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Erratum: A tight formulation for uncapacitated lot-sizing with stock upper bounds

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Abstract

For an n-period uncapacitated lot-sizing problem with stock upper bounds, stock fixed costs, stock overload and backlogging, we present a tight extended shortest path formulation of the convex hull of solutions with O\((n^2)\) variables and constraints, also giving an O\((n^2)\) algorithm for the problem. This corrects and extends a formulation in Section 4.4 of our article “Lot-sizing with production and delivery time windows”, Mathematical Programming A, 107:471–489, 2006, for the problem with just stock upper bounds.

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References

  1. Atamtürk, A., Küçükyavuz, S.: Lot-sizing with inventory bounds and fixed costs: polyhedral study and computation. Oper. Res. 53, 711–730 (2005)

    Article  MATH  Google Scholar 

  2. Atamtürk, A., Küçükyavuz, S.: An O\((n^2)\) algorithm for lot sizing with inventory bounds and fixed costs. Oper. Res. Lett. 36, 297–299 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brahimi. N.: Planification de la production: modèles et algorithmes pour les problemes de dimensionnement de lots. Ph.D. thesis, Université de Nantes (2004)

  4. Brahimi, N., Dauzère-Pérès, S., Najid, N.: Capacitated multi-multi item lot sizing problems with time windows. Oper. Res. 54, 951–987 (2006)

    Article  MATH  Google Scholar 

  5. 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, 182–188 (2010)

    Article  MATH  Google Scholar 

  6. Gade, D., Kucukyavuz, S.: A note on “Uncapacitated lot-sizing with fixed charges on stocks: the convex hull”. Discrete Optim. 8, 385–392 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hwang, H.C.: Dynamic lot-sizing with production time windows. Nav. Res. Logist. Q. 54, 692–701 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hwang, H.C., van den Heuvel, W.: Improved algorithms for lot-sizing problem with bounded inventory and backlogging. Nav. Res. Logist. 59, 244–253 (2012)

    Article  MathSciNet  Google Scholar 

  9. Love, S.F.: Bounded production and inventory models with piecewise concave costs. Manag. Sci. 20, 313–318 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  10. van den Heuvel, W., Wagelmans, A.P.M.: Four equivalent lot-sizing models. Oper. Res. Lett. 36, 465–470 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Van Vyve, M., Ortega, F.: Lot-sizing with fixed charges on stocks:the convex hull. Discrete Optim. 1, 189–203 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. CORE, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Laurence A. Wolsey

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  1. Laurence A. Wolsey
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Correspondence to Laurence A. Wolsey.

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This text presents research results of the Belgian Program on Interuniversity Poles of Attraction initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed by the authors.

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Wolsey, L.A. Erratum: A tight formulation for uncapacitated lot-sizing with stock upper bounds. Math. Program. 161, 603–609 (2017). https://doi.org/10.1007/s10107-016-0999-1

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  • DOI: https://doi.org/10.1007/s10107-016-0999-1

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