activity pattern during the survey days?

No

Yes Update the average duration of each activity in the agenda, earliest departure time from home, latest return time to home, and total time spent on travel based on multiday activity data for the individual

Update terms in the utility function of each activity pattern of 16 possible patterns: For observed and planned pattern, update the terms using the data If the pattern was not observed in the survey days, estimate the attributes of activities in the pattern using the activity statistics in multiday data

Estimate the parameters of each term in utility function associated to each activity pattern using Multinomial logit models

FIGURE 2. Overall analysis framework to generate patterns and infer pattern utility

4. Factors Influential in Tradeoffs between Planned and Performed Patterns An objective of the current research is to identify the characteristics (factors) of an activity pattern that influence an individual’s decisions in terms of replacing a desired set of activities with those that constitute the observed pattern. Our fundamental working hypothesis is that, in the event that the planned activity pattern of the individual (assumed most desirable under conditions existing on the occasion of planning) is modified in the actual (observed/performed) pattern, the performed pattern is selected such that it is the second most desirable pattern out of the other possible patterns that they could have pursued. It should be noted that here we compare the entire patterns as a single, comprehensive, entity, whereas in the next section, we estimate the penalties associated to insertion/deletion or substitution of each activity type in the agenda. We note that, despite their similarities, these two sections are completely independent from the perspective of analysis. In order to identify the influential parameters leading individuals to trade 13

their planned patterns with those actually performed, a Multinomial Probit choice model is used 4, where the model parameters are the relative differences of the attributes for each of the 16 generated patterns from those of the planned pattern. The attributes of the pattern employed in the model are: earliest departure time from home, latest return time to home, total travel time, and duration of each activity category, and the utility is defined as Eq.1.

UP

pt pl

 0pt   s Ts pt  Ts pl   r Tr pt  Tr pl  t Tt pt  Tt pl   M DurMpt  DurMpl

  N DurNpt  DurNp   D DurDpt  DurDpl   K DurKpt  DurKpl  

Eq.1

pt pl

where:

UP

pt pl

: is the utility of activity pattern pt relative to the planned pattern pl .

Ts pt : is the earliest departure time (in minutes) from home if pattern pt is performed; and Ts pl indicates the earliest departure time from home according to the planned pattern. pl Tt pt : is the total travel time during the day if pattern pt is performed; and Tt is the total travel time

during the day according to the planned pattern.

Tr pt : is the latest return time to home (in minutes) according to the pattern pt ; and Tr pl indicates the latest return time to home according to the planned pattern.

DurMpt : is the duration of the mandatory activities (in minutes) in pattern pt , and DurMpl is the duration of the mandatory activities, according to the planned pattern.

DurNpt : is the duration of the maintenance activities (in minutes) in pattern pt , and DurNpl is the duration of the maintenance activities, according to the planned pattern.

DurDpt : is the duration of the discretionary activities (in minutes) in pattern pt , and DurDpl is the duration of the discretionary activities, according to the planned pattern.

DurKpt : is the duration of the pickup/drop off activities in pattern pt , and DurKpl is the duration of the pickup/drop off activities, according to the planned pattern.

p

t

pl

is the error term with the mean of zero and correlation matrix of  .

In Eq.1,  ’s and  are the model parameters, which are estimated by maximizing the likelihood function. Assuming a normal distribution for the random error term in the utility function,

p

t

pl

N  0, 

, the probability of pattern t, pt , for individual i are estimated using a Multinomial Probit model (MNP). The correlation matrix is represented by  ,

4

This model form is appropriate since many of the choice alternatives have common constituent activities.

14

 1,2  1   2,1 1    k ,r    16,1

 1,16 

  ,  15,16   1 

 r ,k  16,15

where we assume that the elements of the covariance matrix are, for every pair of patterns  k , r  , correlated according to the share of number of common activities between the pairs  k ,r  correlation as  k ,r  c.

p

t

pt k pt k

pt r ; we rewrite the pt r

pt r , wherein c is a constant parameter to be estimated in the model, pt r

     N  0,   ,   c.      

pl

pt k pt k

pt1 pt1

1 pt1 pt1

pt 2 pt 2

pt 1 pt 1 pt k pt k

1 pt k pt k

pt1 pt1

pt 2 pt 2 pt r pt k

pt r pt k

pt16 pt16

pt15 pt15 pt15 pt15

pt16 pt16

pt 16   pt 16     . 16  pt  pt16    1  

We use GHK ((Geweke, 1989), (Hajivassiliou and McFadden, 1998), (Keane, 1994)) simulator to estimate the parameters of the MNP model. Details of the estimation procedure are provided in the Appendix. The coefficients in Eq.1 were estimated by maximizing the likelihood function of the pattern choices that individuals made, given their planned agenda. It should be noted that the values of explanatory variables in Eq.1 were scaled in the range of [0,1].

