- Email: [email protected]
A flexible activity scheduling conflict resolution framework
Chapter 16
A flexible activity scheduling conflict resolution framework Ali Shamshiripoura, Ramin Shabanpoura, Nima Golshania, Joshua Auldb, Abolfazl Mohammadiana a
University of Illinois at Chicago, Chicago, IL, United States; bArgonne National Laboratory, Argonne, IL, United States
Chapter outline 1. Introduction 2. Polaris framework 3. The proposed conflict resolution framework 3.1 Data 4. Modeling details 4.1 Propensity to change start time and/or duration
299 301 302 304 305
4.2 Strategic resolution model 5. Tactical resolution model 6. Implementing and testing 7. Conclusions Acknowledgments References
312 315 316 321 322 322
305
1. Introduction The growing complexity of people’s daily activity-travel behavior along with the increased traffic congestion in major urban areas and more diverse policy responses to managing that congestion have motivated the development and use of microsimulation activity-based models (ABMs) as policy sensitive tools to analyze various dynamics of the travel demand. Over the past decade, several ABMs have been developed, among which the early instances are ALBATROSS (Arentze and Timmermans, 2004), TASHA (Miller and Roorda, 2003), CEMDAP (Bhat et al., 2004), and ADAPTS (Auld and Mohammadian, 2012). More recently, POLARIS (Auld et al., 2016) was built upon a similar activity demand core as ADAPTS and added value to the literature by fully integrating the demand components with network supply and operations. The demand component of POLARIS serves as a flexible and easily expandable platform that is able to relax some of the strong behavioral assumptions which were adopted by the predecessors (Auld et al., 2016). For Mapping the Travel Behavior Genome. https://doi.org/10.1016/B978-0-12-817340-4.00016-4 Copyright © 2020 Elsevier Inc. All rights reserved.
299
300 PART | II New research methods and findings
instance, the platform relaxes the assumption that all activity attributes are decided at the exact time that the activity is generated. The framework also suggests an econometric model to account for heterogeneities underlying order of planning for different activity attributes. Another prominent contribution of the framework is introducing an activity conflict resolution model to resolve the potential overlaps between the newly generated activities (hereafter, the new activities) and the ones that are already scheduled (hereafter, the original activities) in order to maintain a consistent activity-travel schedule. This study reports on a recent advancement in the activity conflict resolution model of POLARIS, factoring in more behavioral insights. In more detail, the demand model breaks down the whole day into T time steps. For each travel in each time step, it checks if the individual needs to conduct a new activity of a certain type (i.e., generating a new activity). If yes, another module, the planning attribute model, determines the sequencing of planning for different attributes of the activity. Once all the activity attributes are planned, the activity is pushed into the individual’s daily activity schedule. At this stage, many potential conflicts may occur between the new activity and any original activities that may have previously planned. The activity conflict resolution model is used to resolve the conflicts by modifying/deleting the activities as needed to maintain a consistent schedule. Indeed, this component plays a pivotal role in the overall accuracy of such computational process model frameworks, since any subtle errors in the logic of the module would cause repeated imperfections, leading to significant amount of error in later scheduling and activity execution. Several other ABMs have implemented conflict resolution strategies previously. TASHA (Miller and Roorda, 2003) follows a rule-based procedure which prioritizes some activities over others, mostly based on their type (Miller and Roorda, 2003). Later on, Doherty et al. (2004) proposed an approach specifically for the cases in which a new activity is intended to be placed between two scheduled activities while the orders are to be kept the same. The authors employed parametric hazard models to analyze the tolerable shifts in activities. Afterward, Auld et al. (2009) expanded the literature by developing a bilevel conflict resolution model based on the activity conflict instances derived out of a unique activity planning dataset, CHASE (Doherty and Miller, 2000). In the upper-level, a decision tree determines the resolution strategy depending on whether the individual decides to modify the original and the new activities. Then, in the lower-level, a rule-based module is developed based on based on the resolution strategy and the conflict situation to place the new activity in the schedule, if possible. For presentation clarity, the upperlevel classifier is henceforth called the strategic resolution model and the lower-level component is termed the tactical resolution model. More recently, to improve the later conflict resolution model, Javanmardi et al. (2016) replaced the rule-based tactical resolution model with a novel
A flexible activity scheduling conflict resolution framework Chapter | 16
301
linear mathematical program. Their motivation was to provide a more scalable and easy-to-maintain module, which is of great value in the context of largescale agent-based frameworks. In their proposed tactical resolution model, the individual is assumed to minimize the total changes in his/her activity schedule subject to the constraints imposed by the strategic resolution outcome. In this article, we are enhancing the conflict resolution model of Javanmardi et al. (2016). In our proposed model, we improve the problem formulated for the tactical resolution level to account for the inter-personal heterogeneities in how people define the settings of the problem in different situations. For instance, we relax the assumption that the maximum tolerable shifts in the activity start time and duration are fixed across all individuals by incorporating hazard models. Second, the proposed framework is able to handle more complex activity conflict situations. Third, the flow of information is also reformed such that the lower-level tactical resolution model provides feedback to the upper-level strategic resolution model. The reminder of this paper is organized as follows. Since the proposed conflict resolution model is designed to be embedded within the POLARIS framework, the next section briefly outlines the framework’s structure. Next, the proposed conflict resolution model is introduced. The dataset used to develop the models along with the processes to prepare the data are discussed afterward, followed by the elaborations on modeling details. Finally, we report the results of the implementation of the proposed framework and conclude by summarizing the paper and presenting some directions for future studies.
2. Polaris framework POLARIS (Auld et al., 2016) is an agent-based framework that integrates travel demand, network supply and network operations. This is a fullyintegrated platform in the sense that the demand components continuously integrate with the traffic simulator, and unlike many other similar platforms, the time-dependent traffic network impacts the demand components. The demand component of POLARIS, as laid out in Fig. 16.1, comprises three distinct phases of activity generation, activity planning, and activity scheduling. Activity generation deals with the decision of generating a new activity of a certain type (e.g., shopping, discretionary, personal). At each simulation time step, simultaneous competing hazard models determine the probability of generating a new activity considering the elapsed time from the execution of the previous activity of the same type. This phase only identifies if the individual needs to execute an activity of a certain type regardless of all attributes. Once a new activity is generated, the second phase determines the activity attributes namely start time, duration, location, party composition, and mode of travel to the activity location. Unlike many ABMs that assume that all
302 PART | II New research methods and findings
FIG. 16.1 Demand component of POLARIS framework.
activity attributes are decided at the time of the activity generation, POLARIS allows activity attributes to be planned at different time horizons. In other words, activity attributes can be determined in any order, and the planned attributes can affect the ones that are yet to be planned. In the last phase of the demand part (i.e., activity scheduling), the activities with all attributes being determined will be added to the schedule according to their start time and duration, and potential conflicts will be resolved. Further details about the demand component of POLARIS can be found in Auld et al. (2016).
3. The proposed conflict resolution framework The proposed conflict resolution framework is designed to add to increased accuracy and realism to the current conflict resolution module implemented in POLARIS while keeping it as simple to maintain as possible. Fig. 16.2 depicts the pseudo code of the proposed framework. The updated conflict resolution
A flexible activity scheduling conflict resolution framework Chapter | 16
303
Step 0: Input 0.1. Get the conflicting bundle Step 1: Initialization 1.1. Set , and set and according to the current 1.2. Determine and for 1.3. Determine , for Step 2: Strategic-resolution Effectiveness 2.1. Given the constraints in Eqs. 6, 7, and 8, determine which strategies are effective. Step 3: Strategic Resolution 3.1. From among the effective strategies, select the most desirable choice, . Step 4: Tactical Resolution 4.1. Given the constraints in Eqs. 6, 7, and 8 and the objective function in Eq. 5, determine the conflict resolution details. Here, it is assumed that individuals try to minimize the change. Step 5: Updating 5.1. If then set , set and according to the ; else go to Step 6. 5.2. If the conflict in is yet to be resolved, go to 1-2; else, go to 5.1. Step 6: End.
FIG. 16.2 Algorithm of the proposed framework. s, a particular strategy to resolve the conflict; p, a pair of two conflicting activities (conflict pair); ORG, the activity that is originally scheduled but is conflict with NEW; NEW, the activity that is newly generated but is in conflict with ORG; i, the activity under consideration; i ˛ fORG; NEWg; c, a set of all conflicting pairs p that share one NEW (conflict bundle); Pc, total number of conflicts in the conflicting bundle c; Sji , start time of the travel towards the ith activity in state j; Dji , duration of the ith activity in state j; A, indicating state of a modifiable activity after modification; B, indicating state of a modifiable activity before modification; ShiftCi , the probability that an individual goes for changing start time of activity i; ShortCi , the probability that an individual goes for changing duration of activity i; MaxShifti , maximum change (in min) in start time of activity i that an individual accepts; MaxShorti , maximum change (in percent) in duration of activity i that an individual accepts.
module is similar to the version by Javanmardi et al. (2016) in that it is based on a two-level process: strategic and tactical planning. However, each of the two levels are refactored to address the gaps mentioned in the introduction. The new algorithm loops over every conflicting pair p of a bundle c, resolves it, and moves to the next conflict which is not resolved yet. The terminology used in this article is introduced following Fig. 16.2. The algorithm starts with determining individuals’ propensities toward changing the original and new activities involved in each conflicting pair p. The change is measured from two aspects, start time and duration. To analyze each aspect, two econometrics models are developed, a binary logit and a parametric hazard. The binary choice formulation is used to model whether an individual is willing to change start time/duration of an activity. For those who would decide to change start time or duration of an activity, then, their tolerance is estimated using the hazard functions. In step 2, the framework determines which strategies are effective (i.e. could resolve the conflict if implemented). This is done based on the linearity feature of the tactical resolution model. Linear objective function and the set of linear constraints allow us to check feasibility of each strategy before implementing it. The task can efficiently be done by inputting the constraints to the so-called phase-1 Simplex. Outcomes of this step are then fed into step 3
304 PART | II New research methods and findings
to run the strategic resolution model. The strategy is chosen using decision trees similar to the model developed by (Auld et al., 2009), except for the fact that the new model is smart enough to use information from step 2 and foresee outcome of its prediction. Practical aspects of implementing this idea are expressed in more details, in next sections. In step 4, resolution details are derived putting together the constraints used in Step 2 and a relevant objective function to quantify the extent of the change in the individual’s schedule. The problem setup as well as specifications of the trees, the binary choice, and the hazard models are discussed in next sections, in details. After the conflicting pair p is resolved, if necessary, the framework moves on with the next p in the conflicting bundle c. Resolving the conflict between the new and one of the original activities might end up with resolving the conflict between it and rest of the original activities as well. For example, consider the case that outcome of step 3 is determined as “delete new”.
