Cutting and packing problems under uncertainty: literature review and classification framework

Abstract

Cutting and packing problems are hard combinatorial optimization problems that arise in several manufacturing and process industries or in their supply chains. The solution of these problems is not only a scientific challenge but also has a large economic impact, as it contributes to the reduction of one of the major cost factors for many production sectors, namely raw materials, together with a positive environmental impact. The explicit consideration of uncertainty when solving cutting and packing problems with optimization techniques is crucial for a wider adoption of research results by companies. However, current research has paid little attention to the role of uncertainty in these problems. In this paper, we review the existing literature on uncertainty in cutting and packing problems, propose a classification framework, and highlight the many research gaps and opportunities for scientific contributions.