Column generation approach for 1.5-dimensional cutting stock problem with technical constraints

Year 2024, Volume: 4 Issue: 3, 335 - 350, 30.09.2024

Müjgan Sağır , Tuğba Saraç

https://doi.org/10.53391/mmnsa.1492749

Abstract

In this study, the 1.5-dimensional cutting stock problem with technical constraints is considered. In the literature, this problem is also defined as a strip packing or open dimension problem. When given a strip of infinite length and bounded width, the problem is to define a packing of rectangular objects into a strip that minimizes its final length. Technical constraints, such as the order type and the number of strips, are indispensable in real life; however, they are often neglected in the literature because they make the problem difficult to solve. Only one study was reached in the literature that took into account technical constraints, but in that mentioned study, only a mathematical model was proposed for the problem. In this context, our aim is to solve the problem with a more effective approach. The research question in this study is the usability of the column generation technique to solve the 1.5-dimensional cutting stock problem. In this study, the column generation approach was proposed for the first time for the considered problem. To demonstrate the performance of the proposed solution method, randomly generated test problems were solved with GAMS/Cplex. As we report the results, proposed column generation approach (CG) reaches very close (such as %1 and %2 error) solutions to integrated mathematical model (IM) for small sized problems in a second. On the other hand, while CG solved all the problems in a reasonable time, IM could not produce a feasible solution to some problems. Numerical experiments showed that the column generation algorithm outperforms the integrated mathematical model for the problem.

Keywords

1.5-dimensional cutting problem, column generation, mixed-integer linear programming

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