Solving the Two-Crane Scheduling Problem in the Pre-Steelmaking Process

Abstract

This research is motivated by the practical pre-steelmaking stage in large iron and steel companies, which have steady and heavy demands for the steelmaking production process. Our problem studied the pre-steelmaking stage, which consists of two steps that are needed in each convertor before the steelmaking process. During each step, a necessary transportation must be operated by a crane. In contrast to the classical two-machine flowshop problem during which both machines are fixed, these transporting operations are performed by two mounted, removeable cranes. Our problem is scheduling two-crane operations for the sake of minimizing the last convertors’ completion time (makespan); that is, the last finish time among the total operation of the two cranes is minimized. This study was concerned with resolving the interference between two cranes by determining the sequence of loading operations and how each crane avoids the other in order to let it complete its next operation first. A mixed integer linear programming (MILP) model was developed to represent the problem, and we further present the computational complexity of the problem. The result implies that our problem is very difficult to solve, and it is computationally challenging to solve the model. A special case is provided, which can be optimally solved in polynomial time. Furthermore, an evolutionary algorithm cuckoo search (CS) algorithm was attempted to obtain near-optimal solutions for medium- and large-scale problems. Finally, the efficiency and effectiveness of our methods were validated by numerical results in both simulated instances as well as real data from a practical production process.