Combined cutting stock and lot-sizing problem with pattern setup

This paper considers a real-life problem that arises in a leading company in China involving the production of extra-high-voltage and high-voltage switch equipments. It concerns combining the one-dimensional cutting stock and lot-sizing problems. In addition to minimizing material waste, the number of cutting patterns required is also minimized. Such problem also occurs in other enterprises in paper, furniture and plastic film industries. We develop a mixed-integer linear programming model and propose a dynamic programming-based heuristic (DPH) to solve it. With a recursive formulation, each pattern is explored step by step with a global view. The computational results show that DPH is efficient, and yields results close to optimal solutions, where the average gap is 2.20% for small sized instances. The average cost gap is 4.19% compared with lower bound for medium or large sized instances. We also apply the proposed heuristic to real-life data to elaborate joint production and cutting plans and compare with the current procedure in practice. The total cost is reduced by 8.81% on average, which amounts to 3.46 million RMB in cost saving in 2016 for the investigated company. The average cost gap is 5.03% compared with the lower bound. The total cost is reduced by 3.67% on average compared with the two-stage independent decision-making method commonly applied in industry.