reducing waste with an optimized trimming model in ...1450284/fulltext01.pdf · mttbi´`bt...

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Master Thesis, 30 hp Master of Science in Industrial Engineering and Management – Logistics & Optimization, 300 hp Spring 2020 REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN PRODUCTION PLANNING A Master´s Thesis Project at a Forest Company Ellen Paulsson & Sofia Hallbäck

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Page 1: REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN ...1450284/FULLTEXT01.pdf · mTTbi´`BT TT2`bT`Q/mFiBQMM `T`Q/mFiBQMb`mHH `#2bF `biBHHFmM/`mHH `X1M/2H pbTBHH2i `M º/p M/B;i7 º`

Master Thesis, 30 hp

Master of Science in Industrial Engineering and Management – Logistics & Optimization, 300 hp

Spring 2020

REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN

PRODUCTION PLANNING

A Master´s Thesis Project at a Forest Company

Ellen Paulsson & Sofia Hallbäck

Page 2: REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN ...1450284/FULLTEXT01.pdf · mTTbi´`BT TT2`bT`Q/mFiBQMM `T`Q/mFiBQMb`mHH `#2bF `biBHHFmM/`mHH `X1M/2H pbTBHH2i `M º/p M/B;i7 º`

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Ellen Paulsson Sofia Hallbäck

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9XR h?2 S`Q/m+iBQM S`Q+2bb

Start Board Machine

Dispersion Machine

Converter 1

Converter 3

Stock

Customer

Customer

Stock

Stock Stock

Customer

Converter 2

Stock

Customer

Leftover reels goes back to stock

Possible but not currently used step

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9 References

Allender, E., Loui, M C., Regan, K W., (2009) Ch 27: Complexity Classes. In CRC Handbook on Algorithms and Theory of Computation, 1(2), Publisher: Chapman and Hall/CRC Press [Online] Available via: https://cse.buffalo.edu/~regan/papers/pdf/ALRch27.pdf

Arenales, M., Cherri, A., Yanasse, H., Poldi, K., & Gonçalves Vianna, A. (2014). The one-dimensional cutting stock problem with usable leftovers – A survey. European Journal of Operational Research, 236(2), 395–402. DOI: https://doi.org/10.1016/j.ejor.2013.11.026

Bazaraa, M., Jarvis, J., & Sherali, H. (2010). Linear programming and network flows (3rd ed.). Publisher: Wiley. Pages 1-2 ISBN-10: 0470462728

Cajot, S., & Schüler, N.,(2019) in Urban Energy Systems for Low-Carbon Cities [Online] March 2020. Available via: https://www.sciencedirect.com/topics/earth-and-planetary-sciences/mathematical-programming.

CEPI – Confederation of European Paper Industries, (2020) Paper History. [Online] April 2020. Available via: http://www.cepi.org/system/files/public/static-pages/WEB_Infographic%20Paper%20History.pdf

Chung-Yang, R H., Chao-Yue, L., Kwang-Ting., T C., (2009) Fundamentals of algorithms. Electronic Design Automation, Pages 173-234 DOI: https://doi.org/10.1016/B978-0-12-374364-0.50011-4

Delormea, M., Iori, M., & Martelloa, S., (2016) Binpacking and cutting stock problems: Mathematical models and exact algorithms. European Journal of Operational Research 255, 1–20, DOI: http://dx.doi.org/10.1016/j.ejor.2016.04.030

Gbemileke A. Ogunranti1 & Ayodeji E. Oluleye. (2016). Minimizing Waste (Off-cuts) Using Cutting Stock Model:The Case of One Dimensional Cutting Stock Problem in Wood Working Industry. Journal of Industrial Engineering and Management. [JIEM], 9(3): 834-859 DOI: http://dx.doi.org/10.3926/jiem.1653

Gilmore, P.C. & Gomory, R. E., (1961) A Linear Programming Approach to the Cutting-Stock Problem. Operations Research, 9(6), pp. 849-859.

