A method of solving a large-scale rolling batch scheduling problem in steel production using a variant of column generation

Abstract

This paper presents a transparent model and a solution approach to solve a large-scale rolling batch scheduling problem. First, the problem is formulated as a multiple routes problem with multi-objective ( MRMOP). By defining a hierarchical cost structure it is natural to decompose the MRMOP into several well-studied sub-problems, i.e. the multiple routes minimum cost problem ( MRMCP), the knapsack problem ( KP) and the linear assignment problem ( LAP). Among these sub-problems the MRMCP is considered as the central one and is tackled first of all. The solution procedure for the MRMCP is based on a partial set-partitioning formulation. It makes use of a variant of column generation. Feasible column is generated as needed by solving a resource constrained elementary shortest path problem (RC-ESPP) by a mixed strategy combing an exact method and heuristics. Then a procedure called Adding-Node is introduced to implicitly solve the KP starting from the solution of the MRMCP. Finally, we solve the LAP with Hungarian algorithm to consider the total tardiness and earliness of the production. Computational results are presented compared with several promising methods on benchmark problems and production orders from Shanghai Baoshan Iron and Steel Complex. The results demonstrate the efficiency of the proposed algorithm.