3.1 Data The CHASE (Doherty et al., 2004) activity-diary survey is used as the main source of data. Each observation in this data set represent a change in the person’s activity schedule. A procedure is therefore needed to derive activity conflicts out of the observed scheduling changes. The data processing algorithm used in this research is similar to Auld et al. (2009). After detecting a conflict, original and new activities are identified. The resolution strategy (i.e., modify original, modify new, modify both, delete original, and delete new) is determined in two steps. The first step is based on whether each activity is ultimately executed or not. If, for example, the new activity is conducted but the original is not, the conflict should be given either the resolution-type label “modify original” or “delete original.” In terms of distinguishing between modification from deletion, the activity ai is given the label “deleted” if the three following conditions are met at the same time: (1) ai is not conducted at the end of the day, (2) no instance among the whole set of recorded activity changes of the day could be found in which ai is changed to ai’ , and (3) no activity ai0 could be found that is later added to the schedule, with the same activity attributes as ai (Auld et al., 2009). The activity ai is given the label “modified” if the second condition, the third condition, or both are not met while the first is. The modified version of the activity ai, shown as aAi , is assumed to be an activity for which either of the following conditions are met: (1) a record could be found indicating that ai is changed to aAi , or (2) an activity aAi is added later during the day, with the same activity attributes as ai . Multiple feasibility checks are performed to flag the cases where two or more activities are falsely recognized as being in conflict. Similar to Auld et al. (2009), we have excluded the cases where the conflict is not resolved after the observed change in the activities involved in it. In addition, the conflict
A flexible activity scheduling conflict resolution framework Chapter | 16
305
between two activities that are both executed at the end of the day is not included. Such cases presumably occur when the overlap is due to situations other than scheduling conflicts, for example, instances of multitasking. After processing the data, a total of 1802 conflict resolution records were observed. About 30% of the conflicts were resolved by modifying the original, 4% were resolved by modifying the new, 6% were resolved by modifying both, 38% were resolved by deleting the original, and 22% were resolved by deleting the new activity. In other words, about 40% of the conflicting cases are resolved by modifying the original, new, or both, while 60% are resolved by deleting either one. After excluding irrelevant observations, the modifications made to the original and the new activities are pooled together to form a sample of 705 activity modifications. The binary choice and the hazard models are estimated using this sample. Among the observations in this sub-sample, about 61% are the cases in which only the activity duration is changed, and 5% are the cases in which only the start time is changed. This important finding reveals that an average individual is more flexible in changing duration of an activity than in start time. Fig. 16.3 shows the frequency distributions of the observed changes in start time and duration for the modified activities. Consistent with intuition, this figure supports the robustness of the data processing algorithm. As seen, a person becomes less likely to tolerate more changes in start time and/or duration of an activity as the extent of the change becomes larger. This specific pattern, also, supports the use of hazard model formulations. In order to prepare the data for training the decision tree, the data prepared in the previous steps is first enriched by a set of dummy variables derived as different combinations of the three binary variables: “effective if only modifying original”, “effective if only modifying new”, and “effective if modifying both”. Values of these variables are populated feeding output of the binary choice and the hazard models into step 2 of the framework, strategic-resolution effectiveness (implementation details are provided in the next two sections).
4. Modeling details This section is devoted to more detailed discussions on the models estimated for each step of the framework. This section encompasses specifications of the hazard models, the decision tree, and the proposed set of linear programs.
4.1 Propensity to change start time and/or duration Binary logit models determine if the start time and/or duration of an activity is changed. Then, fully parametric hazard models determine the extent of the change in start time and/or duration, for those who decide to change each. Generally, hazard-based models estimate the probability for occurrence of an event between time t and t þ dt, given that it has not happened until time t.
306 PART | II New research methods and findings
FIG. 16.3 Observed changes in (A) start time and (B) durations of activities while resolving the conflicts.
Using the cumulative density function of the duration (FðtÞ) and its probability density function (f ðtÞ) the survival and hazard functions can be formulated as: SðtÞ ¼ 1 FðtÞ lðtÞ ¼
d ln SðtÞ f ðtÞ ¼ dt SðtÞ
(16.1) (16.2)
here, SðtÞ is the survival function, denotes the probability that extent of change in duration/start time is greater than t; and lðtÞ is the hazard rate, which in our context represents the probability that the person does not tolerate the modification t given that he/she tolerates modifications bellow t. In fully parametric hazard models, we assume a parametric form for the distribution of survival time. The commonly popular hazard functions are Exponential, Log-logistic, Log-Normal, Weibull, and Gamma. Through testing different functional forms, it is observed that the Exponential and Weibull distributions result in the best
A flexible activity scheduling conflict resolution framework Chapter | 16
307
fitted hazard models for the modifications in the start time and duration, respectively. These functions are as follows (Washington et al., 2010): Exponential : Weibull :
lðtÞ ¼ l
(16.3)
lðtÞ ¼ ðlPÞðltÞP1
(16.4)
where l and P are estimable parameters, and q is the variance of the unobserved heterogeneity term. Further, robust standard errors are estimated for the hazard models to make sure of legitimacy of the proportional hazard assumptions. The estimated models are outlined in Table 16.3. The variables introduced into the models sit in three groups of individual characteristics, activity characteristics, and type of the conflict (as depicted in Fig. 16.4). In a nutshell, age, day of week, conflict type, activity type, duration of the activity before modification, activity frequency and travel time toward the activity location are among the most important variables used in the models. Per the results, older individuals tolerate longer shifts in start time of their activities and shorter duration alterations. This makes sense given that elderly individuals have more free time in their schedules, and therefore, they have more opportunities to move an activity to a sooner/later time; as a result, they would need shorter duration alteration. Individuals’ with busier schedules during the weekdays have lower tolerances to start time changes, which is supported by the results of this study. The results also confirm that, in case there is enough time surrounding an activity to accommodate without duration alterations, an individual is more likely to do so. According to Table 16.1, duration of longer activities is more likely to be modified rather than the start time. Also, an individual is more likely to accept a change in duration of a frequent activity. This makes sense, as more frequent activities can possibly make up for an insufficient duration allocated to them. Conforming to the common sense, an individual is more likely to change start time of the original and duration of the new activity in a type 1 conflict, and to change start time of the new and duration of the original activity in a type 2 conflict. Also, the conflicts of type 3 and 4 are more probable to be resolved by changing start time of either of the activities, as compared to the conflicts of type 1 and 2. According to the results, start time of mandatory activities is significantly less likely to be changed compared to other activity types. Also, if an activity involved in a conflict is shopping, the individual would be more flexible in changing duration and start time of the other activity that conflicts with it.
Type 1
Type 2
Type 3
FIG. 16.4 Conflict types by geography.
Typee 4
Start time model Explanatory variable
Duration model
Binary logit
Hazard
Binary logit
Hazard
Effect on original
0.009
0.020***
0.006*
Effect on new
0.009
0.020***
0.006*
Individual: age
Activity: frequency of original 0.042**
0.130***
Effect on original
0.279**
0.539**
Effect on new
0.279**
0.539**
Effect on original Activity: enough free time surrounding the activity
Activity: free time before new, in a type 1 conflict Effect on new
0.049***
Activity: natural logarithm of duration before modification Effect on original
0.426**
Effect on new
0.426**
Activity: new is not flexible in start time Effect on new
0.561***
308 PART | II New research methods and findings
TABLE 16.1 Model estimation results.
Activity: original is flexible in duration
Activity: original is mandatory Effect on original
0.425*
Activity: original is social Effect on original
0.843***
0.805***
0.843***
0.805***
Activity: new is social Effect on new Activity: original is recreation Effect on original Effect on new
0.345** 1.585***
Activity: new is recreation Effect on original
1.585***
Effect on new
0.345**
Activity: original is shopping Effect on new
0.276**
Activity: new is shopping Effect on original
0.731***
0.276**
309
Continued
A flexible activity scheduling conflict resolution framework Chapter | 16
0.420*
Effect on original
Start time model Explanatory variable
Binary logit
Hazard
Activity: original is eating meal Effect on original
0.944***
Activity: new is eating meal Effect on new
0.944***
Activity: original is sleeping 1.152***
Effect on original Effect on new
1.364**
Activity: original is household errand Effect on new
2.489***
Activity: weekday Effect on original
0.933***
Effect on new
0.933***
Activity: travel time to original Effect on original
0.002***
Duration model Binary logit
Hazard
310 PART | II New research methods and findings
TABLE 16.1 Model estimation results.dcont’d
Conflict: type 1 4.253***
Effect on new
1.196***
Conflict: type 2 Effect on original
0.719***
Effect on new
0.698**
Conflict: type 3 Effect on original
1.207
o
Conflict: type 4 1.870***
Effect on original Conflict: type 3 or 4 Equal effects on original and new
0.618***
Constant Effect on original
1.584***
4.171***
0.853
0.632***
Effect on new
1.584***
4.171***
0.853
0.632***
IID EV
Exponential
IID EV
Weibull
Error term distribution Note: Symbols ***, **, * and
o
stand for significance level of 0.01, 0.05, 0.1, and 0.15.
