A simple approach to the two-dimensional guillotine cutting stock problem


1 Department of Industrial Engineering, Iran University of Science and Technology, Tehran 16846-13114, Iran

2 Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, 11518-63411, Iran


Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic
polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in
which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic
method was proposed for such problems. Then, the software implementation and architecture specifications were
explained in order to solve guillotine cutting stock problems. This software was implemented by C++ language in a
way that, while running the program, the operation report of all the functions was recorded and, at the end, the
user had access to all the information related to cutting which included order, dimension and number of cutting
pieces, dimension and number of waste pieces, and waste percentage. Finally, the proposed method was evaluated
using examples and methods available in the literature. The results showed that the calculation speed of the
proposed method was better than that of the other methods and, in some cases, it was much faster. Moreover, it
was observed that increasing the size of problems did not cause a considerable increase in calculation time.
In another section of the paper, the matter of selecting the appropriate size of sheets was investigated; this subject
has been less considered by far. In the solved example, it was observed that incorrect selection from among the
available options increased the amount of waste by more than four times. Therefore, it can be concluded that
correct selection of stocks for a set of received orders plays a significant role in reducing waste.