An Application of Lagrangean Decomposition to the Scheduling of Hot Charged Rolling in Steel Production

-In this paper a Lagrangean decomposition technique for solving the scheduling problem for Hot Charged Rolling (HCR) in the continuous casting process which involves sequencing and grouping. This Lagrangian relaxation algorithm is proposed that incorporate two sets of constraints into the objective function after applying the variable splitting technique. The relaxed problem has a special structure and can be solved as three versions of subproblems. The subgradient algorithm is then used to maximize the Lagrangian dual. Two heuristic algorithms are also proposed to find good primal feasible solutions. Through the three versions of subproblems and two heuristic algorithms, the best one from six combinations is selected to incorporate with branch-and-bound algorithm to find the optimal solution when job size is large. Our methodology provides the optimal solutions for the difficult scheduling problem resulted from the continuous casting process. Key-Words: Hot Charged Rolling, Lagrangian relaxation, Continuous casting.