Reheat furnace scheduling with energy consideration

This paper focuses on the reheat furnace scheduling problem (RFSP) which is to assign the slabs to the reheat furnace, make the slab sequence for each furnace and determine the feed-in time and the residence time for each slab in order to reduce the unnecessary energy consumption reflected by minimising the objective under consideration. Differing from the traditional scheduling problem, the actual residence time of each slab in RFSP needs to be decided and it is correlated with its neighbour slabs in the reheating sequence of the same furnace. Firstly, the RFSP is formulated as a mixed integer programming model with consideration of the practical production requirements. The strong NP-hardness of the problem motivates us to develop a scatter search (SS) algorithm to solve the problem approximately. The SS algorithm is improved by constraint propagation (CP) for filtering the infeasible solutions in both the generation of the initial solutions and the improvement procedure. To verify the algorithm performance, the proposed algorithm is compared with ILOG CP Optimiser for small-scaled problems and the standard SS, genetic algorithm (GA) for large-scaled practical problems, respectively. The computational results illustrate that the proposed algorithm is relatively effective and efficient.