An optimization model to measure utility of joint and solo activities

The choice of 'dining out with friends' or 'wrapping up unfinished tasks at work' depends on the utility/satisfaction gained from performing each activity while being constrained by time and physical resources. In fact, such parameters as 'type', 'time of day', 'duration', 'location', 'companionship', and etc. are defining factors in quantifying the utility of activities - a challenging problem which has been the focus of research for many years. This paper proposes a methodology to estimate the parameters of utility distributions for joint and solo activities, along with the penalty values associated with the deviation of activity start time and duration from their modal values. The study utilizes travel survey data collected in Frauenfeld, Switzerland, over the period of six weeks in 2003. The proposed model is a bi-level optimization model, where the upper level maximizes the accuracy of the activity scheduling on the aggregate level and is measured using the outputs of lower level optimization models. Each lower level model is a variation of pickup and delivery problem and schedules activities for each individual in the population using the parameters of utility distribution and penalty values generated by the Genetic Algorithm. The results indicate that travelers are trying to be more consistent with their arrival time to work, school and pickup/drop off activities: the associated penalty values for deviation from the modal value for arrival time to work and school activities are high. Additionally, significant differences in the parameters of the estimated utility distribution for joint and solo activities are observed, reflecting the fact that utility gained from joint and solo activities are different and needs more in-depth investigation. The proposed methodology has the potential to be applied to any multiday travel survey data, which due to advances made in handheld smart devices and mobile applications are becoming more convenient to collect.