Minimizing Waste and Costs in Multi-Level Manufacturing: A Novel Integrated Lot Sizing and Cutting Stock Model Using Multiple Machines

Abstract

Lot sizing and cutting stock problems are critical for manufacturing companies seeking to optimize resource utilization and minimize waste. This paper addresses the interconnected nature of these problems, often occurring sequentially in industries involving cut items or packaging. We propose a novel mixed integer linear programming (MILP) model that integrates the capacitated lot sizing problem with the one-dimensional cutting stock problem within a multi-level manufacturing framework. The cutting stock problem is addressed using an arc flow formulation. Our model aims to minimize setup, production, holding, and waste material costs while incorporating capacity constraints, setup requirements, inventory balance, and the use of various cutting machines. The effectiveness of our model is demonstrated through numerical experiments using a commercial optimization package. While the model efficiently generates optimal solutions for most scenarios, larger instances pose challenges within the specified time limits. Sensitivity analysis is conducted to evaluate the effect of changing essential parameters of the integrated problem on model performance and to provide managerial insights for real-life applications.