Abstract
Liner container shipping company satisfies container shipping demand from both long-term contracts and spot market. Different from the shipping demand from long-term contracts whose freight rate is usually negotiated between the shipping company and the customer, the freight rate of the spot demand is usually determined by the shipping company itself. This paper thus focuses on how to determine the optimal freight rate of spot containers for each origin and destination (OD) pairs of a shipping network to maximize the total profit. To further reflect industry practice, two types of uncertainties are considered, i.e., the uncertain spot demand volume due to stochastic slot booking arrivals and cancelations, and the uncertain remaining ship capacity for the spot demand after satisfying other demand types with higher priority (e.g. delayed containers). This problem is first formulated as a two-stage stochastic nonlinear and nonconvex programming model. A tailored spatial branch-and-bound-and-Benders algorithm is then developed to obtain the global optimal solution of the model. Numerical experiments also demonstrate the efficiency of the solution algorithm and the applicability of the proposed model in improving the profit from the spot shipping demand.
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