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where ta 1 ⤠t a 2 ⤠ta 3 ⤠ta 4 are the cutoff points dividing the day into four intervals. The intervals define start times at which the activity would not generate any utility (the first and last intervals), the utility is at a maximum (the third interval), and the utility is some fraction of the maximum. Traveling involves effort and sometimes monetary costs, depending on the transport mode used. If it is assumed that travel time is not intrinsically rewarding, the utility of a travel episode is modeled as a negative function of duration. Scheduling Method The model assumes that individualsâ abilities and priori- ties to optimize a schedule are limited by cognitive con- straints and the amount of mental effort that they are willing to make. To find reasonable solutions within the constraints, the model uses a heuristic scheduling method. The heuristic assumes an existing schedule (which may be empty) as given. The schedule should be consistent, and the result of the heuristic is again a consistent schedule with a higher or equal utility value. The heuristic searches for and implements improvements by considering one operation at a time. In the order in which they are consid- ered, these include (i) inserting activities, (ii) substituting activities, (iii) repositioning activities, (iv) deleting activi- ties, (v) changing locations, (vi) changing trip-chaining choices, and (vii) changing transport modes. A single oper- ation is repeated until no more improvement has been made. If the schedule has changed in any one of these steps, the process is repeated. Each step in this procedure is in itself an iterative process that can be written as 1. For all options of <Operation>, a. Implement the option, b. Make the schedule consistent, c. Optimize durations, d. Optimize start times, e. Evaluate the scheduleâs utility, and f. Restore the schedule (i.e., undo Substep a). 2. If <Best Option> improves the schedule, then a. Implement <Best Option> and b. Repeat from Step 1. where <Operation> denotes a specific operation consid- ered in Steps i through vii. As implied by this procedure, operations are always evaluated under conditions of con- sistency and optimal duration and timing decisions. The heuristic nature of this method is emphasized. In none of the steps is the evaluation of options exhaustive. By iter- atively applying the search procedure, the method may still find good solutions. Some pairs of operations, such as mode and location choices, may interact strongly. It is possible to extend the heuristic with a limited number of simultaneous choices so as to reduce the risk of getting trapped in a local optimum. Travel episodes are scheduled as part of activity episodes. The trip to the location and the trip to home after having conducted the activity are considered attri - butes of an activity. The return-home trip is empty if the agent decides to travel to the next activity location directly without first returning home (referred to as trip chaining). Default settings are used for each activity attribute when it is inserted in the schedule by an inser- tion or a substitution operation. Making the schedule consistent (Step 1b) is a subrou- tine that implements minimal adaptations needed to make a schedule consistent with constraints, such as that the individual should return home at the end of the day, start from home at the beginning of the day, use the same transport mode (if vehicle based) for trips that are chained, and so on. Travel times are initially set to defaults and updated each time the destination location, origin location, or transport mode changes. Schedule Implementation It is assumed that an activity schedule is implemented sequentially during the day. To allow for possible resched- uling behavior, it is assumed that agents decide whether to reschedule their activities at every node of the transporta- tion network and after completing each activity. Travel times on links are estimated as a function of the number of agents using the link simultaneously for a given time step by means of the following well-known method: (5) where ti = updated travel time on link i, ti f = free-floating travel time, vi = traffic intensity, ci = capacity of the link, and α and β = parameters. The estimates are used to determine actual travel times in that time step. Unexpected travel times and unforeseen events are two possible causes for a mismatch between a scheduled and actual end time of an episode. A time-surplus or time-lack situation at the moment of completing an episode triggers rescheduling. Learning After having executed the schedule, an agent updates his knowledge about choice sets, default settings of activi- 73MODELING SHORT-TERM DYNAMICS IN ACTIVITY-TRAVEL PATTERNS t t v ci i f i i= +[ ( / ) ]1 α β