A flexible activity scheduling conflict resolution framework Chapter | 16
Effect on original
311
312 PART | II New research methods and findings
Similar results are derived with regards to the start time of a recreational activity, although an opposite relationship holds for recreation durations. In other words, people are more to alter the duration of their recreational activities when having to resolve the scheduling conflicts caused by the activity (whether it is the original activity or the new). Yet, they try to keep start time of their recreational activities unchanged. If an activity is social, the individual would be more flexible on modifying the activity itself rather than the conflicting, both in terms of duration and start time. When an activity is eating a meal out, it is more probable to undergo a start time change. The results also reveal that people usually try not to change start time of a sleeping activity. In other words, they try to go to sleep at the time they usually do.
4.2 Strategic resolution model Using the three feasibility dummy variables generated in the data processing phase, the whole feasible region could be segmented into 5 distinct regions. The segments along with the observed shares of each strategy type can be summarized as: l
l
l
l
l
Any modification is effective (modify original: 23.8%, modify new: 5.6%, modify both: 7.6%, delete original: 31.7%, and delete new: 31.4%). Modifying original is effective while new is not (modify original: 33.5%, modify new: 0.0%, modify both: 7.5%, delete original: 40.8%, and delete new: 18.2%). Modifying original is not effective while new is (modify original: 0.0%, modify new: 3.4%, modify both: 7.4%, delete original: 42.6%, and delete new: 46.6%). Modifying a single activity is not effective while modifying both is (modify original: 0.0%, modify new: 0.0%, modify both: 7.7%, delete original: 58.2%, and delete new: 34.1%). No modifying is effective (modify original: 0.0%, modify new: 0.0%, modify both: 0.0%, delete original: 71.8%, and delete new: 28.2%).
Specific to each of the five segments, a unique decision tree is trained using the data. Doing so, the trained tree is guaranteed only to predict strategies that are feasible to follow by the tactical resolution step. As can be seen above, the data available for all segments is highly imbalanced in terms of the strategy shares, and this could lead to improper training of the trees. To overcome such issues and achieve balanced data sets, the Synthetic Minority Over-sampling Technique (SMOTE) is used to oversample the under-represented strategies using the k-nearest neighbors classifier (Chawla et al., 2002). The classifier looks into 8 neighbors at each step. Further, we conducted a fourfold cross-validation experiment to make sure the accuracy results are true representatives of the trained trees. Table 16.2 summarizes the accuracy results achieved for each of the five trees.
Strategies
Feasibility categories
Accuracy metrics
Any modification is effective
Accuracya b
Precision Recall
c d
F1-score Modifying original is effective while new is not
Modifying original is not effective while new is
Modifying one activity is not effective while modifying both is
Modify original
Modify new
Modify both
Overall Delete original
Delete new 0.54
0.57
0.91
0.65
0.47
0.67
0.53
0.88
0.68
0.52
0.64
0.55
0.89
0.67
0.49
0.65
Accuracy
0.61
Precision
0.60
NA
0.85
0.66
0.76
Recall
0.51
NA
0.93
0.66
0.78
F1-score
0.55
NA
0.89
0.66
0.77
Accuracy
0.71
Precision
NA
0.75
0.96
0.63
0.65
Recall
NA
0.82
0.92
0.67
0.62
F1-score
NA
0.78
0.94
0.65
0.63
Accuracy
0.78 NA
NA
0.82
0.70
0.79
Recall
NA
NA
0.70
0.95
0.66
F1-score
NA
NA
0.76
0.81
0.72
313
Precision
A flexible activity scheduling conflict resolution framework Chapter | 16
TABLE 16.2 Accuracy indices calculated for the set of trees.
Continued
Strategies
Feasibility categories
Accuracy metrics
No modifying is effective
Accuracy
Modify original
Modify new
Delete original
Delete new 0.79
Precision
NA
NA
NA
0.92
0.96
Recall
NA
NA
NA
0.96
0.93
F1-score
NA
NA
NA
0.94
0.95
ðTrue positive þtrue negativeÞ =ðtrue positive þtrue negative þfalse positive þfalse negativeÞ. b True positive=total predicted positive. c True positive=total actual positive. d Precision recall=precision þ recall. a
Modify both
Overall
314 PART | II New research methods and findings
TABLE 16.2 Accuracy indices calculated for the set of trees.dcont’d
A flexible activity scheduling conflict resolution framework Chapter | 16
315
5. Tactical resolution model We modified the program outlined in (Javanmardi et al., 2016) by incorporating the information from binary choice and hazard models to bring more realism into both the objective function and the constraints as: Min:Changep ¼ ð1 ShiftCORG Þ SBORG SA ORG B A þ ð1 ShortCORG Þ DBORG DA ORG þ ð1 ShiftCNEW Þ SNEW SNEW þ ð1 ShortCNEW Þ DBNEW DA NEW (16.5) S.T.: Change should be tolerable
(16.6)
Activities must not overlap after resolution
(16.7)
Non negativity conditions
(16.8)
The assumption that individuals try to minimize the change in their schedule when deciding on how to resolve a conflict, forces the model to come up with schedules in which duration of activities are not increased compared to their duration before the change. That is, even if shifting the activity to less occupied time intervals during the day provides enough room for increasing its duration, the individual would not do so, since he/she is assumed to keep the changes to the minimum extent possible. Regarding the start time, however, the model shown in Eq. (16.5) does allow for shifting both forward or backward, and this flexibility comes at the cost of losing linearity. To linearize Eq. (16.5), it can be broken down into a set of subproblems depending on direction of the shift. The sub-problems considered in this article are shown in Fig. 16.5. After all sub-problems are solved, the answer corresponding to the minimum value of Eq. (16.8) is selected as the global solution to the problem. Breaking down the objective function into the sub-problems and further simplifying the problem yields in the 6 objective functions shown in A A A A A A Table 16.3, where SA ORIG , DORIG , SNEW , DNEW , SORIG1 , SORIG2 , SNEW1 , and A SNEW2 are the decision variables. In this table, the constant term denotes summation of the terms which can be dropped from the objective functions without affecting the final results; and wSORG ¼ ð1 ShiftCORG Þ; wSNEW ¼ D ð1 ShiftCNEW Þ, wD ORG ¼ ð1 ShortCORG Þ; and wNEW ¼ ð1 ShortCNEW Þ are the case-specific coefficients derived according to the results of the hazard and binary choice models. The constraints associated with each sub-problem are specified in Table 16.4 (non-negativity constraints are skipped).
316 PART | II New research methods and findings
base conditions • New is moved backward, if moved • Orig. is moved forward, if moved
sub-problem 1 • New is moved forward, if moved • Orig. is moved backward, if moved
sub-problem 2 • New is moved forward, if moved • Orig. is divided into two activities surrounding New
sub-problem 3 • New is moved backward, if moved • Orig. is divided into two activities surrounding New
sub-problem 4 • Orig.is moved forward, if moved • New is divided into two activities surrounding Orig.
sub-problem 5 • Orig.is moved backward, if moved • New is divided into two activities surrounding Orig.
sub-problem 6
FIG. 16.5 Tactical resolution sub-problems (definitions).
6. Implementing and testing The implementation code was developed in Cþþ using an object-oriented approach to replace the previous version of the conflict resolution module in the simulator. In order to test the accuracy of the estimated model using the observed data, we also modified the code to be a stand-alone application as well. The stand-alone application reads from text files, a list of conflicts and their details as well as the socio demographic characteristics. The code then iterates over each conflict object, forms the explanatory variables based on
Sub-problem
Objective functions
1
A A D wSNEW SANEW þ wSORIG SAORIG wD NEW DNEW wORIG DORIG þ constant
2
A A D wSNEW SANEW wSORIG SAORIG wD NEW DNEW wORIG DORIG þ constant
3
A A A D D wSNEW SANEW wSORIG SAORIG1 wSORIG SAORIG2 wD NEW DNEW wORIG DORIG1 wORIG DORIG2 þ constant
4
A A A D D wSNEW SANEW wSORIG SAORIG1 wSORIG SAORIG2 wD NEW DNEW wORIG DORIG1 wORIG DORIG2 þ constant
5
A A A D D wSNEW SANEW1 wSNEW SANEW2 þ wSORIG SAORIG wD NEW DNEW1 wNEW DNEW2 wORIG DORIG þ constant
6
A A A D D wSNEW SANEW1 wSNEW SANEW2 wSORIG SAORIG wD NEW DNEW1 wNEW DNEW2 wORIG DORIG þ constant
A flexible activity scheduling conflict resolution framework Chapter | 16
TABLE 16.3 Tactical resolution sub-problems (objective functions).
