Mathematical models and heuristics for double-load crane scheduling in slab yards

This paper studies a novel crane scheduling problem with unconstrained double-load operations (CSP-UDL) in slab yards. It aims to optimize the sequence of crane operations to minimize makespan. Unlike conventional crane operations, which handle one or two slabs per trip, the unconstrained double-load operation enables the transport of more than two slabs in a single trip, thereby improving logistic efficiency and reducing the makespan. To tackle this problem, we propose two mixed integer linear programming (MILP) models for solving small- and medium-sized instances. We develop two heuristics for large-sized instances: a hybrid heuristic and a matheuristic. The hybrid heuristic integrates tabu search within an adaptive large neighborhood search (ALNS) framework, while the matheuristic integrates this hybrid heuristic with an MILP model, leveraging the strengths of both exact and heuristic methods. Extensive computational experiments demonstrate that while the proposed MILP models can exactly solve instances with up to 50 tasks, the hybrid heuristic and the matheuristic demonstrate robust performance in solving large-sized instances.