Hayes, A. (2019). Make to Order (MTO), Investopedia, [Online] April 2019. Available via: https://www.investopedia.com/terms/m/make-to-order.asp

Page 36: REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN ...1450284/FULLTEXT01.pdf · mTTbi´`BT TT2`bT`Q/mFiBQMM `T`Q/mFiBQMb`mHH `#2bF `biBHHFmM/`mHH `X1M/2H pbTBHH2i `M º/p M/B;i7 º`

Hoos,H., Stützle, T., (2005) Stochastic Local Search - Foundations and Applications. The Morgan Kaufmann Series in Artificial Intelligence, pages 13-59 DOI: https://doi.org/10.1016/B978-155860872-6/50018-4

Kallrath, J., Rebennack, S., Kallrath, J., & Kusche, R., (2014) Solving real-world cutting stock-problems in the paper industry: Mathematical approaches, experience and challenges. European Journal of Operational Research 238, pp 374–389. DOI: http://dx.doi.org/10.1016/j.ejor.2014.03.027

Kaveh (2013) What is the definition of P, NP, NP-complete and NP-hard? Answers from a Software Engineer at Google. with a Ph.D. in Computer Science, University of Toronto. [Online] 2020 Available via: https://cs.stackexchange.com/questions/9556/what-is-the-definition-of-p-np-np-complete-and-np-hard

Kirwan, M J. (2013), Handbook of Paper and Paperboard Packaging Technology, Second Edition Publisher: John Wiley & Sons © (431 pages) ISBN:9780470670668

Kyungdoc, K., Byung-In, K., & Hyunbo, C., (2014). Multiple-choice knapsack-based heuristic algorithm for the two-stage two-dimensional cutting stock problem in the paper industry, International Journal of Production Research, 52:19, 5675-5689, DOI: http://10.1080/00207543.2014.903347

Lundgren, J., Rönnqvist, M., & Värbrand, P. (2008). Optimization (3. ed.). Publisher: Studentlitteratur AB. Page 13. ISBN : 978-91-44-05314-1

Mannheimer, E.,& Eliason, H. (2019). Master thesis project proposal. [Email] (Personal communication, November 29, 2019)

Merriam Webster (2020). Optimization. Merriam Webster, Dictionary. [Online] March 2020. Available via: https://www.merriam-webster.com/dictionary/optimization

Mobasher, A., & Ekici, A. (2013). Solution approaches for the cutting stock problem with setup cost. Computers and Operations Research, 40(1), 225–235. DOI: https://doi.org/10.1016/j.cor.2012.06.007

Muter, I., & Sezer, Z. (2018). Algorithms for the one-dimensional two-stage cutting stock problem. European Journal of Operational Research, 271(1), 20–32. DOI: https://doi.org/10.1016/j.ejor.2018.04.042

Page 37: REDUCING WASTE WITH AN OPTIMIZED TRIMMING MODEL IN ...1450284/FULLTEXT01.pdf · mTTbi´`BT TT2`bT`Q/mFiBQMM `T`Q/mFiBQMb`mHH `#2bF `biBHHFmM/`mHH `X1M/2H pbTBHH2i `M º/p M/B;i7 º`

Segal, T. (2019). Make To Stock — MTS Definition, Investopedia, [Online] May 2019. Available via: https://www.investopedia.com/terms/m/make-to-stock.asp

The company a (2020). The company in 2019, a summary. [Online] February 2020.

The company b (2020). Our forest holdings. [Online] February 2020.

The company c (2020). About The company. [Online] February 2020.

The company d (2020). Our business idea. [Online] February 2020.

The company e (2020). Innovation. [Online] February 2020.

The company f (2020). Sustainability. [Online] February 2020.

Thomas, J. & Chaudhari, N.S. (2016) An integrated genetic algorithm approach to one-D cutting stock problem, Int. J.Operational Research. Vol. 27(1), pp 23-46 DOI: 10.1023/A:1022955531018

United States Environmental Protection Agency (2020) Greenhouse Gas Equivalencies Calculator [Online] May 2020. Available via: https://www.epa.gov/energy/greenhouse-gas-equivalencies-calculator