Annals of Operations Research

, 166:125

# An effective solution for a real cutting stock problem in manufacturing plastic rolls

• Ramiro Varela
• Camino R. Vela
• Jorge Puente
• María Sierra
• Inés González-Rodríguez
Article

## Abstract

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process.

## Keywords

Cutting stock Iterative sequential heuristics Randomized algorithms Meta-heuristics Multi-objective optimization

## References

1. Belov, G., & Scheithauer, G. (2003). The number of setups (different patterns) in one-dimensional stock cutting. Technical Report, Desden University. Google Scholar
2. Belov, G., & Scheithauer, G. (2006). A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting. European Journal of Operational Research, 171, 85–106.
3. Belov, G., & Scheithauer, G. (2007). Setup and open stacks minimization in one-dimensional stock cutting. INFORMS Journal of Computing, 19(1), 27–35.
4. Chen, C. L. S., Hart, S. M., & Tham, W. M. (1996). A simulated annealing heuristic for the one-dimensional cutting stock problem. European Journal of Operational Research, 93, 522–535.
5. Foerster, H., & Wäscher, G. (1999). Pattern reduction in one-dimensional cutting stock problems. In Proceedings of the 15th trienal conference of the international federation of operational research societies. Google Scholar
6. Gilmore, P. C., & Gomory, R. E. (1961). A linear programming approach to the cutting stock problem. Operations Research, 9, 849–859.
7. Gilmore, P. C., & Gomory, R. E. (1963). A linear programming approach to the cutting stock problem. Operations Research, 11, 863–888.
8. Goulimis, C. (1990). Optimal solutions for the cutting stock problem. European Journal of Operational Research, 44, 197–208.
9. Gradisar, M., Resinovic, G., & Kljajic, M. (2002). Evaluation of algorithms for one-dimensional cutting. Computers and Operations Research, 29, 1207–1220.
10. Haessler, R. W. (1975). Controlling cutting patterns changes in one dimensional trim problems. Operations Research, 23(3), 483–493.
11. Haessler, R. W. (1991). Cutting stock problems and solution procedures. European Journal of Operational Research, 54, 141–150.
12. Johnston, R. E. (1986). Rounding algorithm for cutting stock problems. Journal of Asian-Pacific Operations Research societies, 3, 166–171. Google Scholar
13. Resende, M., & Ribeiro, G. (2002). Greedy randomized adaptive search procedures (pp. 219–249). Dordrecht: Kluwer Academic. Google Scholar
14. Song, X., Chu, C. B., Nie, Y. Y., & Bennell, J. A. (2006). An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem. European Journal of Operational Research, 175, 1870–1889.
15. Suliman, S. M. A. (2001). Pattern generating procedure for the cutting stock problem. International Journal of Production Economics, 74, 293–301.
16. Umetani, S., Yagiura, M., & Ibaraki, T. (2003). One-dimensional cutting stock problem to minimize the number of different patterns. European Journal of Operational Research, 146, 388–402.
17. Vahrenkamp, R. (1996). Random search in the one-dimensional cutting stock problem. European Journal of Operational Research, 95, 191–200.
18. Valério de Carvalho, J. M. (2002). Lp models for bin packing and cutting stock problems. European Journal of Operational Research, 141, 253–273.
19. Vanderbeck, F. (2000). Exact algorithm for minimizing the number of setups in the one-dimensional cutting stock problem. Operations Research, 48, 915–926.

## Authors and Affiliations

• Ramiro Varela
• 1
Email author
• Camino R. Vela
• 1
• Jorge Puente
• 1
• María Sierra
• 2
• Inés González-Rodríguez
• 2
1. 1.Computing Technologies Group. Department of Computing, Artificial Intelligence CenterUniversity of OviedoGijónSpain
2. 2.Department of Mathematics, Statistics and ComputingUniversity of CantabriaSantanderSpain