Two-Stage Robust Liner Container Booking with Uncertain Customer Demand

Since third-party logistics (3PL) offers discounted prices for booking containers in advance, the container booking decisions are preferably made prior to the realization of customer demand by the companies with international trade business. When facing uncertain customer demand influenced by various factors, it is significant for companies to make proper container booking decisions and order fulfillment plans to minimize the total cost, including the container booking cost and the penalty cost of an unfulfilled order. In this paper, a two-stage robust liner container booking problem (2-RLCBP) was investigated, and an exact algorithm with high efficiency was designed to solve the problem based on the column-and-constraint generation (C&CG) framework. Compared to other methods with gaps of more than 70% existing after 3600 s, the proposed algorithm can get the optimal solution of the real case instance in 700 s. Furthermore, compared to the deterministic model, the two-stage robust optimization model can reduce more than 10% of the worst-case total cost when the budget level and demand deviation level are greater than 0.6, which verifies the effectiveness of the proposed robust approach. Furthermore, our work is the first to adopt a two-stage robust optimization approach for the problem of booking a liner container.