Abstract: Based on the discrete state space model of the steel mill soaking pits and the new algorithm for dealing with the constrained optimal control proposed by the authors, the optimal heating patterns, i.e., the optimal temperature trajectories, of the soaking pits have been theoretically developed for minimum fuel consumption. The paper presents the relationship between the operational conditions and the optimal heating patterns of the soaking pits, and the potential economical benefits through using the heating patterns developed. The proposed development method in this paper can also be applied to the synthesis of the optimal control algorithms for other bach processes as well as the high-dimensional, non-linear and time-varyling systems.