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MIP Formulations for a Rich Real-World Lot-Sizing Problem with Setup Carryover

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

Abstract

A rich lot-sizing problem is studied in this manuscript which comes from a real-world application. Our new lot-sizing problem combines several features, i.e., parallel machines, production time windows, backlogging, lost sale and setup carryover. Three mixed integer programming formulations are proposed. We theoretically and computationally compare these different formulations, testing them on real-world and randomly generated instances. Our study is the first step for efficiently tackling and solving this challenging real-world lot-sizing problem.

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References

  1. Absi, N., Kedad-Sidhoum, S., Dauzère-Pérès, S.: Uncapacitated lot-sizing problem with production time windows, early productions, backlogs and lost sales. Int. J. Prod. Res. 49(9), 2551–2566 (2011)

    Article  MATH  Google Scholar 

  2. Brahimi, N., Dauzère-Pérès, S., Wolsey, L.A.: Polyhedral and lagrangian approaches for lot sizing with production time windows and setup times. Comput. Oper. Res. 37(1), 182–188 (2010)

    Article  MATH  Google Scholar 

  3. Dauzère-Pérès, S., Brahimi, N., Najid, N., Nordli, A.: The single-item lot sizing problem with time windows. Technical report 02/4/AUTO, École des Mines de Nantes, France (2002)

    Google Scholar 

  4. Dillenberger, C., Escudero, L.F., Wollensak, A., Zhang, W.: On solving a large-scale resource allocation problem in production planning. In: Fandel, G., Gulledge, T., Jones, A. (eds.) Operations Research in Production Planning and Control, pp. 105–119. Springer, Heidelberg, Berlin (1993)

    Chapter  Google Scholar 

  5. Fiorotto, D.J., Araujo, S.A.D.: Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines. Ann. Oper. Res. 217(1), 213–231 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Gopalakrishnan, M.: A modified framework for modelling set-up carryover in the capacitated lotsizing problem. Int. J. Prod. Res. 38(14), 3421–3424 (2000)

    Article  MATH  Google Scholar 

  7. Gören, H.G., Tunal, S.: Solving the capacitated lot sizing problem with setup carryover using a new sequential hybrid approach. Appl. Intell. 42(4), 805–816 (2015)

    Article  Google Scholar 

  8. Haase, K.: Lotsizing and Scheduling for Production Planning. LNEM, vol. 408. Springer, Berlin (1994)

    MATH  Google Scholar 

  9. Hwang, H.: Dynamic lot-sizing model with production time windows. Nav. Res. Log. 54(6), 692–701 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mittelmann, H.D., Pruessner, A.: A server for automated performance analysis of benchmarking data. Optim. Method Softw. 21(1), 105–120 (2006)

    Article  MATH  Google Scholar 

  11. Pochet, Y., Wolsey, L.A.: Production Planning by Mixed Integer Programming. Springer, New York (2006)

    MATH  Google Scholar 

  12. Sandbothe, R.A., Thompson, G.L.: A forward algorithm for the capacitated lot size model with stockouts. Oper. Res. 38(3), 474–486 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sox, C.R., Gao, Y.: The capacitated lot sizing problem with setup carry-over. IIE Trans. 31(2), 173–181 (1999)

    Google Scholar 

  14. Suerie, C., Stadtler, H.: The capacitated lot-sizing problem with linked lot sizes. Manage. Sci. 49(8), 1039–1054 (2003)

    Article  MATH  Google Scholar 

  15. Toledo, F.M.B.: Dimensionamento de Lotes em Máquinas Paralelas. Tese (Doutorado), Faculdade de Engenharia Elétrica e Computaç\(\tilde{a}\)o, Universidade Estadual de Campinas, Campinas (1998)

    Google Scholar 

  16. Toledo, F.M.B., Armentano, V.A.: A lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines. Eur. J. Oper. Res. 175(2), 1070–1083 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wolsey, L.A.: Lot-sizing with production and delivery time windows. Math. Program. 107(3), 471–489 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zangwill, W.I.: A backlogging model and a multi-echelon model of a dynamic economic lot size production system - a network approach. Manage. Sci. 15(9), 506–527 (1969)

    Article  MATH  Google Scholar 

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Correspondence to Fabio Furini .

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Focacci, F., Furini, F., Gabrel, V., Godard, D., Shen, X. (2016). MIP Formulations for a Rich Real-World Lot-Sizing Problem with Setup Carryover. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

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