Embedding risk attitudes in a scheduling model: Application to the study of commuting departure time

Traditionally, the value of travel time savings (VTTS) and the value of reliability (or reduced variability) are estimated within a linear utility functional form, which assumes risk-neutral attitudes for decision makers. In this paper, we develop non-linear scheduling models to address both risk attitude and preference in the context of a stated choice experiment of car commuters facing risky choices where the risk is associated with the trip time. We also investigate unobserved between-individual heterogeneity in time-related parameters and risk attitudes using a mixed multinomial logit (MMNL) model. More importantly, we calculate the willingness to pay values for reducing the mean travel time and variability (earlier/later than the preferred arrival time) within the non-linear scheduling framework. This model is then used to estimate preferred departure times for commuters, assuming that random link capacities are the source of travel time variability. Results show that the more variable travel times are, the earlier commuters depart, and that the non-linear scheduling model predicts earlier optimal departure times than the traditional linear scheduling model. Some important issues related to modelling non-linearity are also discussed