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Production Scheduling for the Two Furnaces – One Casting Line System

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The paper presents a production scheduling problem in a foundry equipped with two furnaces and one casting line, where the line is a bottleneck and furnaces, of the same capacity, work in parallel. The amount of produced castings may not exceed the capacity of the line and the furnaces, and their loads determine metal type from which the products are manufactured on the casting line. The purpose of planning is to create the processing order of metal production to prevent delays in the delivery of the ordered products to the customers. The problem is a mix of a lot-sizing and scheduling problems on two machines (the furnaces) run in parallel. The article gives a mathematical model that defines the optimization problem, and its relaxed version based on the concept of a rolling-horizon planning. The proposed approaches, i.e. commercial solver and Iterated Local Search (ILS) heuristic, were tested on a sample data and different problem sizes. The tests have shown that rolling horizon approach gives the best results for most problems, however, developed ILS algorithm gives better results for the largest problem instances with tight furnace capacity.
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Bibliogra 10 poz., tab.
  • AGH University of Science and Technology, Faculty of Management, Krakow, Poland
  • [1] Basiura, R., Duda, J. & Stawowy, A. (2015). Production scheduling for the one furnace – two casting lines system, Archives of Foundry Engineering. 15(spec.2), 3-6.
  • [2] Stawowy, A. & Duda, J. (2017). Iterated Local Search for foundry lot-sizing and scheduling problem with setup costs. Archives of Foundry Engineering. 17(4), 161-164. DOI:
  • [3] de Araujo, S.A., Arenales, M.N. & Clark, A.R. (2007). Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups. Journal of Heuristics. 13, 337-358. DOI 10.1007/s10732-007-9011-9.
  • [4] 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.
  • [5] Li, X., Guo, S., Liu, Y. & Du, B. (2017). A production planning model for make-to-order foundry flow shop with capacity constraint, Mathematical Problems in Engineering. 15 pages. doi: 10.1155/2017/6315613.
  • [6] dos Santos-Meza, E., dos Santos, M.O. & Arenales, M.N. (2002). A lot-sizing problem in an automated foundry, European Journal of Operational Research. 139(2), 490-500.
  • [7] Clark, A.R. (2005). Rolling horizon heuristics for production and setup planning with backlogs and error-prone demand forecasts. Production Planning & Control. 16, 81-97. DOI: 10.1080/09537280412331286565.
  • [8] Ferreira, D., Morabito, R. & Rangel, S. (2010). Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants. Computers & Operations Research. 37, 684-691. DOI: 10.1016/ j.cor.2009.06.007.
  • [9] Stützle, T. (1999). Iterated local search for the quadratic assignment problem, Technical Report AIDA-99-03. FG Intellektik. FB Informatik. TU Darmstadt.
  • [10] Lourenço, H.R., Martin, O. & Stützle, T. (2003). Iterated Local Search. Handbook of Metaheuristics. Kluwer Academic Publishers, International Series in Operations Research & Management Science. 57, 321-3. DOI: 10.1007/0-306-48056-5_11.
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
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