Ts  Ts pt



pl adj

Ts pt  Ts pl



Range Ts pt  Ts pl



, is scaled by dividing the deviation of the earliest departure time

from home from the planned departure time with the range of this deviation in the dataset. Similar argument is valid for other variables of the model. The estimated coefficients of different parameters of pattern utility functions are presented as follows.

UP

pt pl

  0pt  3.29  Ts pt  Ts pl

4.47  Dur  Dur pt N

pl N adj

adj

 2.48  Tr pt  Tr pl

adj

 4.64  Dur  Dur pt D

pl D adj

 2.44  Tt pt  Tt pl

adj

 3.62  DurMpt  DurMpl

 3.98  Dur  Dur pt K

pl K adj

The estimated values of the constant term for each pattern are as follows: Patterns

P1

P2

P3

P4

P5

P6

P7

P8

P8

P10

P11

P12

P13

P14

P15

P16

 0p

0.60

0.62

1.83

0.57

0.15

0.13

-0.43

1.27

-0.10

0.05

-0.60

0.12

-0.20

-0.29

-0.37

2.06

t

As hypothesized, these results generally confirm that deviations from the planned activity pattern results in decrease utility; this a result of the negative coefficients in the utility function for all deviations, coupled p with the relatively small values of the constant terms,  0 t .

15

adj

As stated in the equation, the relative utility depends on the composition of the planned agenda, it also depends on the range of the variables used in the equation, since we have normalized all parameters in the equation to be in the range of 0 and 1. Although the magnitude of the coefficients for the duration deviation for mandatory activities is less than the magnitude of the corresponding coefficient for other activity types, mandatory activities have the largest variance as illustrated in FIGURE 3. This leads to the priority of activities in planning and the deviation of activity duration for mandatory activities results to a higher disutility compared to the other activity categories. Furthermore, changes in the duration of the pickup/drop off activities have a smaller disutility compared to the adjustments in the duration of maintenance and discretionary activities; in other words, undertaking such more impulsive activities as maintenance and discretionary activities would raise the disutility of keeping the planned activity-travel patterns.

FIGURE 3. Range of Deviation of Activity Duration from the Planned Durations

The

p

t

pl

value

of

c

  1     N  0 , 0.86     16 pt1   pt   p 16 p 1 t  t 

in

correlation

pt1 pt1

pt16    pt16    .   1  

16

matrix

is

estimated

to

be

0.86,

5. Penalties Associated with Activity Insertion, Deletion and Substitution Operations In this section we present an analysis of the associated penalties to add, delete and/or substitute an activity to/from the planned agenda. To clarify, penalty is used to quantify the degree of unwillingness of individuals to make changes in their planned activity patterns. We assume that disutility of replacing a planned activity depends on what type of activity is replacing the other, e.g. often individuals are more reluctant to go shopping instead of picking up their kids from daycare and this replacement probably has higher penalty compared to the case that they replace a dine-out activity with shopping. Similar argument is valid when individuals want to make in the start time and duration of activities as well. In order to capture the effects of start time and duration of the activities, for each individual in the dataset, 16 combinations of activity patterns together with their planned patterns are generated as shown in FIGURE 4. In the patterns illustrated in FIGURE 4, each letter in the table indicates the activity type in which the person was engaged during the corresponding time slice. The distance, D, between the planned activity pattern and any of the 16 candidate patterns is estimated using the ‘Sequence Alignment Method’ (SAM). In general, the method is used to measure the distance between any pair of text strings by finding the minimum number of steps required to align two sequences under the corresponding penalties for insertion, deletion and substitution operations. Based on the assumption that individuals perform their activities such the resulting pattern has the minimum deviation, or penalty, from their planned patterns, the penalty values for each of the insertion/deletion and substitution operations are estimated.

