The integrated lot sizing and cutting stock problem in an automotive spring factory

In this paper, a manufacturer of automotive springs is studied in order to reduce inventory costs and losses in the steel bar cutting process. For that, a mathematical model is proposed considering parallel machines and operational constraints, besides the demand, inventory costs and limits for items and final products. This one-dimensional integrated lot sizing and cutting stock problem is solved by a price-and-branch approach, using column generation and a method for obtaining integer solutions. Results using real data show that the proposed method achieved, in reasonable computational time, considerably better solutions than current practice at the company. Furthermore, focused on managerial insights, tests with random data were performed to analyze the influence that different parameters have in the solution, as well as the overall performance of the method.