A dynamic programming for solving crane scheduling in steel coil warehouse

This paper focuses on a single crane scheduling problem in order to pick all demanded coils for downstream stage production or for customer which is motivated by cooled-rolling material warehouse in the iron and steel enterprise. If a demanded coil is in the upper level, it can be picked up directly to designated place (transportation operation). If a demanded coil in the lower level is blocked by one or two un-demanded coils, the coil can not be transported until all the blocking coils are picked up to another position (shuffling operation). Both the transportation and the shuffling operations are performed by a mounted traveling crane. Our problem combines transportation and shuffling simultaneously for crane to pick up all demanded coils as early as possible to designated place, that is, the optimality criterion considered is the minimum makespan. We show its complexity by reduction from a demonstrated strongly NP-hard problem. Furthermore we introduce a dynamic programming (DP) for solving the problem optimally.