Genetic Algorithm and Its Performance Analysis for Scheduling a Single Crane

This paper studies a single crane scheduling problem arising in the cold-rolling material warehouse in an iron and steel enterprise. A set of coils stored in two levels are needed to be picked up and transported to designated positions. If a required coil is at the upper level, it can be picked up right away and transported to its designated position (transportation operation). A required coil at the lower level cannot be picked up until all its blocking coils at the upper level are moved to other positions (shuffling operation). One overhead crane is used to perform all the transportation and shuffling operations. Our problem is to schedule the crane operations so as to all required coils retrieve to their designated positions in the shortest possible time ( makespan ). Since the problem is shown to be NP-hard, a genetic algorithm (GA) is proposed. We identify some analytical properties which enable us to develop an effective heuristic algorithm as initial solutions of the GA. We further analyze its performance from the worst-case point of view. To evaluate the average performances, a numerical test compared with some existing methods is carried out and its results show the good quality of the proposed algorithm.