317
Sub-problem (order of activities after resolution) 1 (prev, NEW, ORIG, next)
2 (prev, ORIG, NEW, next)
3 (prev; ORIG1; NEW; ORIG2; next)
Presumed direction of the change
Change should be tolerable
Activities must not overlap after resolution
SBORIG þ SAORIG 0
SBORIG þ SAORIG MaxShiftORIG
SANEW Sprev þ Dprev þ TTprev
DBORIG DAORIG 0
DBORIG DAORIG MaxShortORIG
SAORIG SANEW þ DANEW þ TTNEW
SBNEW SANEW 0 DBNEW DANEW 0
SBNEW SANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
Snext SAORIG þ DAORIG þ TTORIG
SBORIG SAORIG 0
SBORIG SAORIG MaxShiftORIG
SAORIG Sprev þ Dprev þ TTprev
DBORIG DAORIG 0 SBNEW þ SANEW 0 DBNEW DANEW 0
DBORIG DAORIG MaxShortORIG SBNEW þSANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
SANEW SAORIG þ DAORIG þ TTORIG
SBORIG SAORIG1 0
SBORIG SAORIG1 MaxShiftORIG
SAORIG1 Sprev þ Dprev þ TTprev
SBORIG SAORIG2 0
SBORIG SAORIG2 MaxShiftORIG
SANEW SAORIG1 þ DAORIG1 þ TTORIG1
DBORIG
DBORIG
SAORIG2 SANEW þ DANEW þ TTNEW
DAORIG1
DAORIG2
DAORIG1
DAORIG2
0
MaxShortORIG
DBORIG DAORIG1 0 DBORIG DAORIG2 0 SBNEW þ SANEW 0 DBNEW DANEW 0
DBORIG DAORIG1 MaxShortORIG DBORIG DAORIG2 MaxShortORIG SBNEW þ SANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
Snext SANEW þ DANEW þ TTNEW
Snext SAORIG2 þ DAORIG2 þ TTORIG2
318 PART | II New research methods and findings
TABLE 16.4 Tactical resolution sub-problems (constraints).
4 (prev; ORIG1; NEW; ORIG2; next)
SBORIG SAORIG1 MaxShiftORIG
SAORIG1 Sprev þ Dprev þ TTprev
SBORIG SAORIG2 0 DBORIG DAORIG1 DAORIG2
SBORIG SAORIG2 MaxShiftORIG DBORIG DAORIG1 DAORIG2
SANEW SAORIG1 þ DAORIG1 þ TTORIG1
0
MaxShortORIG
Snext SAORIG2 þ DAORIG2 þ TTORIG2
DBORIG DAORIG1 0 DBORIG DAORIG2 0 SBNEW SANEW 0 DBNEW DANEW 0
DBORIG DAORIG1 MaxShortORIG DBORIG DAORIG2 MaxShortORIG SBNEW SANEW MaxShiftNEW
SBORIG þ SAORIG 0
SBORIG þ SAORIG MaxShiftORIG
SANEW1 Sprev þ Dprev þ TTprev
DBORIG DAORIG 0 SBNEW SANEW1 0 SBNEW SANEW2 0 DBNEW DANEW1 DANEW2 DBNEW DANEW1 0 DBNEW DANEW2 0
DBORIG DAORIG MaxShortORIG SBNEW SANEW1 MaxShiftNEW SBNEW SANEW2 MaxShiftNEW DBNEW DANEW1 DANEW2
SAORIG SANEW1 þ DANEW1 þ TTNEW1
0
SAORIG2 SANEW þ DANEW þ TTNEW
SANEW2 SAORIG þ DAORIG þ TTORIG Snext SANEW2 þ DANEW2 þ TTNEW2
MaxShortNEW DBNEW DANEW1 MaxShortNEW DBNEW DANEW2 MaxShortNEW
6 (prev; NEW1; ORIG; NEW2; next)
0
SBORIG SAORIG MaxShiftORIG
SANEW1 Sprev þ Dprev þ TTprev
DBORIG DAORIG MaxShortORIG
SAORIG SANEW1 þ DANEW1 þ TTNEW1
SBNEW SANEW1 MaxShiftNEW SBNEW SANEW2 MaxShiftNEW DBNEW DANEW1 DANEW2
SANEW2 SAORIG þ DAORIG þ TTORIG
MaxShortNEW DBNEW DANEW1 MaxShortNEW DBNEW DANEW2 MaxShortNEW
Snext SANEW2 þ DANEW2 þ TTNEW2
319
SBORIG SAORIG 0 DBORIG DAORIG 0 SBNEW SANEW1 0 SBNEW SANEW2 0 DBNEW DANEW1 DANEW2 DBNEW DANEW1 0 DBNEW DANEW2 0
A flexible activity scheduling conflict resolution framework Chapter | 16
5 (prev; NEW1; ORIG; NEW2; next)
SBORIG SAORIG1 0
320 PART | II New research methods and findings
Ineffective to modify
(A)
Modify Orig.
Modify New
Modify Both
Delete Orig.
Delete New
Both
New
Orig. 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Observed share for each strategy
(B) Ineffective to modify
Modify Orig.
Modify New
Modify Both
Delete Orig.
Delete New
Both
New
Orig. 0%
20%
40%
60%
80%
100%
Predicted share for each strategy
FIG. 16.6 (A) Observed and (B) predicted shares for chosen strategies when a particular strategy is ineffective.
attributes of the inner objects, runs the models, and goes through the procedure shown in Fig. 16.2. According to the results, the proposed framework is fairly robust with respect to the observed and predicted shares of choosing each strategy. Fig. 16.6 shows the shares for chosen strategies, when a particular strategy does not work. Per the results, the predicted shares are at most 9.47% different from the observed shares, when separating for strategy feasibilities. Fig. 16.7 60% Predicted
Observation
50% 40% 30% 20% 10% 0% Modify Orig.
FIG. 16.7
Modify New
Modify Both
Delete Orig.
Delete New
Observed and predicted shares for chosen strategies.
A flexible activity scheduling conflict resolution framework Chapter | 16
321
provides a more aggregate basis for testing robustness of the framework. This figure depicts the predicted versus the observed shares for each strategy. Per this figure, the maximum deviation of the predicted shares from the observations is 9.8%.
7. Conclusions This study establishes a new framework to model how individuals resolve the activity conflicts that might occur while adding a new activity to their daily schedule. The framework is optimized for use in the POLARIS agent-based model and is designed as a scalable and easy-to-maintain module to facilitate future developments. The framework is composed of two levels. In the upper level, decision tree classifiers determine the strategic resolution to conflict cases depending on the individual’s decision on modifying either of the activities, modifying both of them, or ignoring either of them. Then, in the lower tactical level, a mathematical model determines exactly how the conflict is resolved, based on three types of information: 1) the requirements dictated by the upper-level strategic resolution component, 2) the parametric hazard models that determines the maximum modification tolerated by the individual, and 3) the binary choice models to estimate the propensity toward changing the start time of an activity versus its duration. An interesting feature of the framework is that it establishes an efficient linkage between the two levels, in that the upper-level model can easily obtain feedback from the lower-level model and set boundaries of the lower-level model more effectively. Attributes of the conflict itself along with the activities involved in it, along with the individual’s socio demographics are incorporated into the different components of the framework to achieve a behaviorally sound model. Day of week, activity type (i.e. mandatory, social, recreation, shopping, etc.), geometry of the conflict, duration and average frequency of conducting the activity, as well as age of the individual are among the most influential variables. The framework also has certain drawbacks that can be addressed in the future research. Future study could account for: l
l
Multi-day scheduling processes; for instance, an individual might decide to postpone a conflicting activity to another day instead of totally ignoring it. Intra-household interactions; the interactions between members of a household could add constraints to their schedule.
322 PART | II New research methods and findings
Acknowledgments This report and the work described were sponsored by the US Department of Energy (DOE) Vehicle Technologies Office (VTO) under the Systems and Modeling for Accelerated Research in Transportation (SMART) Mobility Laboratory Consortium, an initiative of the Energy Efficient Mobility Systems (EEMS) Program. The following DOE Office of Energy Efficiency and Renewable Energy (EERE) managers played important roles in establishing the project concept, advancing implementation, and providing ongoing guidance: David Anderson.
References Arentze, T.A., Timmermans, H.J., 2004. A learning-based transportation oriented simulation system. Transportation Research Part B: Methodological 38, 613e633. https://doi.org/ 10.1016/j.trb.2002.10.001. Auld, J., Hope, M., Ley, H., Sokolov, V., Xu, B., Zhang, K., 2016. POLARIS: agent-based modeling framework development and implementation for integrated travel demand and network and operations simulations. Transportation Research Part C: Emerging Technologies 64, 101e116. https://doi.org/10.1016/j.trc.2015.07.017. Auld, J., Mohammadian, A., 2012. Activity planning processes in the agent-based dynamic activity planning and travel scheduling (ADAPTS) model. Transportation Research Part A Policy Pract. 46, 1386e1403. https://doi.org/10.1016/j.tra.2012.05.017. Auld, J., Mohammadian, A.(Kourous), Doherty, S.T., 2009. Modeling activity conflict resolution strategies using scheduling process data. Transportation Research Part A Policy Pract. 43, 386e400. https://doi.org/10.1016/j.tra.2008.11.006. Bhat, C., Guo, J., Srinivasan, S., Sivakumar, A., 2004. Comprehensive econometric microsimulator for daily activity-travel patterns. Transportation Research Record Journal of the Transportation Research Board 1894, 57e66. https://doi.org/10.3141/1894-07. Chawla, N.V., Bowyer, K.W., Hall, L.O., Kegelmeyer, W.P., 2002. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research 16, 321e357. Doherty, S., Nemeth, E., Roorda, M., Miller, E., 2004. Computerized household activityscheduling survey for Toronto, Canada, area: design and assessment. Transportation Research Record Journal of the Transportation Research Board 1894, 140e149. https:// doi.org/10.3141/1894-15. Doherty, S.T., Miller, E.J., 2000. A computerized household activity scheduling survey. Transportation 27, 75e97. https://doi.org/10.1023/A:1005231926405. Javanmardi, M., Fasihozaman Langerudi, M., Shabanpour, R., Mohammadian, A., 2016. An optimization approach to resolve activity scheduling conflicts in ADAPTS activity-based model. Transportation 43, 1023e1039. https://doi.org/10.1007/s11116-016-9721-7. Miller, E., Roorda, M., 2003. Prototype model of household activity-travel scheduling. Transportation Research Record Journal of the Transportation Research Board 1831, 114e121. https://doi.org/10.3141/1831-13. Washington, S.P., Karlaftis, M.G., Mannering, F.L., 2010. Statistical and Econometric Methods for Transportation Data Analysis. CRC Press.