Edit distance

P1

P2 H M H

Performed H N D H

D1

D2

Dp

P16 H N M F K H D16

Planned H D N H

FIGURE 4. Illustrating Sets of Activity Patterns and their Edit-Distance to Planned Patterns

The sequence alignment technique has been widely used in activity pattern analysis to either classify or to analyze patterns (Joh et al., 1999; Wilson, 1998). However in the literature, a constant penalty for any operation (typically the penalty for insertion/deletion is 1 and for substitution is 2) is considered in the computation process. Here, with access to a complete multiday dataset, we present a methodology that helps to delineate the differences among these penalty values in those operations. Here in this analysis we segment all patterns to chains of activities wherein length of each segment in the chain is 15 minutes and it represents the type of activity that the person was engaged during 15 minutes. Looking at the problem from the multinomial probit choice model’s perspective, the probability of each pattern Pt being performed by individual i , given his/her planned pattern Pl is described as:





Pr Pt i Pl i , t 1,...,16 and is estimated using GHK simulator as explained in previous section.

17

Pri pt  pt i ,iter

Pr

Eq.2

1  Pri,pitert , R iter

 Vi1 pl    c  1,1



  Vi 2 pl  c2,11iter       c2,2  

    



  Vi15 pl  c15,11iter    c15,15 

In this equation Vi pt  j pl  uipt pl  u jpt pl  Vi pt  j pl   ipt  j pl and



c15,1414iter  .  

p pl

ui t indicates the relative utility of

activity pattern pt for individual i conditional on his/her planned pattern. The relative utility in Eq.2 is estimated based on the number of adjustment operations required to match planned patterns to those actually performed. It is assumed that individuals will perform the pattern which has the highest probability, equivalent to the highest utility relative to the planned pattern. Model variables, which are the parameters of the utility function, are estimated using maximum likelihood, presented in Eq.3.

Z

  Pr  N

max

 0 , in , dl , sb

16

pt

i 1 pt 1

y pt ,i

i

Eq.3

s.t : p pl ui t  Fi  Pt i , Pl i ,  inh ,  dlh ,  sbhm ,...,  ink ,  dlk ,  sbkf  , i  1,..., N  , t  1,...,16 ,

aa ' aa ' where the utility is a function of pt , pl ,  ina ,  dla , and  sb . The variables set includes  ina ,  dla , and  sb

, respectively indicating the associated penalties for insertion of an activity type a to individual i ‘s planned agenda, deleting activity type a from the planned agenda, and/or replacing activity type a with the activity type a ' in the planned agenda. In this equation, F indicates the minimum distance between any pair of activities, which is represented as a function of:  variables, set of activity patterns, and the planned patterns. F is computed using edit distance measure, as follows: Suppose we have two activity patterns as P1 and P2 with lengths of l p1 and l p2 . For a given set of  variables, and a large penalty value L , the algorithm to compute the distance between these two patterns follows as:

f  0,0   0,

  f  0, j   j  L , j  0,..., l , a  H , M , N , D, K ,

f  r,0   r  L , r  0,..., l p1 , a  H , M , N , D, K ,

Eq.4

p2

 f  r  1, j    a dl   f  r , j   min  f  r , j  1   ina    f  r  1, j  1  C  P1  r  , P2  j   , r  1,..., l p1 , j  1,..., l p2 ,



where

18







Eq.5

rj   sb C  P1  r  , P2  j      0

if P1  r   P2  j 

Eq.6

if P1  r   P2  j 





F in Eq.3 is the minimum distance between P1 , P2 is computed through F  C lP1 1 , lP2 1 .

F is a recursive function where the distance between the strings of patterns at

 i, j 

state is computed

using the values of previous states. We use a Parallel Genetic Algorithm (PGA), to estimate model variables,

 0p1 ,...,  0p16 ,  inh ,  dlh ,  sbhm ,...,  ink ,  dlk ,  sbkf , with the fitness function in the PGA is the negative of

values of likelihood function estimated through Eq.3. PGA is a heuristic search technique that consists of ‘M’ subpopulations, or demes, where on each of these subpopulation a GA algorithm is performed and, at some points along the search, communication occurs among different demes. As stated by (Allahviranloo et al., 2014; Cantú-paz, 1998) PGA is a very fast and efficient algorithm, which finds near-to-optimal solutions in 1/10th of the computation time for a regular GA. The steps of the algorithm are as follows: Step1. Initialization: a. Generate ‘M’ sub-population of chromosomes, where each subpopulation has ‘m’ chromosomes inside. Every chromosome consists of set of penalty values for each operation (deletion/insertion/substitution) for each activity type. For our dataset, we categorize activities into 5 types (home, mandatory, maintenance, discretionary, and pickup/delivery). Each chromosome comprises 21 variables; 5 variables indicating the penalty associated with inserting an activity to the planned agenda, 5 variables indicating the penalty associated with deleting an activity from the planned agenda, 10 variables indicating the penalty associated with replacing an activity with another activity in the agenda, and 1 variable for coefficient of covariance matrix, FIGURE 5. Sub-population 1

