The use of space–time constraints for the selection of discretionary activity locations Andreas Justen a,⇑ , Francisco J. Martínez b , Cristián E. Cortés b a German Aerospace Center (DLR), Institute of Transport Research, Rutherfordstr. 2, 12489 Berlin, Germany b University of Chile, Faculty of Physical and Mathematical Sciences, Division of Transport Engineering, Blanco Encalada 2002, Santiago, Chile article info Keywords: Space–time constraints Potential path area Location choice Discretionary activity Detour factor abstract The development of methods of studying individuals’ selection of discretionary activity locations remains a challenge for empirical analysts and transport modelers. Time geography and, in particular, the concept of space–time constraints provides a useful framework for these selection processes. In this work we empirically determine space–time constraints from the Chilean household and travel survey. Based on a specific activity pattern example, where trips are made from home to work to a discretionary activity and back home, we estimate detour factors. Detour factors describe the spatial deviations that are made from the home-work axis to conduct the discretionary activity. Using GIS we estimate potential path areas (PPAs), where discretionary activities may be located. Within the PPAs, applying a time constraint that is the maximum daily travel time refines the selection of discretionary activity locations. The thresh- olds of the daily travel time vary according to the PPA-size and mode combinations. We were able to reproduce between 38% and 72% of the discretionary location choices observed in the survey (according to the rigor of the constraints applied). Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction and background The objective of this article is to introduce a method applicable in transport models of different kinds to identify a set of discretion- ary activity locations. In today’s transport planning practice, aggre- gate four-stage models of transport demand still dominate the scene. Only a few newer approaches, such as activity-based trans- port models, have achieved practical suitability (Davidson et al., 2007, p. 469; Bradley et al., 2010, p. 2). With regard to the abilities of the models to simulate individual or group-based spatial choice behavior, advantages and disadvantages are well documented by different authors (see e.g. Cascetta, 2009; Hensher and Button, 2008). Common to both model types is that they are able to predict the home-work relation, i.e. the commuting behavior, relatively well. This is often because of reliable empirical bases regarding the geo-coded origin (O) and destination (D) locations of the trip, and better information about number, type and location of jobs. This is different for discretionary activities (e.g. shopping, leisure, private errands) where location choices are much more flexible and spatially disperse in the study area. The methods applied in the models to achieve a behaviorally sound estimation of the spa- tial distribution of discretionary trips remains an important and ongoing research issue. In this context, time geography and space–time constraints pro- vide an important methodological framework for the analysis and prediction of individual activity and travel behavior. First intro- duced by Hägerstrand (1970), the theory has been refined and ap- plied to develop simulations of individual activity and travel behavior (Lenntorp, 1978) or to measure accessibility (e.g. Miller, 1991; Kwan, 1998; Kim and Kwan, 2003). Regarding the modeling of travel behavior, space–time constraints support identifying loca- tions spatially pertaining to an area delimited by the constraints set. Most generally, the inclusion of space–time constraints limits the accessibility of choice options and the number of possible spa- tial paths (Miller, 2004). One positive effect of applying constraints is the lower number of feasible choice options to consider in the analysis. With respect to transport models, this has led over time to the development of various time/space-based approaches and models of travel demand (Timmermans et al., 2002). Following the time geographic concept, the area resulting from the application of a set of space–time constraints is a prism. Its shape is defined by the activity locations, the distances between them and the time available for travel and activity participation (Burns, 1979). The three-dimensional area delimited by the activity locations and the time spent to conduct activities or travel between them is called the potential path space (PPS). The PPS contains all points in space–time that can be reached given an available time- budget. For practical applications more important is the projection of the prism onto the two-dimensional geographical space, that is the potential path area (PPA) (Miller, 1991, 2004; Dijst, 1999). The 0966-6923/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtrangeo.2013.10.009 ⇑ Corresponding author. Tel.: +41 31 3234158; fax: +41 31 3227869. E-mail address: andreas.justen@are.admin.ch (A. Justen). Journal of Transport Geography 33 (2013) 146–152 Contents lists available at ScienceDirect Journal of Transport Geography journal homepage: www.elsevier.com/locate/jtrangeo