A flexible activity scheduling conflict resolution framework Ali Shamshiripoura, Ramin Shabanpoura, Nima Golshania, Joshua Auldb, Abolfazl Mohammadiana a
University of Illinois at Chicago, Chicago, IL, United States; bArgonne National Laboratory, Argonne, IL, United States
Chapter outline 1. Introduction 2. Polaris framework 3. The proposed conflict resolution framework 3.1 Data 4. Modeling details 4.1 Propensity to change start time and/or duration
299 301 302 304 305
4.2 Strategic resolution model 5. Tactical resolution model 6. Implementing and testing 7. Conclusions Acknowledgments References
312 315 316 321 322 322
305
1. Introduction The growing complexity of people’s daily activity-travel behavior along with the increased traffic congestion in major urban areas and more diverse policy responses to managing that congestion have motivated the development and use of microsimulation activity-based models (ABMs) as policy sensitive tools to analyze various dynamics of the travel demand. Over the past decade, several ABMs have been developed, among which the early instances are ALBATROSS (Arentze and Timmermans, 2004), TASHA (Miller and Roorda, 2003), CEMDAP (Bhat et al., 2004), and ADAPTS (Auld and Mohammadian, 2012). More recently, POLARIS (Auld et al., 2016) was built upon a similar activity demand core as ADAPTS and added value to the literature by fully integrating the demand components with network supply and operations. The demand component of POLARIS serves as a flexible and easily expandable platform that is able to relax some of the strong behavioral assumptions which were adopted by the predecessors (Auld et al., 2016). For Mapping the Travel Behavior Genome. https://doi.org/10.1016/B978-0-12-817340-4.00016-4 Copyright © 2020 Elsevier Inc. All rights reserved.
299
300 PART | II New research methods and findings
instance, the platform relaxes the assumption that all activity attributes are decided at the exact time that the activity is generated. The framework also suggests an econometric model to account for heterogeneities underlying order of planning for different activity attributes. Another prominent contribution of the framework is introducing an activity conflict resolution model to resolve the potential overlaps between the newly generated activities (hereafter, the new activities) and the ones that are already scheduled (hereafter, the original activities) in order to maintain a consistent activity-travel schedule. This study reports on a recent advancement in the activity conflict resolution model of POLARIS, factoring in more behavioral insights. In more detail, the demand model breaks down the whole day into T time steps. For each travel in each time step, it checks if the individual needs to conduct a new activity of a certain type (i.e., generating a new activity). If yes, another module, the planning attribute model, determines the sequencing of planning for different attributes of the activity. Once all the activity attributes are planned, the activity is pushed into the individual’s daily activity schedule. At this stage, many potential conflicts may occur between the new activity and any original activities that may have previously planned. The activity conflict resolution model is used to resolve the conflicts by modifying/deleting the activities as needed to maintain a consistent schedule. Indeed, this component plays a pivotal role in the overall accuracy of such computational process model frameworks, since any subtle errors in the logic of the module would cause repeated imperfections, leading to significant amount of error in later scheduling and activity execution. Several other ABMs have implemented conflict resolution strategies previously. TASHA (Miller and Roorda, 2003) follows a rule-based procedure which prioritizes some activities over others, mostly based on their type (Miller and Roorda, 2003). Later on, Doherty et al. (2004) proposed an approach specifically for the cases in which a new activity is intended to be placed between two scheduled activities while the orders are to be kept the same. The authors employed parametric hazard models to analyze the tolerable shifts in activities. Afterward, Auld et al. (2009) expanded the literature by developing a bilevel conflict resolution model based on the activity conflict instances derived out of a unique activity planning dataset, CHASE (Doherty and Miller, 2000). In the upper-level, a decision tree determines the resolution strategy depending on whether the individual decides to modify the original and the new activities. Then, in the lower-level, a rule-based module is developed based on based on the resolution strategy and the conflict situation to place the new activity in the schedule, if possible. For presentation clarity, the upperlevel classifier is henceforth called the strategic resolution model and the lower-level component is termed the tactical resolution model. More recently, to improve the later conflict resolution model, Javanmardi et al. (2016) replaced the rule-based tactical resolution model with a novel
A flexible activity scheduling conflict resolution framework Chapter | 16
301
linear mathematical program. Their motivation was to provide a more scalable and easy-to-maintain module, which is of great value in the context of largescale agent-based frameworks. In their proposed tactical resolution model, the individual is assumed to minimize the total changes in his/her activity schedule subject to the constraints imposed by the strategic resolution outcome. In this article, we are enhancing the conflict resolution model of Javanmardi et al. (2016). In our proposed model, we improve the problem formulated for the tactical resolution level to account for the inter-personal heterogeneities in how people define the settings of the problem in different situations. For instance, we relax the assumption that the maximum tolerable shifts in the activity start time and duration are fixed across all individuals by incorporating hazard models. Second, the proposed framework is able to handle more complex activity conflict situations. Third, the flow of information is also reformed such that the lower-level tactical resolution model provides feedback to the upper-level strategic resolution model. The reminder of this paper is organized as follows. Since the proposed conflict resolution model is designed to be embedded within the POLARIS framework, the next section briefly outlines the framework’s structure. Next, the proposed conflict resolution model is introduced. The dataset used to develop the models along with the processes to prepare the data are discussed afterward, followed by the elaborations on modeling details. Finally, we report the results of the implementation of the proposed framework and conclude by summarizing the paper and presenting some directions for future studies.
2. Polaris framework POLARIS (Auld et al., 2016) is an agent-based framework that integrates travel demand, network supply and network operations. This is a fullyintegrated platform in the sense that the demand components continuously integrate with the traffic simulator, and unlike many other similar platforms, the time-dependent traffic network impacts the demand components. The demand component of POLARIS, as laid out in Fig. 16.1, comprises three distinct phases of activity generation, activity planning, and activity scheduling. Activity generation deals with the decision of generating a new activity of a certain type (e.g., shopping, discretionary, personal). At each simulation time step, simultaneous competing hazard models determine the probability of generating a new activity considering the elapsed time from the execution of the previous activity of the same type. This phase only identifies if the individual needs to execute an activity of a certain type regardless of all attributes. Once a new activity is generated, the second phase determines the activity attributes namely start time, duration, location, party composition, and mode of travel to the activity location. Unlike many ABMs that assume that all
302 PART | II New research methods and findings
FIG. 16.1 Demand component of POLARIS framework.
activity attributes are decided at the time of the activity generation, POLARIS allows activity attributes to be planned at different time horizons. In other words, activity attributes can be determined in any order, and the planned attributes can affect the ones that are yet to be planned. In the last phase of the demand part (i.e., activity scheduling), the activities with all attributes being determined will be added to the schedule according to their start time and duration, and potential conflicts will be resolved. Further details about the demand component of POLARIS can be found in Auld et al. (2016).
3. The proposed conflict resolution framework The proposed conflict resolution framework is designed to add to increased accuracy and realism to the current conflict resolution module implemented in POLARIS while keeping it as simple to maintain as possible. Fig. 16.2 depicts the pseudo code of the proposed framework. The updated conflict resolution
A flexible activity scheduling conflict resolution framework Chapter | 16
303
Step 0: Input 0.1. Get the conflicting bundle Step 1: Initialization 1.1. Set , and set and according to the current 1.2. Determine and for 1.3. Determine , for Step 2: Strategic-resolution Effectiveness 2.1. Given the constraints in Eqs. 6, 7, and 8, determine which strategies are effective. Step 3: Strategic Resolution 3.1. From among the effective strategies, select the most desirable choice, . Step 4: Tactical Resolution 4.1. Given the constraints in Eqs. 6, 7, and 8 and the objective function in Eq. 5, determine the conflict resolution details. Here, it is assumed that individuals try to minimize the change. Step 5: Updating 5.1. If then set , set and according to the ; else go to Step 6. 5.2. If the conflict in is yet to be resolved, go to 1-2; else, go to 5.1. Step 6: End.
FIG. 16.2 Algorithm of the proposed framework. s, a particular strategy to resolve the conflict; p, a pair of two conflicting activities (conflict pair); ORG, the activity that is originally scheduled but is conflict with NEW; NEW, the activity that is newly generated but is in conflict with ORG; i, the activity under consideration; i ˛ fORG; NEWg; c, a set of all conflicting pairs p that share one NEW (conflict bundle); Pc, total number of conflicts in the conflicting bundle c; Sji , start time of the travel towards the ith activity in state j; Dji , duration of the ith activity in state j; A, indicating state of a modifiable activity after modification; B, indicating state of a modifiable activity before modification; ShiftCi , the probability that an individual goes for changing start time of activity i; ShortCi , the probability that an individual goes for changing duration of activity i; MaxShifti , maximum change (in min) in start time of activity i that an individual accepts; MaxShorti , maximum change (in percent) in duration of activity i that an individual accepts.
module is similar to the version by Javanmardi et al. (2016) in that it is based on a two-level process: strategic and tactical planning. However, each of the two levels are refactored to address the gaps mentioned in the introduction. The new algorithm loops over every conflicting pair p of a bundle c, resolves it, and moves to the next conflict which is not resolved yet. The terminology used in this article is introduced following Fig. 16.2. The algorithm starts with determining individuals’ propensities toward changing the original and new activities involved in each conflicting pair p. The change is measured from two aspects, start time and duration. To analyze each aspect, two econometrics models are developed, a binary logit and a parametric hazard. The binary choice formulation is used to model whether an individual is willing to change start time/duration of an activity. For those who would decide to change start time or duration of an activity, then, their tolerance is estimated using the hazard functions. In step 2, the framework determines which strategies are effective (i.e. could resolve the conflict if implemented). This is done based on the linearity feature of the tactical resolution model. Linear objective function and the set of linear constraints allow us to check feasibility of each strategy before implementing it. The task can efficiently be done by inputting the constraints to the so-called phase-1 Simplex. Outcomes of this step are then fed into step 3
304 PART | II New research methods and findings
to run the strategic resolution model. The strategy is chosen using decision trees similar to the model developed by (Auld et al., 2009), except for the fact that the new model is smart enough to use information from step 2 and foresee outcome of its prediction. Practical aspects of implementing this idea are expressed in more details, in next sections. In step 4, resolution details are derived putting together the constraints used in Step 2 and a relevant objective function to quantify the extent of the change in the individual’s schedule. The problem setup as well as specifications of the trees, the binary choice, and the hazard models are discussed in next sections, in details. After the conflicting pair p is resolved, if necessary, the framework moves on with the next p in the conflicting bundle c. Resolving the conflict between the new and one of the original activities might end up with resolving the conflict between it and rest of the original activities as well. For example, consider the case that outcome of step 3 is determined as “delete new”.
