Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
권호 표지

A Best-First Branch and Bound Algorithm for Unweighted Unconstrained Two-Dimensional Cutting Problems

비가중 무제한 2차원 절단문제에 대한 최적-우선 분지한계 해법

  • Yoon, Ki-Seop (Department of Information and Industrial Engineering, Hanyang University, Ansan Campus) ;
  • Yoon, Hee-Kwon (CJ GLS(S) Infotech Pte. Ltd.) ;
  • Kang, Maing-Kyu (Department of Information and Industrial Engineering, Hanyang University, Ansan Campus)
  • 윤기섭 (한양대학교 정보경영공학과) ;
  • 윤희권 (CJ GLS(S) 인포텍) ;
  • 강맹규 (한양대학교 정보경영공학과)
  • Published : 2009.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a best-first branch and bound algorithm based upon the bottom-up approach for the unweighted unconstrained two-dimensional cutting problem is proposed to find the optimal solution to the problem. The algorithm uses simple and effective methods to prevent constructing duplicated patterns and reduces the searching space by dividing the branched node set. It also uses a efficient bounding strategy to fathom the set of patterns. Computational results are compared with veil-known exact algorithms and demonstrate the efficiency of the proposed algorithm.

Keywords

References

  1. 김종수, 유비쿼터스 경영과학, 박영사, 145-146, 2005
  2. 윤기섭, 방성규, 강맹규; “무제한 2차원 절단문제에 대해 개선된 최적-우선 분지한계 해법”, 한국경영과학회지, 30(4) : 61-70, 2005
  3. Christofides, N. and Whitlock, C.; "An algorithm for two-dimensional cutting problems," Operations Research, 26 : 30-44, 1977 https://doi.org/10.1287/opre.25.1.30
  4. Cung, V. D., Hifi, M., and Cun, B. L.; "Constrained twodimensional cutting stock problems a best-first branch-and-bound algorithm," International Transactions in Operational Research, 7 : 185-210, 2000 https://doi.org/10.1111/j.1475-3995.2000.tb00194.x
  5. G., Y. G., Seong, Y. J., and Kang, M. K.; "A best-first branch and bound algorithm for unconstrained two-dimensional cutting problems," Journal of the Operational Research Society, 53 : 587-591, 2002 https://doi.org/10.1057/palgrave.jors.2601326
  6. Gilmore, P. C. and Gomory, R. E.; "A linear programming approach to the cutting-stock problem," Operations Research, 9 : 849-859, 1961 https://doi.org/10.1287/opre.9.6.849
  7. Hifi, M.; "The DH/KD algorithm : a hybrid approach for unconstrained two-dimensional cutting problems," European Journal of Operational Research, 97 : 41-52, 1997 https://doi.org/10.1016/S0377-2217(96)00060-4
  8. Hifi, M.; Retrieved July 30, 2008, http://www.laria.u-picardie.fr/hifi/OR-Benchmark/2Dcutting/
  9. Hifi, M. and Zissimopoulos, V.; "A recursive exact algorithm for weighted two-dimensional cutting," European Journal of Operational Research, 91 : 553-564, 1996 https://doi.org/10.1016/0377-2217(95)00343-6
  10. Viswanathan, K. V. and Bagchi, A.; "Best-first search methods for constrained two-dimensional cutting stock problems," Operations Research, 41 : 768-776, 1993 https://doi.org/10.1287/opre.41.4.768
  11. Wang, P. Y.; "Two algorithms for constrained two-dimensional cutting stock problems," Operations Research, 31 : 573-586, 1983 https://doi.org/10.1287/opre.31.3.573