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A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

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  • Tempelmeier, Horst

Abstract

This paper deals with the dynamic multi-item capacitated lot-sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fill rate constraint is in effect. It is assumed that, according to the static-uncertainty strategy of Bookbinder and Tan [1], all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed ABC[beta] heuristic is proposed.

Suggested Citation

  • Tempelmeier, Horst, 2011. "A column generation heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint," Omega, Elsevier, vol. 39(6), pages 627-633, December.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:6:p:627-633
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    References listed on IDEAS

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    1. Wijngaard, J. & Wortmann, J. C., 1985. "MRP and inventories," European Journal of Operational Research, Elsevier, vol. 20(3), pages 281-293, June.
    2. Alan S. Manne, 1958. "Programming of Economic Lot Sizes," Management Science, INFORMS, vol. 4(2), pages 115-135, January.
    3. Silver, Edward A. & Bischak, Diane P., 2011. "The exact fill rate in a periodic review base stock system under normally distributed demand," Omega, Elsevier, vol. 39(3), pages 346-349, June.
    4. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    5. Sox, Charles R. & Jackson, Peter L. & Bowman, Alan & Muckstadt, John A., 1999. "A review of the stochastic lot scheduling problem," International Journal of Production Economics, Elsevier, vol. 62(3), pages 181-200, September.
    6. James H. Bookbinder & Jin-Yan Tan, 1988. "Strategies for the Probabilistic Lot-Sizing Problem with Service-Level Constraints," Management Science, INFORMS, vol. 34(9), pages 1096-1108, September.
    7. Cattrysse, Dirk & Maes, Johan & Van Wassenhove, Luk N., 1990. "Set partitioning and column generation heuristics for capacitated dynamic lotsizing," European Journal of Operational Research, Elsevier, vol. 46(1), pages 38-47, May.
    8. Martel, Alain & Diaby, Moustapha & Boctor, Fayez, 1995. "Multiple items procurement under stochastic nonstationary demands," European Journal of Operational Research, Elsevier, vol. 87(1), pages 74-92, November.
    9. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2011. "The cost of using stationary inventory policies when demand is non-stationary," Omega, Elsevier, vol. 39(4), pages 410-415, August.
    10. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
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    Cited by:

    1. Özen, Ulaş & Doğru, Mustafa K. & Armagan Tarim, S., 2012. "Static-dynamic uncertainty strategy for a single-item stochastic inventory control problem," Omega, Elsevier, vol. 40(3), pages 348-357.
    2. repec:eee:jomega:v:76:y:2018:i:c:p:1-17 is not listed on IDEAS
    3. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
    4. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "Using branch-and-price approach to solve the directed network design problem with relays," Omega, Elsevier, vol. 40(5), pages 672-679.
    5. Pauls-Worm, Karin G.J. & Hendrix, Eligius M.T. & Alcoba, Alejandro G. & Haijema, René, 2016. "Order quantities for perishable inventory control with non-stationary demand and a fill rate constraint," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 238-246.
    6. Koca, Esra & Yaman, Hande & Selim Aktürk, M., 2015. "Stochastic lot sizing problem with controllable processing times," Omega, Elsevier, vol. 53(C), pages 1-10.
    7. repec:spr:annopr:v:264:y:2018:i:1:d:10.1007_s10479-017-2662-5 is not listed on IDEAS
    8. Yan, Changyuan & Liao, Yi & Banerjee, Avijit, 2013. "Multi-product lot scheduling with backordering and shelf-life constraints," Omega, Elsevier, vol. 41(3), pages 510-516.
    9. Tunc, Huseyin & Kilic, Onur A. & Tarim, S. Armagan & Eksioglu, Burak, 2013. "A simple approach for assessing the cost of system nervousness," International Journal of Production Economics, Elsevier, vol. 141(2), pages 619-625.
    10. Govindan, Kannan, 2015. "The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory," European Journal of Operational Research, Elsevier, vol. 242(2), pages 402-423.
    11. Pauls-Worm, Karin G.J. & Hendrix, Eligius M.T. & Haijema, René & van der Vorst, Jack G.A.J., 2014. "An MILP approximation for ordering perishable products with non-stationary demand and service level constraints," International Journal of Production Economics, Elsevier, vol. 157(C), pages 133-146.
    12. Choudhary, Devendra & Shankar, Ravi, 2015. "The value of VMI beyond information sharing in a single supplier multiple retailers supply chain under a non-stationary (Rn, Sn) policy," Omega, Elsevier, vol. 51(C), pages 59-70.
    13. Chen, Haoxun, 2015. "Fix-and-optimize and variable neighborhood search approaches for multi-level capacitated lot sizing problems," Omega, Elsevier, vol. 56(C), pages 25-36.
    14. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.

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