3.1 Data The CHASE (Doherty et al., 2004) activity-diary survey is used as the main source of data. Each observation in this data set represent a change in the person’s activity schedule. A procedure is therefore needed to derive activity conflicts out of the observed scheduling changes. The data processing algorithm used in this research is similar to Auld et al. (2009). After detecting a conflict, original and new activities are identified. The resolution strategy (i.e., modify original, modify new, modify both, delete original, and delete new) is determined in two steps. The first step is based on whether each activity is ultimately executed or not. If, for example, the new activity is conducted but the original is not, the conflict should be given either the resolution-type label “modify original” or “delete original.” In terms of distinguishing between modification from deletion, the activity ai is given the label “deleted” if the three following conditions are met at the same time: (1) ai is not conducted at the end of the day, (2) no instance among the whole set of recorded activity changes of the day could be found in which ai is changed to ai’ , and (3) no activity ai0 could be found that is later added to the schedule, with the same activity attributes as ai (Auld et al., 2009). The activity ai is given the label “modified” if the second condition, the third condition, or both are not met while the first is. The modified version of the activity ai, shown as aAi , is assumed to be an activity for which either of the following conditions are met: (1) a record could be found indicating that ai is changed to aAi , or (2) an activity aAi is added later during the day, with the same activity attributes as ai . Multiple feasibility checks are performed to flag the cases where two or more activities are falsely recognized as being in conflict. Similar to Auld et al. (2009), we have excluded the cases where the conflict is not resolved after the observed change in the activities involved in it. In addition, the conflict
A flexible activity scheduling conflict resolution framework Chapter | 16
305
between two activities that are both executed at the end of the day is not included. Such cases presumably occur when the overlap is due to situations other than scheduling conflicts, for example, instances of multitasking. After processing the data, a total of 1802 conflict resolution records were observed. About 30% of the conflicts were resolved by modifying the original, 4% were resolved by modifying the new, 6% were resolved by modifying both, 38% were resolved by deleting the original, and 22% were resolved by deleting the new activity. In other words, about 40% of the conflicting cases are resolved by modifying the original, new, or both, while 60% are resolved by deleting either one. After excluding irrelevant observations, the modifications made to the original and the new activities are pooled together to form a sample of 705 activity modifications. The binary choice and the hazard models are estimated using this sample. Among the observations in this sub-sample, about 61% are the cases in which only the activity duration is changed, and 5% are the cases in which only the start time is changed. This important finding reveals that an average individual is more flexible in changing duration of an activity than in start time. Fig. 16.3 shows the frequency distributions of the observed changes in start time and duration for the modified activities. Consistent with intuition, this figure supports the robustness of the data processing algorithm. As seen, a person becomes less likely to tolerate more changes in start time and/or duration of an activity as the extent of the change becomes larger. This specific pattern, also, supports the use of hazard model formulations. In order to prepare the data for training the decision tree, the data prepared in the previous steps is first enriched by a set of dummy variables derived as different combinations of the three binary variables: “effective if only modifying original”, “effective if only modifying new”, and “effective if modifying both”. Values of these variables are populated feeding output of the binary choice and the hazard models into step 2 of the framework, strategic-resolution effectiveness (implementation details are provided in the next two sections).
4. Modeling details This section is devoted to more detailed discussions on the models estimated for each step of the framework. This section encompasses specifications of the hazard models, the decision tree, and the proposed set of linear programs.
4.1 Propensity to change start time and/or duration Binary logit models determine if the start time and/or duration of an activity is changed. Then, fully parametric hazard models determine the extent of the change in start time and/or duration, for those who decide to change each. Generally, hazard-based models estimate the probability for occurrence of an event between time t and t þ dt, given that it has not happened until time t.
306 PART | II New research methods and findings
FIG. 16.3 Observed changes in (A) start time and (B) durations of activities while resolving the conflicts.
Using the cumulative density function of the duration (FðtÞ) and its probability density function (f ðtÞ) the survival and hazard functions can be formulated as: SðtÞ ¼ 1 FðtÞ lðtÞ ¼
d ln SðtÞ f ðtÞ ¼ dt SðtÞ
(16.1) (16.2)
here, SðtÞ is the survival function, denotes the probability that extent of change in duration/start time is greater than t; and lðtÞ is the hazard rate, which in our context represents the probability that the person does not tolerate the modification t given that he/she tolerates modifications bellow t. In fully parametric hazard models, we assume a parametric form for the distribution of survival time. The commonly popular hazard functions are Exponential, Log-logistic, Log-Normal, Weibull, and Gamma. Through testing different functional forms, it is observed that the Exponential and Weibull distributions result in the best
A flexible activity scheduling conflict resolution framework Chapter | 16
307
fitted hazard models for the modifications in the start time and duration, respectively. These functions are as follows (Washington et al., 2010): Exponential : Weibull :
lðtÞ ¼ l
(16.3)
lðtÞ ¼ ðlPÞðltÞP1
(16.4)
where l and P are estimable parameters, and q is the variance of the unobserved heterogeneity term. Further, robust standard errors are estimated for the hazard models to make sure of legitimacy of the proportional hazard assumptions. The estimated models are outlined in Table 16.3. The variables introduced into the models sit in three groups of individual characteristics, activity characteristics, and type of the conflict (as depicted in Fig. 16.4). In a nutshell, age, day of week, conflict type, activity type, duration of the activity before modification, activity frequency and travel time toward the activity location are among the most important variables used in the models. Per the results, older individuals tolerate longer shifts in start time of their activities and shorter duration alterations. This makes sense given that elderly individuals have more free time in their schedules, and therefore, they have more opportunities to move an activity to a sooner/later time; as a result, they would need shorter duration alteration. Individuals’ with busier schedules during the weekdays have lower tolerances to start time changes, which is supported by the results of this study. The results also confirm that, in case there is enough time surrounding an activity to accommodate without duration alterations, an individual is more likely to do so. According to Table 16.1, duration of longer activities is more likely to be modified rather than the start time. Also, an individual is more likely to accept a change in duration of a frequent activity. This makes sense, as more frequent activities can possibly make up for an insufficient duration allocated to them. Conforming to the common sense, an individual is more likely to change start time of the original and duration of the new activity in a type 1 conflict, and to change start time of the new and duration of the original activity in a type 2 conflict. Also, the conflicts of type 3 and 4 are more probable to be resolved by changing start time of either of the activities, as compared to the conflicts of type 1 and 2. According to the results, start time of mandatory activities is significantly less likely to be changed compared to other activity types. Also, if an activity involved in a conflict is shopping, the individual would be more flexible in changing duration and start time of the other activity that conflicts with it.
Type 1
Type 2
Type 3
FIG. 16.4 Conflict types by geography.
Typee 4
Start time model Explanatory variable
Duration model
Binary logit
Hazard
Binary logit
Hazard
Effect on original
0.009
0.020***
0.006*
Effect on new
0.009
0.020***
0.006*
Individual: age
Activity: frequency of original 0.042**
0.130***
Effect on original
0.279**
0.539**
Effect on new
0.279**
0.539**
Effect on original Activity: enough free time surrounding the activity
Activity: free time before new, in a type 1 conflict Effect on new
0.049***
Activity: natural logarithm of duration before modification Effect on original
0.426**
Effect on new
0.426**
Activity: new is not flexible in start time Effect on new
0.561***
308 PART | II New research methods and findings
TABLE 16.1 Model estimation results.
Activity: original is flexible in duration
Activity: original is mandatory Effect on original
0.425*
Activity: original is social Effect on original
0.843***
0.805***
0.843***
0.805***
Activity: new is social Effect on new Activity: original is recreation Effect on original Effect on new
0.345** 1.585***
Activity: new is recreation Effect on original
1.585***
Effect on new
0.345**
Activity: original is shopping Effect on new
0.276**
Activity: new is shopping Effect on original
0.731***
0.276**
309
Continued
A flexible activity scheduling conflict resolution framework Chapter | 16
0.420*
Effect on original
Start time model Explanatory variable
Binary logit
Hazard
Activity: original is eating meal Effect on original
0.944***
Activity: new is eating meal Effect on new
0.944***
Activity: original is sleeping 1.152***
Effect on original Effect on new
1.364**
Activity: original is household errand Effect on new
2.489***
Activity: weekday Effect on original
0.933***
Effect on new
0.933***
Activity: travel time to original Effect on original
0.002***
Duration model Binary logit
Hazard
310 PART | II New research methods and findings
TABLE 16.1 Model estimation results.dcont’d
Conflict: type 1 4.253***
Effect on new
1.196***
Conflict: type 2 Effect on original
0.719***
Effect on new
0.698**
Conflict: type 3 Effect on original
1.207
o
Conflict: type 4 1.870***
Effect on original Conflict: type 3 or 4 Equal effects on original and new
0.618***
Constant Effect on original
1.584***
4.171***
0.853
0.632***
Effect on new
1.584***
4.171***
0.853
0.632***
IID EV
Exponential
IID EV
Weibull
Error term distribution Note: Symbols ***, **, * and
o
stand for significance level of 0.01, 0.05, 0.1, and 0.15.
