## SCAPES ? a Dynamic Microeconomic Model of Activity Scheduling

### Authors

R D Jonsson, A KarlstrÃ¶m, Royal Institute of Technology, SE

### Description

SCAPES, a model scheduling daily activity patterns, is presented. It treats sequential decision making under uncertainty in a framework consistent with microeconomics.

### Abstract

We present a model, SCAPES, scheduling daily activity patterns, that treat sequential decision making under uncertainty in a framework consistent with microeconomics. The scheduling is modelled as a Markov Decision Process, which allows for an explicitly sequential decision making in an uncertain environment. For instance, the travel time to work in the morning may be stochastic, although with a known distribution. They may be taken into account when deciding departure time for the work trip in the morning. When arriving to work, the uncertainty is dissolved. Variation in travel time for one trip can thus affect the schedule for the whole day. Computer experiments show that a emph{dynamic programming} approach is computationally efficient enough that we can solve the utility maximising problem of one individual not only for one day, but also introduce between-day interdependencies. This feature can for instance show up as a larger than usual travel time causing a shopping trip being postponed to the next day.

The computer experiments show that it is reasonable to expect that the model is possible to estimate on survey data, especially since estimation of dynamic programming models is common practice in other fields, such as labour economics. We argue that a microeconomic framework is needed for any activity based model that is to be used for welfare evaluation of policies. The model should also be dynamically consistent. The main advantage of the modelling approach we suggest is that it retains the sequential nature of daily scheduling decisions, and that it can be useful when analysing effects of travel time uncertainty and congestion charges. We plan to develop and use the model for the evaluation of the congestion charge experiment under way in Stockholm.

Another example of where a model of this kind could be useful is to analyse to what extent time constraints are causing congestion. It might for instance be the case that flexible working hours are partly off-set by non-flexible school hours, and that at least one of the parents gets a narrow time window of travel. Also, since the model deals with the whole day, a change in the time constraints in the morning would affect the travel pattern over the whole day.

The prototype of SCAPES described here was designed to illustrate the possibilities of the dynamic programming approach to activity based modelling of travel behaviour. We solve the Markov Decision Problem as a dynamic programming problem, where each day is treated as a finite horizon problem. The between day interdependencies are viewed as a dynamic programming problem with an infinite time horizon. By imposing some reasonable constraints on schedules, such as that the agents start and end their days at home, allows us to contract the state space of the infinite horizon problem to a very manageable size. The combined problem is solved using a policy iteration algorithm.

The computer experiments, which include some examples of applying policy measures, show promising model responsiveness. At the same time, we acknowledge that further development is needed in order to use these techniques in a household activity model. However, we believe that having efficient methods for the one-individual problem will prove useful in the development of such a household model. This is left for further research.

#### Publisher

Association for European Transport