A Polynomially Solvable Case for Solving Crane Scheduling Problem in Batch Annealing Process

Abstract

This paper investigates a special case for scheduling of the multi-crane operations in batch annealing process in an iron and steel enterprise so that the completion time of the last annealed coil (makespan) is minimized. Additional no-delay and no-buffer constraints for taking fully advantage of machines are considered. No-delay constraints for machine unloading means technological requires fixed heating time and cooling time that once the heating (cooling) is completed, the furnace (cooler) must be unloaded immediately without any delay by crane. No-buffer constraints for machine unloading means the time gap between the unloading time of one machine for one job and its start time on the next job is exactly equal to the corresponding transportation time. We prove that this problem can be solved optimally in polynomial time where the starting time and ending time of every possible crane movement are formulated.