A flexible activity scheduling conflict resolution framework Chapter | 16
Effect on original
311
312 PART | II New research methods and findings
Similar results are derived with regards to the start time of a recreational activity, although an opposite relationship holds for recreation durations. In other words, people are more to alter the duration of their recreational activities when having to resolve the scheduling conflicts caused by the activity (whether it is the original activity or the new). Yet, they try to keep start time of their recreational activities unchanged. If an activity is social, the individual would be more flexible on modifying the activity itself rather than the conflicting, both in terms of duration and start time. When an activity is eating a meal out, it is more probable to undergo a start time change. The results also reveal that people usually try not to change start time of a sleeping activity. In other words, they try to go to sleep at the time they usually do.
4.2 Strategic resolution model Using the three feasibility dummy variables generated in the data processing phase, the whole feasible region could be segmented into 5 distinct regions. The segments along with the observed shares of each strategy type can be summarized as: l
l
l
l
l
Any modification is effective (modify original: 23.8%, modify new: 5.6%, modify both: 7.6%, delete original: 31.7%, and delete new: 31.4%). Modifying original is effective while new is not (modify original: 33.5%, modify new: 0.0%, modify both: 7.5%, delete original: 40.8%, and delete new: 18.2%). Modifying original is not effective while new is (modify original: 0.0%, modify new: 3.4%, modify both: 7.4%, delete original: 42.6%, and delete new: 46.6%). Modifying a single activity is not effective while modifying both is (modify original: 0.0%, modify new: 0.0%, modify both: 7.7%, delete original: 58.2%, and delete new: 34.1%). No modifying is effective (modify original: 0.0%, modify new: 0.0%, modify both: 0.0%, delete original: 71.8%, and delete new: 28.2%).
Specific to each of the five segments, a unique decision tree is trained using the data. Doing so, the trained tree is guaranteed only to predict strategies that are feasible to follow by the tactical resolution step. As can be seen above, the data available for all segments is highly imbalanced in terms of the strategy shares, and this could lead to improper training of the trees. To overcome such issues and achieve balanced data sets, the Synthetic Minority Over-sampling Technique (SMOTE) is used to oversample the under-represented strategies using the k-nearest neighbors classifier (Chawla et al., 2002). The classifier looks into 8 neighbors at each step. Further, we conducted a fourfold cross-validation experiment to make sure the accuracy results are true representatives of the trained trees. Table 16.2 summarizes the accuracy results achieved for each of the five trees.
Strategies
Feasibility categories
Accuracy metrics
Any modification is effective
Accuracya b
Precision Recall
c d
F1-score Modifying original is effective while new is not
Modifying original is not effective while new is
Modifying one activity is not effective while modifying both is
Modify original
Modify new
Modify both
Overall Delete original
Delete new 0.54
0.57
0.91
0.65
0.47
0.67
0.53
0.88
0.68
0.52
0.64
0.55
0.89
0.67
0.49
0.65
Accuracy
0.61
Precision
0.60
NA
0.85
0.66
0.76
Recall
0.51
NA
0.93
0.66
0.78
F1-score
0.55
NA
0.89
0.66
0.77
Accuracy
0.71
Precision
NA
0.75
0.96
0.63
0.65
Recall
NA
0.82
0.92
0.67
0.62
F1-score
NA
0.78
0.94
0.65
0.63
Accuracy
0.78 NA
NA
0.82
0.70
0.79
Recall
NA
NA
0.70
0.95
0.66
F1-score
NA
NA
0.76
0.81
0.72
313
Precision
A flexible activity scheduling conflict resolution framework Chapter | 16
TABLE 16.2 Accuracy indices calculated for the set of trees.
Continued
Strategies
Feasibility categories
Accuracy metrics
No modifying is effective
Accuracy
Modify original
Modify new
Delete original
Delete new 0.79
Precision
NA
NA
NA
0.92
0.96
Recall
NA
NA
NA
0.96
0.93
F1-score
NA
NA
NA
0.94
0.95
ðTrue positive þtrue negativeÞ =ðtrue positive þtrue negative þfalse positive þfalse negativeÞ. b True positive=total predicted positive. c True positive=total actual positive. d Precision recall=precision þ recall. a
Modify both
Overall
314 PART | II New research methods and findings
TABLE 16.2 Accuracy indices calculated for the set of trees.dcont’d
A flexible activity scheduling conflict resolution framework Chapter | 16
315
5. Tactical resolution model We modified the program outlined in (Javanmardi et al., 2016) by incorporating the information from binary choice and hazard models to bring more realism into both the objective function and the constraints as: Min:Changep ¼ ð1 ShiftCORG Þ SBORG SA ORG B A þ ð1 ShortCORG Þ DBORG DA ORG þ ð1 ShiftCNEW Þ SNEW SNEW þ ð1 ShortCNEW Þ DBNEW DA NEW (16.5) S.T.: Change should be tolerable
(16.6)
Activities must not overlap after resolution
(16.7)
Non negativity conditions
(16.8)
The assumption that individuals try to minimize the change in their schedule when deciding on how to resolve a conflict, forces the model to come up with schedules in which duration of activities are not increased compared to their duration before the change. That is, even if shifting the activity to less occupied time intervals during the day provides enough room for increasing its duration, the individual would not do so, since he/she is assumed to keep the changes to the minimum extent possible. Regarding the start time, however, the model shown in Eq. (16.5) does allow for shifting both forward or backward, and this flexibility comes at the cost of losing linearity. To linearize Eq. (16.5), it can be broken down into a set of subproblems depending on direction of the shift. The sub-problems considered in this article are shown in Fig. 16.5. After all sub-problems are solved, the answer corresponding to the minimum value of Eq. (16.8) is selected as the global solution to the problem. Breaking down the objective function into the sub-problems and further simplifying the problem yields in the 6 objective functions shown in A A A A A A Table 16.3, where SA ORIG , DORIG , SNEW , DNEW , SORIG1 , SORIG2 , SNEW1 , and A SNEW2 are the decision variables. In this table, the constant term denotes summation of the terms which can be dropped from the objective functions without affecting the final results; and wSORG ¼ ð1 ShiftCORG Þ; wSNEW ¼ D ð1 ShiftCNEW Þ, wD ORG ¼ ð1 ShortCORG Þ; and wNEW ¼ ð1 ShortCNEW Þ are the case-specific coefficients derived according to the results of the hazard and binary choice models. The constraints associated with each sub-problem are specified in Table 16.4 (non-negativity constraints are skipped).
316 PART | II New research methods and findings
base conditions • New is moved backward, if moved • Orig. is moved forward, if moved
sub-problem 1 • New is moved forward, if moved • Orig. is moved backward, if moved
sub-problem 2 • New is moved forward, if moved • Orig. is divided into two activities surrounding New
sub-problem 3 • New is moved backward, if moved • Orig. is divided into two activities surrounding New
sub-problem 4 • Orig.is moved forward, if moved • New is divided into two activities surrounding Orig.
sub-problem 5 • Orig.is moved backward, if moved • New is divided into two activities surrounding Orig.
sub-problem 6
FIG. 16.5 Tactical resolution sub-problems (definitions).
6. Implementing and testing The implementation code was developed in Cþþ using an object-oriented approach to replace the previous version of the conflict resolution module in the simulator. In order to test the accuracy of the estimated model using the observed data, we also modified the code to be a stand-alone application as well. The stand-alone application reads from text files, a list of conflicts and their details as well as the socio demographic characteristics. The code then iterates over each conflict object, forms the explanatory variables based on
Sub-problem
Objective functions
1
A A D wSNEW SANEW þ wSORIG SAORIG wD NEW DNEW wORIG DORIG þ constant
2
A A D wSNEW SANEW wSORIG SAORIG wD NEW DNEW wORIG DORIG þ constant
3
A A A D D wSNEW SANEW wSORIG SAORIG1 wSORIG SAORIG2 wD NEW DNEW wORIG DORIG1 wORIG DORIG2 þ constant
4
A A A D D wSNEW SANEW wSORIG SAORIG1 wSORIG SAORIG2 wD NEW DNEW wORIG DORIG1 wORIG DORIG2 þ constant
5
A A A D D wSNEW SANEW1 wSNEW SANEW2 þ wSORIG SAORIG wD NEW DNEW1 wNEW DNEW2 wORIG DORIG þ constant
6
A A A D D wSNEW SANEW1 wSNEW SANEW2 wSORIG SAORIG wD NEW DNEW1 wNEW DNEW2 wORIG DORIG þ constant
A flexible activity scheduling conflict resolution framework Chapter | 16
TABLE 16.3 Tactical resolution sub-problems (objective functions).
