Abstract: The slabs left in steel-making procedure and not belonging to any order at the moment are called open-order slabs. The open-order slab matching problem is how to assign these slabs to compatible orders in the hot-rolling plan. For an actual problem, a multiple objective 0-1 integer programming model is established. It is an NP-hard problem, so we take the algorithm of ant colony optimization (ACO) to obtain its approximate solution. We propose decomposition strategy based steel grade, meanwhile we construct a random perturbation strategy and the compound neighborhood to improve the performance of the algorithm. At present, the decision support system for open-order slab matching is already verified by application. Compared with the manual work, the system increases the weight of the slabs matched by 52.42% per day on average and reduces the scraps of 100 ton matched slabs by 11.36% on average.