Integrated problem of soaking pit heating and hot rolling scheduling in steel plants

Abstract

This paper considers an integrated problem of soaking pit heating and hot rolling scheduling that arises in steel plants. Both soaking pit and hot rolling mill are batching machines with capacity considerations. The processing time of a batch in the soaking pit is equal to the longest processing time of the jobs in the batch, whereas the processing time of a batch on the hot rolling mill is equal to the sum of the processing times of the jobs in the batch. Setup time is required whenever a batch is formed on the hot rolling mill. For this problem, we must determine the formation of batches and the sequences of these batches in the soaking pit and on the hot rolling mill such that makespan is minimized. First, we formulate the problem as a mixed integer linear programming model (MILPM) and analyze its computational complexity. Second, we provide a fast heuristic algorithm with worst-case bound to generate near-optimal solutions, and a branch and bound algorithm to solve the problem to optimality. Finally, computational experiments using randomly generated data demonstrate that our heuristic algorithm is very efficient and effective, and the branch and bound algorithm significantly outperforms CPLEX on MILPM in terms of computational time and the number of instances solved to optimality within the given time limit.