Mathematical Methods of Operations Research

, Volume 87, Issue 2, pp 285–307 | Cite as

A commuter departure-time model based on cumulative prospect theory

  • Guang Yang
  • Xinwang Liu
Original Article


With a focus on planning of departure times during peak hours for commuters, an optimal arrival-time choice is derived using cumulative prospect theory. The model is able to explain the influence of behavioral characteristics on the choice of departure time. First, optimal solutions are derived explicitly for both early and late-arrival prospects. It is shown that the optimal solution is a function of a subjective measure, namely, the gain–loss ratio (GLR), indicating that the actual arrival time of a commuter depends on his or her attitude to the deviation between gains and losses. Some properties of the optimal solution and the GLR are discussed. These properties suggest that the more that the pleasure of gain exceeds the pain of loss, the greater the correlation between actual and preferred arrival times. Finally, a sensitivity analysis of the results is performed, and the use of the model is illustrated with a numerical example based on a skew-normal distribution.


Departure-time choice Cumulative prospect theory Gain–loss ratio Optimal solution 



The authors gratefully acknowledge financial support by the National Science Foundation of China (NSFC) (71371049, 71771051, 71701158) and Ph.D. Program Foundation of Chinese Ministry of Education CSC201706090142.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Economics and ManagementSoutheast UniversityNanjingChina

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