A Comparative Study of Mathematical Models for Two-Dimensional Cutting Stock Problems and Solving Algorithms

Abstract Two-dimensional cutting problem involves cutting a set of small pieces from large sheets in a way that optimizes one or more objectives. The objective of this problem can be minimizing the number of sheets used, waste, cost, and so forth. These problems have various applications in different industries such as glass, paper, wood, plastic, steel, etc. This paper studies one of the recent exact polynomial models proposed for these problems. Although the presented model, named Original(a), is quite promising for finding a solution, since these problems belong to the mixed integer non-linear programming model (MINLP) group, solving them will be difficult. Therefore, a linearization technique by multiplying continuous variables for this model would be used. The goal is to find an optimum solution. The studied models are implemented in the Matlab environment and the results of numerical experiments are presented.