Abstract
Many practical applications of the cutting stock problem (CSP) have additional costs for setting up machine configurations. In this paper we describe a post-processing method which can improve solutions in general, but works especially well if additional setup costs are considered. We formalize a general cutting stock problem and a solution merging problem which can be used as a post-processing step. To solve the solution merging problem we propose an integer linear programming (ILP) model, a greedy approach, a PILOT method and a beam search. We apply the approaches to different real-world problems and compare their results. They show that in up to 50% of the instances the post-processing could improve the previous best solution.
We thank Lodestar Technology Ges.m.b.H. for the collaboration, the Austrian Research Promotion Agency FFG for funding this project under contract “Innovationsscheck Plus Nr. 855569” and the Vienna Graduate School on Computational Optimization, financed by the Austrian Science Fund (FWF) under grant W1260.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dusberger, F., Raidl, G.R.: A scalable approach for the K-staged two-dimensional cutting stock problem with variable sheet size. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2015. LNCS, vol. 9520, pp. 384–392. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27340-2_48
Cheng, C., Feiring, B., Cheng, T.: The cutting stock problem—a survey. Int. J. Prod. Econ. 36(3), 291–305 (1994)
Cui, Y., Zhong, C., Yao, Y.: Pattern-set generation algorithm for the one-dimensional cutting stock problem with setup cost. EJOR 243(2), 540–546 (2015)
Yang, J., Leung, J.Y.T.: A generalization of the weighted set covering problem. Naval Res. Logist. 52(2), 142–149 (2005)
Duin, C., Voß, S.: The Pilot method: a strategy for heuristic repetition with application to the Steiner problem in graphs. Networks 34(3), 181–191 (1999)
Lowerre, B.T.: The HARPY speech recognition system. Ph.D thesis, Carnegie Mellon University, Pittsburgh, PA, USA (1976)
Gurobi Optimization Inc: Gurobi optimizer reference manual, version 7.0.1 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Klocker, B., Raidl, G.R. (2018). Solving a Weighted Set Covering Problem for Improving Algorithms for Cutting Stock Problems with Setup Costs by Solution Merging. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2017. EUROCAST 2017. Lecture Notes in Computer Science(), vol 10671. Springer, Cham. https://doi.org/10.1007/978-3-319-74718-7_43
Download citation
DOI: https://doi.org/10.1007/978-3-319-74718-7_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-74717-0
Online ISBN: 978-3-319-74718-7
eBook Packages: Computer ScienceComputer Science (R0)