Sub-population M

Ch 1

Ch 2

Ch m

Ch 1

Ch2

Ch m











h in

 inh

 inm

 inm

 inm

h in

h in

h in

h in

 inm

 inm

 inm

⋮

⋮

⋮

⋮

⋮

⋮

 sbkf

 sbkf

 sbkf

 sbkf

 sbkf

 sbkf

…

FIGURE 5. Representation of M sub-population used in PGA

b. For each combination of penalty values in each sub-population, compute the edit-distance between the planned patterns and all potential activities using Eq.4 to Eq.6. Then, by inserting 19

the value of the edit distance, compute the value of log likelihood function N

16





LL   y pt ,i log Pri pt , which is the log function of the objective function stated in Eq.3. i 1 pt 1

The negative of log likelihood function is then used as the fitness function in GA operations. Step2. Evolution within each sub-population a. Crossover  Select a random number, rc , for every chromosome in subpopulation, generate a random number u , if u  rc , add chromosome to crossover population Popcr . 

Select two chromosomes

Ch1, Ch2  randomly

from Popcr and cross them over to

generate children (Liu, 2009) using following steps:

Child1  c  Ch1  1  c)   Ch2 Child 2  1  c   Ch1  c  Ch2



Generate a random number, v . If v  0.2 and the value of fitness function for any child is better than the worst parent in the population, replace parent with child.

b. Mutation  Select a random number, Pm . 

For every chromosome in population, generate a random number u ' , if u '  Pm , add chromosome to mutation population Popm .



Select a chromosome for the mutation population and mutate it by generating a random vector d (Liu, 2009). The mutation equation is as follows: C  Chi  d



If a mutated child is better than the worst case in the population, replace the worst case with the child.

Step3. Communication 

Replace the worst chromosomes in each subpopulation, with the best chromosomes from the other sub-populations, this step will result in ‘M-1’ replacement inside each subpopulation.

Step4. Iterate Step2 and 3 for a default number of iterations or when the improvements in the objective function are small. PGA is used to estimate the penalty values such that communication among different demes occurs after some iterations. For this analysis, the 1200 chromosomes in the initial population were segmented into 12 sub-populations. FIGURE 6 illustrates the change in the value of objective function,   LL  , for the first 30 iterations among different subpopulation of PGA.

20

FIGURE 6. Change in the value of fitness function as the iterations proceed

Associated penalties to insert, delete and replace an activity in the agenda for our dataset is stated in TABLE8, TABLE9, and TABLE10. According to these tables, penalties associated with deleting/inserting or replacing a mandatory activity are the highest. Penalties associated with deleting and replacing a pickup and drop off activities are high as well. For discretionary activities corresponding penalties to delete them from the agenda, or replacing them with other activities is not significant. Operations related to replacing an in-home activity with a discretionary activity or deleting a maintenance activity from the agenda have the smallest penalty values when compared to the other categories. According to the results, mandatory activities are more robust in the activity agenda and participants tend to minimize changes in their mandatory activity since it comes with higher disutility. This argument is in-line with other studies in travel behavior wherein modeling activity scheduling of non-work activities are normally made around the work activity of workers (Rajagopalan et al., 2009). For pickup/drop off activity, the costs associated to replacing them with another activity or deleting them form the agenda is high. This can be due to the nature of the activity where it normally involves more than one participant and any modification in the attributes of pickup/drop off activities comes with adjustments in the patterns of more than one individual. TABLE8. Penalties associated to deleting an activity from the planned activity pattern

Activity type Penalty value

Home 0.54

Mandatory 5.68

Maintenance 0.01

Discretionary 0.80

Pickup/drop off 1.30

TABLE9. Penalties associated to inserting an activity to the activity pattern

Activity type Penalty value

Home 0.43

Mandatory 3.18

Maintenance 1.24

21

Discretionary 2.31

Pickup/drop off 0.78

TABLE10. Penalties associated to replacing an activity in the planned agenda with a new activity

