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International investments in the port development become popular including the cases of Chinese companies who are continuously signing concession contracts with many other countries to promote the Belt and Road Initiative. One important issue in a concession contract between an investor and a container terminal operator is how the rental fee is calculated. This study discusses how the port investor optimises the parameters of fixed and variable rental fees for both the cases with a deterministic and an uncertain cargo demand. This study analyzes cases with an uncertain cargo demand in which terminal operators and the port investor may have the same or different degrees of uncertainty on cargo demand. The uncertainty in the cargo demand was found to decrease the revenue of the port investor and increase the profits of the terminal operators..
Yanjie Zhou and Kap Han Kim
A game theoretic model was proposed for multiple container terminals competing with each other to maximize their own profits by determining their terminal handling charges (THCs) that affect the market shares of terminals. The pricing model can describe both the competitive and cooperative games. The congestion cost of the terminals was also considered in the cost term, and revenue sharing rental fee schemes with two-step unit fees were analyzed. To overcome the difficulty in obtaining the Nash Equilibrium of the THCs for container terminals, this study proposed a coevolution-based procedure that adopts the neighborhood structure on toroidal grids and supports localized interactions among species. The numerical experiments showed that both the cost model with the congestion cost and the revenue sharing scheme help improve the total profit of the port. In addition, the results obtained by the coevolution-based procedure in this study were compared with those in previous studies.
Yanjie Zhou and Kap Han Kim
This paper proposes a method for designing an optimal concession contract under various revenue-sharing schemes with a quantity discount between a port authority and two container-terminal operators. The revenue-sharing scheme with an incremental or all-unit quantity discount provides a discount on the unit fee per container when the amount of cargo of a container terminal is over a predefined breakpoint, which is one of the popular methods for boosting the traffic volume of a port. This study defines a Stackelberg two-stage game model, in which the port authority determines the parameters of the revenue-sharing scheme to maximize its total revenue in the first stage, and two container-terminal operators compete with each other to maximize their profit by determining the terminal handling charge in the second stage. Numerical experiments show that the revenue-sharing scheme with a quantity discount results in higher revenue to the port authority than that from the traditional revenue-sharing scheme with a single rate. Moreover, revenue sharing with an all-unit discount provides higher revenue than that with an incremental discount in almost all the experimental results.
Yanjie Zhou and Kap Han Kim
This paper proposes a method for designing an optimal concession contract under various revenue-sharing schemes with a quantity discount between a port authority and two container-terminal operators. The revenue-sharing scheme with an incremental or all-unit quantity discount provides a discount on the unit fee per container when the amount of cargo of a container terminal is over a predefined breakpoint, which is one of the popular methods for boosting the traffic volume of a port. This study defines a Stackelberg two-stage game model, in which the port authority determines the parameters of the revenue-sharing scheme to maximize its total revenue in the first stage, and two container-terminal operators compete with each other to maximize their profit by determining the terminal handling charge in the second stage. Numerical experiments show that the revenue-sharing scheme with a quantity discount results in higher revenue to the port authority than that from the traditional revenue-sharing scheme with a single rate. Moreover, revenue sharing with an all-unit discount provides higher revenue than that with an incremental discount in almost all the experimental results.
Yanjie Zhou and Gyu Min Lee