A smart predict-then-optimize method for targeted and cost-effective maritime transportation

In maritime transportation, port state control (PSC) is the last line of defense against substandard ships. During a PSC inspection, PSC officers (PSCOs) identify ship deficiencies that lead to a ship's detention, which can cause severe economic and reputational losses to the ship operator. Therefore, this study innovatively uses PSC inspection data to design ship maintenance plans for ship operators to minimize overall operational costs. We identify three types of operational costs associated with each deficiency code: inspection cost, repair cost, and risk cost in the ship operators’ decision-making process. The risk cost of a deficiency code is strongly related to the detention contribution of the deficiency items under a deficiency code, as indicated by the feature importance of that code in the random forest (RF) model used to predict detention outcomes. To design ship maintenance plans, the sequential predict-then-optimize (PO) method typically solves the optimization problem using input parameters, including the predicted probabilities of having deficiency items under each code and the three types of operational costs. However, the loss function in this two-stage framework does not consider the effect of predictions on the downstream decisions. Hence, we use a smart predict-then-optimize (SPO) method using an ensemble of SPO trees (SPOTs). Each SPOT uses an SPO loss function that measures the sub-optimality of the decisions derived from the predicted parameters. By exploiting the structural properties of the optimization problem analyzed in this study, we demonstrate that training an SPOT for this problem can be simplified tremendously by using the relative class frequency of true labels within a leaf node to yield a minimum SPO loss. Computational experiments show that the SPO-based ship maintenance scheme is superior to other schemes and can reduce a ship's total operating expenses by approximately 1% over the PO-based scheme and by at least 3% over schemes that do not use machine learning methods. In the long run, SPO-based ship maintenance plans also improve the efficiency of port logistics by reducing the resources needed for formal PSC inspections and alleviating port congestion.