Scheduling heterogeneous yard cranes for port decarbonization: power constraints, crane interference, and safety distances

Yard equipment upgrades are vital for port decarbonization, yet the coexistence of legacy and new yard cranes creates challenges in coordinating operations and allocating limited electrical power. This paper studies the integrated container allocation and conflict-free scheduling of multiple yard crane types, including slipline rail-mounted gantry crane (RMG), hybrid diesel-electric RMG, cable rubber-tyred gantry crane (RTG), and diesel-powered RTG, under power capacity, interference, and safety-distance constraints. We propose a mixed-integer linear programming (MILP) model that minimizes energy cost, carbon penalty, and makespan penalty. Because general-purpose solvers struggle with large instances, we develop a tailored logic-based Benders decomposition (TLBBD) algorithm with several enhancement strategies. Numerical experiments based on data from a real port demonstrate that TLBBD significantly outperforms Gurobi, an existing LBBD method, and real-world scheduling schemes, obtaining optimal or near-optimal solutions within 15 minutes for instances with five cranes and 100 containers. Sensitivity analyses on cable RTG cable length, yard crane layout, and carbon tax further illustrate the practical applicability of the proposed approach.