On the other half of the story: allowing for discrete penalties for excessive travel times in scheduling models

In this paper, we introduce a discrete penalty for excessive travel times into scheduling models whose maximal expected utilities have attractive theoretical features of linearity in standard deviation or variance. The extended models maintain the properties of linearity, and its maximal expected utility depends on the shape of the travel time distribution. The value of travel time and its variability could be measured indirectly by the scheduling preferences. The results from empirical data reveal that the extended models, with such a discrete penalty, provide a highly significant better goodness of fit to the data. Furthermore, introducing the penalty for excessive travel time has a strong effect on the estimates of the other scheduling parameters, thus affecting the valuations of travel time. Our findings indicate that, apart from the mean and standard deviation (or variance), individuals value other characteristics of travel time distribution, in particular the probability of excessive travel time.