A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron-steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.