In this paper, the hot rolling batch scheduling problem is formulated as a multi-objective vehicle routing problem with double time windows model, in which the first time window deals with the surface grade constraint and the second one is for the linkage modes. In view of the complexity of the proposed model and the priority of considered objectives in practical production, a decomposition-based hierarchical optimization algorithm is proposed to solve the model. Firstly, the model is decomposed into two sub-problems: vehicle routing problem with time windows (VRPTW) and single vehicle routing problem with time windows (SVRPTW). Secondly, MACS-VRPTW is used to optimize the VRPTW sub-problem, in which the first objective is prior to the second one. Then, dynamic programming and genetic algorithm are used to optimize the SVRPTW sub-problem so as to reach a higher hot charge temperature. Experimental results based on the practical production instances have indicated that the proposed model and algorithm are effective and efficient.

The hot rolling batch scheduling problem is a hard problem in the steel industry. In this paper, the problem is formulated as a multi-objective prize collecting vehicle routing problem (PCVRP) model. In order to avoid the selection of weight coefficients encountered in single objective optimisation, a multi-objective optimisation algorithm based on Pareto-dominance is used to solve this model. Firstly, the Pareto MAX -MI N Ant System (P-MMAS), which is a brand new multi-objective ant colony optimisation algorithm, is proposed to minimise the penalties caused by jumps between adjacent slabs, and simultaneously maximise the prizes collected. Then a multi-objective decision-making approach based on TOPSIS is used to select a final rolling batch from the Pareto-optimal solutions provided by P-MMAS. The experimental results using practical production data from Shanghai Baoshan Iron & Steel Co., Ltd. have indicated that the proposed model and algorithm are effective and efficient.

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