317
Sub-problem (order of activities after resolution) 1 (prev, NEW, ORIG, next)
2 (prev, ORIG, NEW, next)
3 (prev; ORIG1; NEW; ORIG2; next)
Presumed direction of the change
Change should be tolerable
Activities must not overlap after resolution
SBORIG þ SAORIG 0
SBORIG þ SAORIG MaxShiftORIG
SANEW Sprev þ Dprev þ TTprev
DBORIG DAORIG 0
DBORIG DAORIG MaxShortORIG
SAORIG SANEW þ DANEW þ TTNEW
SBNEW SANEW 0 DBNEW DANEW 0
SBNEW SANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
Snext SAORIG þ DAORIG þ TTORIG
SBORIG SAORIG 0
SBORIG SAORIG MaxShiftORIG
SAORIG Sprev þ Dprev þ TTprev
DBORIG DAORIG 0 SBNEW þ SANEW 0 DBNEW DANEW 0
DBORIG DAORIG MaxShortORIG SBNEW þSANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
SANEW SAORIG þ DAORIG þ TTORIG
SBORIG SAORIG1 0
SBORIG SAORIG1 MaxShiftORIG
SAORIG1 Sprev þ Dprev þ TTprev
SBORIG SAORIG2 0
SBORIG SAORIG2 MaxShiftORIG
SANEW SAORIG1 þ DAORIG1 þ TTORIG1
DBORIG
DBORIG
SAORIG2 SANEW þ DANEW þ TTNEW
DAORIG1
DAORIG2
DAORIG1
DAORIG2
0
MaxShortORIG
DBORIG DAORIG1 0 DBORIG DAORIG2 0 SBNEW þ SANEW 0 DBNEW DANEW 0
DBORIG DAORIG1 MaxShortORIG DBORIG DAORIG2 MaxShortORIG SBNEW þ SANEW MaxShiftNEW DBNEW DANEW MaxShortNEW
Snext SANEW þ DANEW þ TTNEW
Snext SAORIG2 þ DAORIG2 þ TTORIG2
318 PART | II New research methods and findings
TABLE 16.4 Tactical resolution sub-problems (constraints).
4 (prev; ORIG1; NEW; ORIG2; next)
SBORIG SAORIG1 MaxShiftORIG
SAORIG1 Sprev þ Dprev þ TTprev
SBORIG SAORIG2 0 DBORIG DAORIG1 DAORIG2
SBORIG SAORIG2 MaxShiftORIG DBORIG DAORIG1 DAORIG2
SANEW SAORIG1 þ DAORIG1 þ TTORIG1
0
MaxShortORIG
Snext SAORIG2 þ DAORIG2 þ TTORIG2
DBORIG DAORIG1 0 DBORIG DAORIG2 0 SBNEW SANEW 0 DBNEW DANEW 0
DBORIG DAORIG1 MaxShortORIG DBORIG DAORIG2 MaxShortORIG SBNEW SANEW MaxShiftNEW
SBORIG þ SAORIG 0
SBORIG þ SAORIG MaxShiftORIG
SANEW1 Sprev þ Dprev þ TTprev
DBORIG DAORIG 0 SBNEW SANEW1 0 SBNEW SANEW2 0 DBNEW DANEW1 DANEW2 DBNEW DANEW1 0 DBNEW DANEW2 0
DBORIG DAORIG MaxShortORIG SBNEW SANEW1 MaxShiftNEW SBNEW SANEW2 MaxShiftNEW DBNEW DANEW1 DANEW2
SAORIG SANEW1 þ DANEW1 þ TTNEW1
0
SAORIG2 SANEW þ DANEW þ TTNEW
SANEW2 SAORIG þ DAORIG þ TTORIG Snext SANEW2 þ DANEW2 þ TTNEW2
MaxShortNEW DBNEW DANEW1 MaxShortNEW DBNEW DANEW2 MaxShortNEW
6 (prev; NEW1; ORIG; NEW2; next)
0
SBORIG SAORIG MaxShiftORIG
SANEW1 Sprev þ Dprev þ TTprev
DBORIG DAORIG MaxShortORIG
SAORIG SANEW1 þ DANEW1 þ TTNEW1
SBNEW SANEW1 MaxShiftNEW SBNEW SANEW2 MaxShiftNEW DBNEW DANEW1 DANEW2
SANEW2 SAORIG þ DAORIG þ TTORIG
MaxShortNEW DBNEW DANEW1 MaxShortNEW DBNEW DANEW2 MaxShortNEW
Snext SANEW2 þ DANEW2 þ TTNEW2
319
SBORIG SAORIG 0 DBORIG DAORIG 0 SBNEW SANEW1 0 SBNEW SANEW2 0 DBNEW DANEW1 DANEW2 DBNEW DANEW1 0 DBNEW DANEW2 0
A flexible activity scheduling conflict resolution framework Chapter | 16
5 (prev; NEW1; ORIG; NEW2; next)
SBORIG SAORIG1 0
320 PART | II New research methods and findings
Ineffective to modify
(A)
Modify Orig.
Modify New
Modify Both
Delete Orig.
Delete New
Both
New
Orig. 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Observed share for each strategy
(B) Ineffective to modify
Modify Orig.
Modify New
Modify Both
Delete Orig.
Delete New
Both
New
Orig. 0%
20%
40%
60%
80%
100%
Predicted share for each strategy
FIG. 16.6 (A) Observed and (B) predicted shares for chosen strategies when a particular strategy is ineffective.
attributes of the inner objects, runs the models, and goes through the procedure shown in Fig. 16.2. According to the results, the proposed framework is fairly robust with respect to the observed and predicted shares of choosing each strategy. Fig. 16.6 shows the shares for chosen strategies, when a particular strategy does not work. Per the results, the predicted shares are at most 9.47% different from the observed shares, when separating for strategy feasibilities. Fig. 16.7 60% Predicted
Observation
50% 40% 30% 20% 10% 0% Modify Orig.
FIG. 16.7
Modify New
Modify Both
Delete Orig.
Delete New
Observed and predicted shares for chosen strategies.
A flexible activity scheduling conflict resolution framework Chapter | 16
321
provides a more aggregate basis for testing robustness of the framework. This figure depicts the predicted versus the observed shares for each strategy. Per this figure, the maximum deviation of the predicted shares from the observations is 9.8%.
7. Conclusions This study establishes a new framework to model how individuals resolve the activity conflicts that might occur while adding a new activity to their daily schedule. The framework is optimized for use in the POLARIS agent-based model and is designed as a scalable and easy-to-maintain module to facilitate future developments. The framework is composed of two levels. In the upper level, decision tree classifiers determine the strategic resolution to conflict cases depending on the individual’s decision on modifying either of the activities, modifying both of them, or ignoring either of them. Then, in the lower tactical level, a mathematical model determines exactly how the conflict is resolved, based on three types of information: 1) the requirements dictated by the upper-level strategic resolution component, 2) the parametric hazard models that determines the maximum modification tolerated by the individual, and 3) the binary choice models to estimate the propensity toward changing the start time of an activity versus its duration. An interesting feature of the framework is that it establishes an efficient linkage between the two levels, in that the upper-level model can easily obtain feedback from the lower-level model and set boundaries of the lower-level model more effectively. Attributes of the conflict itself along with the activities involved in it, along with the individual’s socio demographics are incorporated into the different components of the framework to achieve a behaviorally sound model. Day of week, activity type (i.e. mandatory, social, recreation, shopping, etc.), geometry of the conflict, duration and average frequency of conducting the activity, as well as age of the individual are among the most influential variables. The framework also has certain drawbacks that can be addressed in the future research. Future study could account for: l
l
Multi-day scheduling processes; for instance, an individual might decide to postpone a conflicting activity to another day instead of totally ignoring it. Intra-household interactions; the interactions between members of a household could add constraints to their schedule.
322 PART | II New research methods and findings
Acknowledgments This report and the work described were sponsored by the US Department of Energy (DOE) Vehicle Technologies Office (VTO) under the Systems and Modeling for Accelerated Research in Transportation (SMART) Mobility Laboratory Consortium, an initiative of the Energy Efficient Mobility Systems (EEMS) Program. The following DOE Office of Energy Efficiency and Renewable Energy (EERE) managers played important roles in establishing the project concept, advancing implementation, and providing ongoing guidance: David Anderson.
References Arentze, T.A., Timmermans, H.J., 2004. A learning-based transportation oriented simulation system. Transportation Research Part B: Methodological 38, 613e633. https://doi.org/ 10.1016/j.trb.2002.10.001. Auld, J., Hope, M., Ley, H., Sokolov, V., Xu, B., Zhang, K., 2016. POLARIS: agent-based modeling framework development and implementation for integrated travel demand and network and operations simulations. Transportation Research Part C: Emerging Technologies 64, 101e116. https://doi.org/10.1016/j.trc.2015.07.017. Auld, J., Mohammadian, A., 2012. Activity planning processes in the agent-based dynamic activity planning and travel scheduling (ADAPTS) model. Transportation Research Part A Policy Pract. 46, 1386e1403. https://doi.org/10.1016/j.tra.2012.05.017. Auld, J., Mohammadian, A.(Kourous), Doherty, S.T., 2009. Modeling activity conflict resolution strategies using scheduling process data. Transportation Research Part A Policy Pract. 43, 386e400. https://doi.org/10.1016/j.tra.2008.11.006. Bhat, C., Guo, J., Srinivasan, S., Sivakumar, A., 2004. Comprehensive econometric microsimulator for daily activity-travel patterns. Transportation Research Record Journal of the Transportation Research Board 1894, 57e66. https://doi.org/10.3141/1894-07. Chawla, N.V., Bowyer, K.W., Hall, L.O., Kegelmeyer, W.P., 2002. SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research 16, 321e357. Doherty, S., Nemeth, E., Roorda, M., Miller, E., 2004. Computerized household activityscheduling survey for Toronto, Canada, area: design and assessment. Transportation Research Record Journal of the Transportation Research Board 1894, 140e149. https:// doi.org/10.3141/1894-15. Doherty, S.T., Miller, E.J., 2000. A computerized household activity scheduling survey. Transportation 27, 75e97. https://doi.org/10.1023/A:1005231926405. Javanmardi, M., Fasihozaman Langerudi, M., Shabanpour, R., Mohammadian, A., 2016. An optimization approach to resolve activity scheduling conflicts in ADAPTS activity-based model. Transportation 43, 1023e1039. https://doi.org/10.1007/s11116-016-9721-7. Miller, E., Roorda, M., 2003. Prototype model of household activity-travel scheduling. Transportation Research Record Journal of the Transportation Research Board 1831, 114e121. https://doi.org/10.3141/1831-13. Washington, S.P., Karlaftis, M.G., Mannering, F.L., 2010. Statistical and Econometric Methods for Transportation Data Analysis. CRC Press.