Page 20 - IJOCTA-15-2

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.2, pp.215-224 (2025)
https://doi.org/10.36922/ijocta.1660

RESEARCH ARTICLE

A MILP model for one dimensional cutting stock problem with
adjustable leftover threshold and cutting cost

Anett R´acz *

Department of Applied Mathematics and Probability Theory, University of Debrecen,Hungary
racz.anett@inf.unideb.hu

ARTICLE INFO ABSTRACT
Article History: This paper presents a MILP model for one dimensional cutting stock (CSP)
Received: August 6, 2024 problems that considers the most commonly used objectives all together. These
Accepted: January 15, 2025 are the minimization of the trim loss which is the leftover that is not large
Published Online: March 19, 2025 enough to be reused in the future, minimization of the total cutting cost and
number of bars involved. We carried out computational experiments in order to
Keywords:
find out the limitations of our model and to compare it with the most commom
One dimensional cutting stock
linear cutting software on the market.
problem
Mixed-integer linear-programming
Optimization
AMS Classification:
90-08

1. Introduction each case, the number of rods needed to service
the orders is an important consideration.
Optimization is an essential element of modern Various articles about the CSP can be found
economic life. Increasing the efficiency of pro- in the literature from the first formulation by
4
duction is a key point of industrial optimiza- Kantorovich to the latest papers. These mod-
tion. There are studies from several areas of in- els can be diverse in terms of the objective. Most
dustry that focus on cost efficiency in business common goals are the three previously mentioned:
operations. 1–3 • Minimizing the number of bars involved
in serving the orders.
In this paper I deal with one dimensional cut- • Minimizing the number of cuts.
ting problems. One dimensional Cutting Stock • Minimizing the amount of waste.
Problems (1DCSP) are real-world industrial opti-
mization problems, where one dimensional stock The simplest models have only one objective.
pieces (bars) need to be cut in order to serve cus- Most often, this is to minimize trim loss, consider-
tomers demand. In order to achieve efficiency, ing a certain lower bound above which the leftover
5–7
businesses must also think about the cost of cuts, can be reused. Examples of such models are :
the number of one dimensional items used and the There are models that combine different ob-
amount of waste generated in the process. These jectives, such as, 8 where the authors used two
factors may vary widely from one industry to an- goals, one to minimize uncut orders and the other
other. In the metal industry, the cost of cutting to minimize trim loss. Multi-objective approaches
is significant, while also shorter leftovers have a are often industry specific and vary widely due
good chance of being recycled, while in the wood to different cost factors. Sinuany-Stern et al cre-
industry the cost of cutting could be lower, but ated a personalized model with two objectives for
typically only the longer trims can be sold. In metal cutting problems in. 9 Primary objective of
*Corresponding Author
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