Activity type Home Mandatory Maintenance Discretionary Pickup/drop off

Home 0.00 6.03 2.36 0.01 0.67

Mandatory 6.03 0.00 1.38 3.61 2.98

Maintenance 2.36 1.38 0.00 0.01 0.78

Discretionary 0.01 3.61 0.01 0.00 4.89

Pickup/drop off 0.67 2.98 0.78 4.89 0.00

TABLE11 presents the covariate matrix among 16 activity patterns. The structure of the matrix follows the argument stated before where the correlation among any pair of activity patterns  k , r  is estimated by the share of common activities in the set of agenda for those two patterns,  k ,r  c.

pt k pt k

pt r ; the value of pt r

parameter c , for this dataset is 5.24. TABLE11. Covariance matrix among different activity patterns

P1

P2

P3

P4

P5

P1 P2

5.24 2.62

5.24

P3 P4 P5

2.62 2.62 2.62

P6 P7 P8 P9 P10 P11 P12 P13

P6

P7

P8

P9

P10

P11

P12

P13

1.75 1.75 1.75

5.24 1.75 1.75

5.24 1.75

5.24

1.75 1.75 1.75 1.75 1.75 1.75 1.31 1.31

3.49 3.49 3.49 1.31 1.31 1.31 2.62 2.62

3.49 1.31 1.31 3.49 3.49 1.31 2.62 2.62

1.31 3.49 1.31 3.49 1.31 3.49 2.62 1.05

P14 P15

1.31 1.31

2.62 1.05

1.05 2.62

P16

1.05

2.09

2.09

P14

P15

1.31 1.31 3.49 1.31 3.49 3.49 1.31 2.62

5.24 2.62 2.62 2.62 2.62 1.05 3.93 3.93

5.24 2.62 2.62 1.05 2.62 3.93 2.09

5.24 1.05 2.62 2.62 2.09 3.93

5.24 2.62 2.62 3.93 2.09

5.24 2.62 2.09 3.93

5.24 2.09 2.09

5.24 3.14

5.24

2.62 2.62

2.62 2.62

2.09 2.09

3.93 2.09

3.93 2.09

2.09 3.93

2.09 3.93

3.93 3.93

3.14 3.14

3.14 3.14

5.24 3.14

5.24

2.09

2.09

3.14

3.14

3.14

3.14

3.14

3.14

4.19

4.19

4.19

4.19

6. Discussion and Closing Remarks In this paper, using data obtained from a detailed survey performed in Belgium, the differences between the stated preferences of individuals in terms of their planned and their actual (realized) activity participation are analyzed. The analysis assesses the flexibility of travelers in making changes in their mental plans in reaction to the external events impacting them. A three-stage analysis was performed to compare the differences in the patterns: In stage 1, we compared differences evident in the empirical data based purely on the performed and planned patterns reported by travelers. According to the results of this stage, although individuals perform at least 79% of their planned activities, the share of unplanned activities in the performed activity pattern

