Solutions for flexible container leasing contracts with options under capacity and order constraints

The container-shipping market becomes prosperous with the development of the global economy. As shipping networks become more complex and heterogeneous, container capacity planning becomes more difficult. This paper tackles the container planning problem from the carrier's perspective in a two-echelon container shipping service chain (CSSC), which includes one carrier and one upstream rental company. A flexible contract with options is introduced into the one-period container planning mechanism. With the flexible options contract, the rental company requires the carrier to make a commitment or place an order in advance. Options give buyer the right to modify the initial orders to better match the supply with the demand. Based on the carrier's decision tendency, i.e., aggressive or conservative, we analyze the application strategies of the unilateral options and the bidirectional options in different practical scenarios. In particular, for the applicability of the decision models, we further consider the shipping capacity and the minimum order constraints and formulate the carrier's option policies with constrained nonlinear programs. Numerical examples show that the proposed decision strategies with option contract cannot only effectively increase the container trading quantity between the rental company and the carrier, but also significantly reduce the carrier's container capacity risk while increasing its profit.