Integrated optimization on yard crane scheduling and vehicle positioning at container yards

A container yard is a storage facility that allows handling resources to improve operational efficiency by facilitating container flows at a container terminal. The container yard system consists of a set of storage blocks with yard cranes performing stacking and unstacking operations for containers to be transported by vehicles. High operational efficiency can be achieved by managing and coordinating the handling operations of yard cranes and vehicles (e.g., the yard crane scheduling, vehicle job dispatching, and coordinating handshakes between yard cranes and vehicles). This study proposes an integrated optimization approach for simultaneously determining the yard crane schedules and the vehicle parking positions under the Chebyshev movement allowing for the simultaneous movement of gantry and trolley of the yard crane. A mixed-integer programming model is formulated to optimize the problem, and the two-stage heuristic algorithm is developed to solve the problem efficiently. Several propositions are also provided to search the optimal boundary of vehicle parking slots for pairs of jobs. Numerical experiments are conducted to show the outperformance of the proposed heuristic algorithm compared to the well-known rule-based heuristics.