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Entropy 2019, 21(2), 161; https://doi.org/10.3390/e21020161

Incentive Contract Design for the Water-Rail-Road Intermodal Transportation with Travel Time Uncertainty: A Stackelberg Game Approach

1
,
1,* and 1,2,*
1
School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
2
School of Mathematical Sciences, Monash University, Clayton VIC 3800, Australia
*
Authors to whom correspondence should be addressed.
Received: 26 December 2018 / Revised: 6 February 2019 / Accepted: 7 February 2019 / Published: 9 February 2019
PDF [492 KB, uploaded 9 February 2019]   |   Review Reports

Abstract

In the management of intermodal transportation, incentive contract design problem has significant impacts on the benefit of a multimodal transport operator (MTO). In this paper, we analyze a typical water-rail-road (WRR) intermodal transportation that is composed of three serial transportation stages: water, rail and road. In particular, the entire transportation process is planned, organized, and funded by an MTO that outsources the transportation task at each stage to independent carriers (subcontracts). Due to the variability of transportation conditions, the travel time of each transportation stage depending on the respective carrier’s effort level is unknown (asymmetric information) and characterized as an uncertain variable via the experts’ estimations. Considering the decentralized decision-making process, we interpret the incentive contract design problem for the WRR intermodal transportation as a Stackelberg game in which the risk-neutral MTO serves as the leader and the risk-averse carriers serve as the followers. Within the framework of uncertainty theory, we formulate an uncertain bi-level programming model for the incentive contract design problem under expectation and entropy decision criteria. Subsequently, we provide the analytical results of the proposed model and analyze the optimal time-based incentive contracts by developing a hybrid solution method which combines a decomposition approach and an iterative algorithm. Finally, we give a simulation example to investigate the impact of asymmetric information on the optimal time-based incentive contracts and to identify the value of information for WRR intermodal transportation.
Keywords: intermodal transportation; asymmetric information; stackelberg game; uncertain theory; entropy intermodal transportation; asymmetric information; stackelberg game; uncertain theory; entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Zhang, W.; Wang, X.; Yang, K. Incentive Contract Design for the Water-Rail-Road Intermodal Transportation with Travel Time Uncertainty: A Stackelberg Game Approach. Entropy 2019, 21, 161.

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