Optimal Assignment and Scheduling of Cranes in Slab Yard for Iron and Steel Production Enterprises

Slab yards serve as temporary slab storage between a continuous casting stage and a rolling stage. Considering non-crossing and safe clearance constraints of slab yard cranes, this work studies a multi-crane assignment and scheduling problem in the slab yard. An mixed-integer linear programming (MILP) is formulated to minimize the slab completion time. Due to its NP-hardness, the problem for large-sized instances is computationally intractable. Thus, we develop a logic-based benders decomposition algorithm (LBBD) to solve it. First, we exploit a generalized decomposition of this problem into a relaxed main problem (RMP) and a sub-problem (SP). Solving the former allocates slabs to each crane. Then, the sequence of the assigned slabs can be found by solving its corresponding sub-problem. Finally, to verify the effectiveness of LBBD, we identify a lower bound (LB) of the optimal objective function. The problem instances on real data from an iron and steel plant are created. The result of LBBD is close to such lower bound and can be found efficiently.the completion time. Its time complexity grows exponentially with the problem size. Thus, we develop a LBBD to solve it. The numerical results reveal that LBBD can find the optimal or near-optimal solution for all realistic instances in affordable computational time. Its use can ensure the high utilization of cranes and efficient service in iron and steel plants.