Operational Research

, Volume 17, Issue 1, pp 187–204 | Cite as

A study on decision making of cutting stock with frustum of cone bars

  • Lin LiuEmail author
  • Xinbao Liu
  • Jun Pei
  • Wenjuan Fan
  • Panos M. Pardalos
Original Paper


This paper considers the cutting stock problem with frustum of cone bars. A multiple objective optimization model is established by taking into account trim loss, the number of cutting patterns and usable leftovers. A decision-making method for solving this cutting stock problem is designed. First, an improved non-dominated sorting heuristic evolutionary algorithm is developed for generating the Pareto non-dominated solutions. Then the weights of the objectives are calculated by combining the subjective methods (subjectively determined by the decision maker) and objective methods (objectively determined by numerical computing). Finally, a multi-attribute decision making method is used for choosing a cutting plan from the Pareto non-dominated solutions. Computational results indicate that the method proposed is feasible.


Cutting stock Multi-objective optimization Multi-attribute decision making Frustum of cone bars 



Supported by the Decision Science and Technology Research Institute, Hefei University of Technology, Hefei, China is gratefully appreciated. This research was supported in part by the National Natural Science Foundation under the Grant Nos.: 71171071, 71231004 and Anhui Universities Natural Science Project under the Grant No.: KJ2011A215.


  1. Adriana CC, Marcos NA, Horacio HY (2009) The one-dimensional cutting stock problem with usable leftover—a heuristic approach. Eur J Oper Res 3:897–908Google Scholar
  2. Cheng Q (2010) Strueture entropy weight method to confirm the weight of evaluating index. Syst Eng Theory Pract 7:1225–1228Google Scholar
  3. Claudio A, Fabrizio M (2014) On cutting stock with due dates. Omega 46:11–20CrossRefGoogle Scholar
  4. Cui YD, Yang YL (2010) A heuristic for the one-dimensional cutting stock problem with usable leftover. Eur J Oper Res 2:245–250CrossRefGoogle Scholar
  5. Cui YD, Zhong C, Yao Y (2015) Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost. Eur J Oper Res 243:540–546CrossRefGoogle Scholar
  6. Deb K, Pratap A, Agrawal S (2002) A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2:182–197CrossRefGoogle Scholar
  7. Erjavec J, Gradisar M, Trkman P (2012) Assessment of stock size to minimize cutting stock production costs. Int J Prod Econ 135:170–176CrossRefGoogle Scholar
  8. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, MAGoogle Scholar
  9. Gracia C, Andrés C, Gracia L (2013) A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company. J Heuristics 19:253–273CrossRefGoogle Scholar
  10. Harald R, Thomas WMV (2010) The one-dimensional cutting stock problem with due dates. Eur J Oper Res 3:701–711Google Scholar
  11. Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New YorkCrossRefGoogle Scholar
  12. Lin XY, Wang Y (2003) On optimization for multi-objective cutting problem. Nat Sci J Harbin Norm Univ 5:14–16Google Scholar
  13. Liu R, Yan X, Chen F (2010) One-dimension layout system considering multi-objective optimization. Comput Appl Softw 1:23–25Google Scholar
  14. Vacharapoom B, Sdhabhon B (2014) Three-step solutions for cutting stock problem of construction steel bars. J Civil Eng 5:1239–1247Google Scholar
  15. Wang ZY, Gu HF, Yi XY (2003) A method of determining the linear combination weights based on entropy. Syst Eng Theory Pract 3:112–116Google Scholar
  16. Yan CP, Song TF, Liu F (2010) Manufacturability-oriented one-dimensional cutting-stock problem under complex constraints status. Comput Integr Manuf Syst 1:195–201Google Scholar
  17. Zheng XJ, Hang YG, Teng HF (2009) Simulated annealing algorithm based on satisfaction degree for one-dimensional cutting-stock problems with multiple stock lengths. J Dalian Univ Technol 6:865–871Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Lin Liu
    • 1
    Email author
  • Xinbao Liu
    • 1
  • Jun Pei
    • 1
  • Wenjuan Fan
    • 1
  • Panos M. Pardalos
    • 2
  1. 1.School of ManagementHefei University of TechnologyHefeiChina
  2. 2.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

Personalised recommendations