Embedding Risk Attitudes in a Scheduling Model: Application to the Study of Commuting Departure Time

In traditional travel time reliability valuation studies, the value of travel time savings and the value of travel time reliability (or reduced time variability) are estimated within a linear utility functional form, which assumes risk-neutral attitudes for decision makers. In this paper, we develop nonlinear 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 model. The willingness-to-pay values for reducing the mean travel time and variability (earlier/later than the preferred arrival time) are also estimated within the nonlinear scheduling framework. The 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 nonlinear scheduling model predicts earlier optimal departure times than the linear scheduling model does. The application in this paper helps to bridge the gap between theory and practice.

Embedding risk attitude and decisions weights in non-linear logit to accommodate time variability in the value of expected travel time savings

In recent years we have seen important extensions of logit models in behavioural research such as incorporation of preference and scale heterogeneity, attribute processing heuristics, and estimation of willingness to pay (WTP) in WTP space. With rare exception, however, a non-linear treatment of the parameter set to allow for behavioural reality, such as embedded risk attitude and perceptual conditioning of occurrence probabilities attached to specific attributes, is absent. This is especially relevant to the recent focus in travel behaviour research on identifying the willingness to pay for reduced travel time variability, which is the source of estimates of the value of trip reliability that has been shown to take on an increasingly important role in project appraisal. This paper incorporates, in a generalised non-linear (in parameters) logit model, alternative functional forms for perceptual conditioning (known as probability weighting) and risk attitude in the utility function to account for travel time variability, and then derives an empirical estimate of the willingness to pay for trip time variability-embedded travel time savings as an alternative to separate estimates of time savings and trip time reliability. We illustrate the richness of the approach using a stated choice data set for commuter choice between unlabelled attribute packages. Statistically significant risk attitude parameters and parameters underlying decision weights are estimated for multinomial logit and mixed multinomial logit models, along with values of expected travel time savings.