The cutting stock problem applied to the hardening process in an automotive spring factory

Abstract

In this paper, an automotive spring factory is studied to optimize its hardening process. The assignment of items to the hardening furnace is treated as a one-dimensional cutting stock problem, an approach not found in the literature. To make a feasible decision in this assignment, the activity that follows the furnace, i.e. the bending of the items, is also analyzed. In order to consider practical constraints of the company, as the position of items on the furnace, the proposed mathematical model is based on an arc flow formulation and it is validated through instances with real and random data. A heuristic approach was developed to simulate the company's decision, and to compare the random instances results. Results with real data demonstrate that the model found, in viable computational time, a solution significantly better than that of current company practice, increasing the production by 51.2%. This increase was mainly made possible by a 71.5% reduction in wasted space in the furnace and by a 26.2% reduction of time spent on setups. In random instances, the mathematical model also far outperformed the company's practice, finding the optimal solution in 98.9% of the cases. It was identified that computational time is the most sensitive criterion to the variation in the parameters and the length of the items is the parameter that most influences the results.