Lot Sizing and Cutting Stock Problems in a Paper Production Process

Abstract

In many manufacturing industries, the production process involves the production of objects and the cutting of such objects into smaller pieces in order to meet a specific demand. In the optimization of these processes, one can identify the lot sizing and the cutting stock problems. In the literature, these problems are mostly separately dealt. However, treating these two problems in an integrated approach can decrease overall costs. In this research, we deal with the coupled lot sizing and cutting stock problem. It is proposed a mathematical formulation for the production and cutting of paper based on a real case, which considers setup costs and limited machine capacity in the production process of the objects. For the solution of the proposed model, we used a column generation approach and a relax-and-fix heuristic. Computational tests were carried out in order to analyze the methodology used in the resolution of the model. The results showed to be competitive in a reasonable computational time.

Impact of minimum distance constraints on sheet metal waste for plasma cutting

“…The strip bottom position and left area are represented by A2 and A3, respectively, as shown in Eq (14) and Eq (15).…”

“…The number of rectangles is 7 and the rectangles' geometric dimensions are: w 1 = w 2 = w 3 = w 4 = 2; w 5 = w 6 = 3; w 7 = 1;, h 1 = h 2 = 15; h 3 = h 4 = 12; h 5 = h 7 = 9; and h 6 = 8. From Eqs (13)(14)(15), A1 = 270, A2 = 10, and A3 = 30, respectively. Therefore, ML h = 17 and ML 0 = 31.…”

“…Recently, practical applications have been addressed by other cutting and packing problems, such as the cutting stock problem in concrete [ 11 ], construction [ 12 ], mattress [ 13 ], glass manufacturing [ 14 ], and paper production [ 15 ] industries. In addition, multi-objective lot sizing and cutting stock approaches were inspired by practical applications [ 16 ].…”

Genetic Algorithm Approach for Cutting Stock Problems in Construction Industries

“…Minimizing waste is the goal of Cutting Stock Problem (CSP). In many literatures (Abuhassan & Nasereddin, 2011) (Yan Chen, Xiang Song, Djamila Ouelhadj, 2017) (Pierini & Poldi, 2021), the example is in paper mills where production machines can produce fixed width paper rolls, but the requirements are for smaller-width rolls, although with the same length. The paper mill then needs to slice the paper rolls into several narrow-width rolls.…”