22

P16

5.24

is also high—close to half of the maintenance and flexible activities are added to the agenda without previous planning. In stage 2, we take the analysis one step forward and attempt to quantify the weights that travelers put on different aspects of their itineraries when they adjust planned activity participation due to external factors. This objective is addressed by proposing a concept of relative utility of different activity chains compared to the planned patterns. It is assumed that the planned pattern is the most desirable set of activities while the performed one has the utility closest to that of the planned. The terms of the utility function in this stage are: earliest departure time from home, return time to home, out of home time spent, and duration of different types of activities. We assume that the choice of a particular activity pattern follows the structure of a Multinomial Probit model with parameters estimated using the corresponding Maximum Likelihood function. The results obtained from this analysis indicate that deviations in the earliest departure time from the planned earliest departure time have a higher penalty weight compared to deviation from the latest return time to home, meaning that travelers tend to depart from home at the time they had originally planned; this can be due to within-family responsibilities (a parent dropping off a child at daycare), importance of commencing a work activity at its scheduled time, transit schedule, or simply because of the fact that, as the time passes along the day, the gap between planned and performed patterns accumulates and toward the end of the day this gap becomes larger. Changes in the duration of mandatory activities have a smaller value compared to that of other activity types. This can be due to the length of the activity as well, since mandatory activities tend to have larger durations compared to such other activities as pickup/drop off activities. In stage 3, we evaluate the penalties associated with adding, deleting or substituting any activity in the planned agenda with the ones in the performed agenda. Using multiday data, we first generate all possible sequences of activities. Then we segment daily patterns into 15-minute intervals. For a given set of penalties for each operation (insertion, deletion, substitution), and under the assumption that performed pattern has the utility closest to that of the planned and the choice model has MNP structure, the likelihood function is estimated using a parallel genetic algorithm. The results indicates that: (1) the penalty values for each operation and each set of activities are not identical, (2) deleting/inserting or replacing a mandatory activity with other types of the activities has the highest penalty value, and (3) the penalty associated to the replacing pairs of non-mandatory activities is not significant. What have we learned from this study and how can it be used in policy formations? In this paper, the use of multiday activity data, along with some mathematical models, has enabled us to conduct an analysis of trade-offs among the various choices related to travelers’ behavior and preferences brought on by events that have required adaptation from what had been planned originally. The analysis indicates that any change in the scheduling features of such mandatory activities as attending school or going to work is associated with a high cost to travelers. Alternatively, flexible activities can be rescheduled with a lower cost and they can be more easily moved in the schedule, cancelled or added to the agenda. In other words, planning policies impacting mandatory activities of travelers may be more difficult to impose than those directed toward other types of activities. Furthermore, travelers are more willing to adapt or change their planned itinerary as the day passes; they tend to follow their planned itinerary at the start of the day, and their scheduling decisions regarding the first activity of the day is most robust. Such information can be important as the provision of on-demand transportation services based on platforms wherein a planned itinerary is uploaded by a traveler for service during the day. For such services, the degree of robustness of the travelers’ decisions is a critical factor in providing efficient service and making proper decisions 23

regarding service allocation in space and time. Knowing the latitude of possible adjustments to such scheduled demands can be an important factor in providing efficient service, extending the concept of reliability that has largely been studied from the perspective of the service reliability of transportation systems to also that of the users.

Acknowledgement: The data used in this paper were originally collected in a joint project between Hasselt Transport group/IMOB and the Urban Planning Group, TU/e. We express our gratitude for making available these data for this analysis. Responsibility for any errors remains ours.

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Habib, K.N., El-Assi, W., Hasnine, S., Lamers, J., 2016. Activity-Travel Behaviour of Non-Workers in the National Capital Region of Canada : Application of a Comprehensive Utility Maximizing System of Travel Option Modelling ( CUSTOM ), in: 95th Annual Meetings of Transportation Research Board. Hajivassiliou, V., McFadden, D., 1998. The method of simulated scores for the estimation of LDV models. Econom. J. Econom. Soc. 66, 863–896. doi:10.2307/2999576 Joh, C., Arentze, T. a, Timmermans, H.J.P., 1999. Multidimensional Sequence Alignment Methods for Activity Pattern Analysis :, in: 39 ERSA Conference. Dublin, Ireland, pp. 1–19. Kang, H., Scott, D.M., 2010. Exploring day-to-day variability in time use for household members. Transp. Res. Part A Policy Pract. 44, 609–619. doi:10.1016/j.tra.2010.04.002 Keane, M.P., 1994. A Computationally Practical Simulation Estimator for Panel Data. Econom. J. Econom. Soc. 62, 95–116. Kitamura, R., Chen, C., Pendyala, R.A.M.M., Narayanan, R., 2000. Micro-simulation of daily activitytravel patterns for travel. Transportation (Amst). 27, 25–51. Kitamura, R., Fujii, S., Pa, E.I., 1997. Time-use data , analysis and modeling : toward the next generation of transportation planning methodologies. Transp. Policy 4, 225–235. Lee, M.S., McNally, M.G., 2003. On the structure of weekly activity/travel patterns. Transp. Res. Part A Policy Pract. 37, 823–839. doi:10.1016/S0965-8564(03)00047-8 Meister, K., Frick, M., Axhausen, K.W., 2005. A GA-based household scheduler. Transportation (Amst). 32, 473–494. doi:10.1007/s11116-005-5325-3 Meloni, I., Guala, L., Loddo, A., 2004. Time allocation to discretionary in-home, out-of-home activities and to trips. Transportation (Amst). 31, 69–96. doi:10.1023/B:PORT.0000007228.44861.ae Miller, E.J., Roorda, M.J., 2003. Prototype Model of Household Activity-Travel Scheduling. Transporation Res. Rec. 1831, 114–121. Paleti, R., Jenkins, S., Bhat, C., Sources, D., Description, S., 2009. Additional Information on Data Sources and Sample Description 2, 1–5. Pendyala, R., Kitamura, R., Kikuchi, A., Yamamoto, T., Fujii, S., 2005. Florida Activity Mobility Simulator: Overview and Preliminary Validation Results. Transp. Res. Rec. 1921, 123–130. doi:10.3141/1921-14 Rajagopalan, B.S., Pinjari, A.R., Bhat, C.R., 2009. Comprehensive Model of Worker Nonwork-Activity Time Use and Timing Behavior. Transp. Res. Rec. J. Transp. Res. Board 2134, 51–62. doi:10.3141/2134-07 Recker, W.W., 1995. The Household Activity Pattern Problem: General Formulation and Solution. Transp. Res. Part B Methodol. 29, 61–77. Roorda, M.J., Carrasco, J. a., Miller, E.J., 2009. An integrated model of vehicle transactions, activity scheduling and mode choice. Transp. Res. Part B Methodol. 43, 217–229. doi:10.1016/j.trb.2008.05.003 Schwanen, T., Kwan, M.P., Ren, F., 2008. How fixed is fixed? Gendered rigidity of space-time constraints and geographies of everyday activities. Geoforum 39, 2109–2121. doi:10.1016/j.geoforum.2008.09.002 Smith, L., Beckman, R., Doug, A., Nagel, K., Williams, M., 1995. TRANSIMS: TRansportation ANalysis and SIMulation System, in: 5th National Transportation Planning Methods Application. Wilson, W.C., 1998. Activity pattern analysis by means of sequence-alignment methods. Environ. Plan. A 30, 1017–1038. doi:10.1068/a301017 25

