The optimization of a production process is often based on the efficient utilization of the production facility and equipment. In particular, reducing the time to change from producing one product to another is critical to the fulfillment of demand at a minimum cost. We study the production of steel coils in the context of searching for groups of products with similar characteristics in order to create production batches that minimize the cost of fulfilling production orders originated by a known demand. We formulate the problem as mixed-integer program and develop a heuristic solution procedure. We show that a simplified version of the problem is equivalent to the clique partition problem, which in turn is equivalent to the graph-coloring problem. Computational experiments show that the heuristic procedure is effective in finding high-quality solutions to both the clique partition problem and the original grouping problem that includes additional costs.
