Modelling and Solution to Production Planning in Cold Rolling*

Cold rolling production process is characterized by the restriction that the starting time of the item in the downstream production lines cannot be earlier than the completion time in the upstream production lines. To make the production capacity utilized sufficiently and coordinate the multiple production lines, a production planning problem in cold rolling is derived, which is to decide which orders to produce and what quantities in each production line in each day, with consideration of the production capacity restrictions and the material distribution throughout the production process. To describe the problem, an integer programming model is formulated. To solve the problem, a branch and pricing algorithm is proposed. Firstly, the primal model is reformulated, where the master problem is to coordinate the production plans, the sub-problem is to decide which order to be processed and its production volume in each production line in each day. The lower bound could be obtained by column generation. Then the optimal solution is found by a branch-and-bound approach. Moreover, a differential evolution algorithm is developed to solve the large-scale instances. Finally, the performance of the proposed approaches is illustrated by computational experiments based on randomly generated instances.