The block relocation problem with appointment scheduling

In many container terminals, containers are piled vertically and horizontally in the terminal yard, limited mainly by the dimensions of the yard crane. Import and export containers are typically stacked separately. An external truck can access the terminal to pick up an import container only after making an appointment reserving a pickup time. To reduce truck waiting time inside the terminal, container pickup appointments are normally scheduled on a time window basis. However, when a truck arrives at the terminal yard at the appointed time, it is common for the target container not to be at the top of its stack, resulting in unproductive relocations to remove all the containers stacked above the target container and thus increasing the truck's waiting time. To minimize the number of relocations, the Block Relocation Problem (BRP) is usually solved independently, without consideration of appointment scheduling. In this paper, we introduce a new optimization problem—the Block Relocation Problem with Appointment Scheduling (BRPAS)—to jointly address the two issues. To solve the problem, two binary IP models are proposed, and examples from the literature are solved to confirm the performance of the two models. The proposed formulations are further extended to cover several operational aspects related to the flexibility of container pickup operations. Results show that the proposed approach can improve container relocation operations at terminal yards by coordinating with appointment scheduling.