26

Appendix: Model Estimation Using GHK Simulator We use GHK ((Geweke, 1989), (Hajivassiliou and McFadden, 1998), (Keane, 1994)) simulator to estimate the parameters of the MNP model. We define index j as the performed pattern by the individual and subtract the relative utility of alternative j from the other 15 alternatives as: p  j pl

Ui t

 UPi

pr  j pl

 UPi

j pl

 Vi

pt  j pl

p  j pl

 i t

p  j pl

where  i t





N 0,  and  is derived from  .

Let L be the Choleski factor of  as  c1,1  c2,1 Lj      c15,1

 ipt  j pl

0 c2,2

0

c15,2

0   0  , then   c15,15 

 ip  j pl can be written as: t

 1i     L j    , where parameters of  have iid normal distributions. The choice probability can 15i   

be written as:



p  j pl

Pri pt  Pr U i t

1 pl  Vi  Pr 1   c1,1 



0

 



2 pl  1 pl  Vi  c2,11  Vi  1    Pr 2   c2,2 c1,1  

15 pl   Vi  c15,11    Pr 15   c15,15 

c15,1414



   



1 pl  Vi Vi  &...&   1 14 c1,1

14 pl

 c14,11  c14,14



c14,1313    

The steps of GHK simulator are as follows: 1 pl   Vi1 pl  Vi  1- Compute Pr1  Pr 1       c1,1    c1,1 

  Vi1 pl   iter 1        2- Draw as random number 1  1  c1,1   ,where   



  Vi 2 pl  c2,11iter [0,1] and compute Pr2     c2,2 

27

  .  

1

is random number in the range of

3- Draw as random number 

iter 2



   Vi 2 pl  c2,11iter    2     c2,2   1

   ,where    



  Vi 3 pl  c3,11iter  c3,22iter range of [0,1], then compute Pr3     c3,3 

2

is random number in the

  ,  

4- Compute probabilities for all 15 alternatives. The simulated probability for iteration ' iter ' pt i ,iter

Pr

 Vi1 pl    c  1,1



  Vi 2 pl  c2,11iter       c2,2  

  



  Vi15 pl  c15,11iter    c15,15 

 

5- Repeat steps 1-4 for iter  1,..., R then simulated probability is Pri p  1 t

R

Having

computed N

16



L(  )   Pri pt i 1 pt 1

performed pattern

5

pt

the



y pt ,i

probabilities

the

corresponding

UPi



pl pl

 Pr

pt i ,iter

.

iter

likelihood

function

will

be

, where y p ,i is binary variable and takes the value of 1, if individual i has t

and zero otherwise5.

We note that in this formulation, the utility of the planned pattern, pl pl



c15,1414iter  .  

UPi

, and has the greatest utility (assuming the coefficients

28

pl pl

, which is always included in the choice set is

 are negative).