The integrated lot-sizing and cutting stock problem under demand uncertainty
研究了在需求不确定下集成批量与下料问题，通过随机规划和鲁棒优化方法，结合列生成和滚动时域程序，实验表明考虑不确定性可降低成本高达39.7%。
Interest in integrating lot-sizing and cutting stock problems has been increasing over the years. This integrated problem has been applied in many industries, such as paper, textile and furniture. Yet, there are only a few studies that acknowledge the importance of uncertainty to optimise these integrated decisions. This work aims to address this gap by incorporating demand uncertainty through stochastic programming and robust optimisation approaches. Both robust and stochastic models were specifically conceived to be solved by a column generation method. In addition, both models are embedded in a rolling-horizon procedure in order to incorporate dynamic reaction to demand realisation and adapt the models to a multistage stochastic setting. Computational experiments are proposed to test the efficiency of the column generation method and include a Monte Carlo simulation to assess both stochastic programming and robust optimisation for the integrated problem. Results suggest that acknowledging uncertainty can cut costs by up to 39.7%, while maintaining or reducing variability at the same time.