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Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem


  • Hartmut Stadtler

    () (Technische Universität Darmstadt, Institut für Betriebswirtschaftslehre, Fachgebiet Fertigungs- und Materialwirtschaft, Hochschulstra\beta e 1, D 64289 Darmstadt, Germany)


A major argument for favoring simple lot-sizing heuristics---like the Silver/Meal or Groff's heuristic---to solve instances of the dynamic single-level uncapacitated lot-sizing problem (SLLSP) instead of exact algorithms---like those of Wagner/Whitin or Federgruen/Tzur---is that exact algorithms applied in a rolling horizon environment are heuristics too and may be outperformed by simple heuristics. This article shows how to modify the model of the SLLSP by looking beyond the planning horizon. Extensive tests within a rolling horizon environment have demonstrated that the modified model solved by an exact algorithm now performs at least as well as well-known heuristics and is fairly insensitive to the length of the planning horizon. Furthermore, our principal idea of improving rolling schedules by considering only a portion of the fixed cost related to a decision with an impact on periods beyond the planning horizon is applicable to a wide range of decision models.

Suggested Citation

  • Hartmut Stadtler, 2000. "Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem," Management Science, INFORMS, vol. 46(2), pages 318-326, February.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:2:p:318-326

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    References listed on IDEAS

    1. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    2. Stadtler, Hartmut, 1997. "Reformulations of the shortest route model for dynamic multi-item multi-level capacitated lotsizing," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 7096, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
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    8. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
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    Cited by:

    1. Christopher Suerie & Hartmut Stadtler, 2003. "The Capacitated Lot-Sizing Problem with Linked Lot Sizes," Management Science, INFORMS, vol. 49(8), pages 1039-1054, August.
    2. repec:eee:proeco:v:190:y:2017:i:c:p:31-36 is not listed on IDEAS
    3. Wilco van den Heuvel & Albert P.M. Wagelmans, 2002. "A Note on Ending Inventory Valuation in Multiperiod Production Scheduling," Tinbergen Institute Discussion Papers 02-067/4, Tinbergen Institute.
    4. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    6. Pürgstaller, Peter & Missbauer, Hubert, 2012. "Rule-based vs. optimisation-based order release in workload control: A simulation study of a MTO manufacturer," International Journal of Production Economics, Elsevier, vol. 140(2), pages 670-680.
    7. Sahin, Funda & Powell Robinson, E. & Gao, Li-Lian, 2008. "Master production scheduling policy and rolling schedules in a two-stage make-to-order supply chain," International Journal of Production Economics, Elsevier, vol. 115(2), pages 528-541, October.
    8. Meixell, Mary J., 2005. "The impact of setup costs, commonality, and capacity on schedule stability: An exploratory study," International Journal of Production Economics, Elsevier, vol. 95(1), pages 95-107, January.
    9. Dellaert, Nico & Jeunet, Jully, 2003. "Controlling multi-level production in a rolling-schedule environment," International Journal of Production Economics, Elsevier, vol. 85(1), pages 113-121, July.
    10. Nguyen, Christine & Dessouky, Maged & Toriello, Alejandro, 2014. "Consolidation strategies for the delivery of perishable products," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 69(C), pages 108-121.
    11. Toy, Ayhan Özgür & Berk, Emre, 2013. "Dynamic lot sizing for a warm/cold process: Heuristics and insights," International Journal of Production Economics, Elsevier, vol. 145(1), pages 53-66.
    12. repec:eee:ejores:v:263:y:2017:i:3:p:838-863 is not listed on IDEAS
    13. Umetani, Shunji & Fukushima, Yuta & Morita, Hiroshi, 2017. "A linear programming based heuristic algorithm for charge and discharge scheduling of electric vehicles in a building energy management system," Omega, Elsevier, vol. 67(C), pages 115-122.
    14. Jeunet, Jully, 2006. "Demand forecast accuracy and performance of inventory policies under multi-level rolling schedule environments," International Journal of Production Economics, Elsevier, vol. 103(1), pages 401-419, September.
    15. repec:dau:papers:123456789/2078 is not listed on IDEAS
    16. Wilco Van den Heuvel & Albert P. M. Wagelmans, 2010. "Worst-Case Analysis for a General Class of Online Lot-Sizing Heuristics," Operations Research, INFORMS, vol. 58(1), pages 59-67, February.
    17. Dellaert, N. & Jeunet, J., 2005. "An alternative to safety stock policies for multi-level rolling schedule MRP problems," European Journal of Operational Research, Elsevier, vol. 163(3), pages 751-768, June.
    18. Tom Vogel & Bernardo Almada-Lobo & Christian Almeder, 2017. "Integrated versus hierarchical approach to aggregate production planning and master production scheduling," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 193-229, January.
    19. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    20. Narayanan, Arunachalam & Robinson, Powell, 2010. "Evaluation of joint replenishment lot-sizing procedures in rolling horizon planning systems," International Journal of Production Economics, Elsevier, vol. 127(1), pages 85-94, September.
    21. Merce, C. & Fontan, G., 2003. "MIP-based heuristics for capacitated lotsizing problems," International Journal of Production Economics, Elsevier, vol. 85(1), pages 97-111, July.
    22. 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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    lot-sizing; rolling schedules; planning horizon;


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