Cutting stock problem with usable leftovers: A review

Abstract

This article presents a comprehensive literature review of the Cutting Stock Problem with Usable Leftovers (CSPUL). The most recent review on this topic dates to 2014, covering articles published before 2013. Since then, the number of publications on CSPUL has increased significantly, driven by new applications and more efficient solution approaches. We analyze fifty two relevant articles from twenty four different journals, focusing on works published after 2008 while acknowledging foundational contributions from the 1980s and 1990s. This review categorizes variations of CSPUL based on their dimensions (1D, 2D, and 3D), planning period characteristics (single-period and multi-period), objective functions, and solution methods. The article provides a detailed summary of the key features in the mathematical models and solution methods proposed in these studies. Additionally, it highlights several industrial applications of CSPUL, illustrating its practical relevance. Through this analysis, we identify important applications and propose promising directions for future research. The findings and insights presented here have practical implications for optimizing resource utilization and promoting sustainability in industries facing cutting challenges.