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Application of Interval Arithmetic to Production Planning in a Foundry

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A novel approach for treating the uncertainty about the real levels of finished products during production planning and scheduling process is presented in the paper. Interval arithmetic is used to describe uncertainty concerning the production that was planned to cover potential defective products, but meets customer’s quality requirement and can be delivered as fully valuable products. Interval lot sizing and scheduling model to solve this problem is proposed, then a dedicated version of genetic algorithm that is able to deal with interval arithmetic is used to solve the test problems taken from a real world example described in the literature. The achieved results are compared with a standard approach in which no uncertainty about real production of valuable castings is considered. It has been shown that interval arithmetic can be a valuable method for modeling uncertainty, and proposed approach can provide more accurate information to the planners allowing them to take more tailored decisions.
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Bibliogr. 10 poz., tab., wzory
  • AGH University of Science and Technology, Faculty of Management ul. Gramatyka 10, 30-067 Kraków
  • AGH University of Science and Technology, Faculty of Management ul. Gramatyka 10, 30-067 Kraków,
  • [1] de Araujo, S.A., Arenales, M.N. & Clark, A.R. (2008). Lot sizing and furnace scheduling in small foundries. Computers & Operations Research. 35(3), 916-932. DOI: 10.1016/ j.cor.2006.05.010.
  • [2] Duda, J. & Stawowy, A. (2015). Production scheduling under fuzziness for the furnace-casting line system. Archives of Foundry Engineering. 15(4), 29-32. DOI: 10.1515/afe-2015-0074.
  • [3] Han, Y., Gong, D., Jin, Y. & Pan, Q. (2016). Evolutionary multi-objective blocking lot-streaming flow shop scheduling with interval processing time. Applied Soft Computing. 42, 229-245. DOI: 10.1016/j.asoc.2016.01.033.
  • [4] Hickey, T., Ju, Q. & van Emden, M.H. (2001). Interval arithmetic: from principles to implementation. Journal of the ACM. 48(5), 1038-1068. DOI: 10.1145/502102.502106.
  • [5] Lei, D. (2012). Interval job shop scheduling problems. The International Journal of Advanced Manufacturing Technology. 60(1), 291-301. DOI: 10.1007/s00170-011-3600-3.
  • [6] Lei, D. & Guo, X. (2015). An effective neighborhood search for scheduling in dual-resource constrained interval job shop with environmental objective. International Journal of Production Economics. 159, 296-303. DOI: 10.1016/ j.ijpe.2014.07.026.
  • [7] Moore, R.E. (1966). Interval analysis. Englewood Cliffs: Prentice-Hall.
  • [8] Pereira, J. (2016). The robust (minmax regret) single machine scheduling with interval processing times and total weighted completion time objective. Computers & Operations Research. 66(C), 141-152. DOI: 10.1016/j.cor.2015.08.010.
  • [9] Stawowy, A. & Duda, J. (2012). Models and algorithms for production planning and scheduling in foundries – current state and development perspectives. Archives of Foundry Engineering. 12(2), 69-74. DOI: 10.2478/v10266-012- 0039-4.
  • [10] Stawowy, A. & Duda, J. (2013). Production scheduling for the furnace-casting line system. Archives of Foundry Engineering. 13(3), 84-87. DOI: 10.2478/afe-2013-0065 90.
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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