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Approximation Methods for the Uncapacitated Dynamic Lot Size Problem


  • Gabriel R. Bitran

    (Sloan School of Management, MIT, Cambridge, Massachusetts 02139)

  • Thomas L. Magnanti

    (Sloan School of Management, MIT, Cambridge, Massachusetts 02139)

  • Horacio H. Yanasse

    (Instituto de Pesquisas Espaciais, Sao Paulo, Brizil)


We provide worst case error bounds for several approximation methods (heuristics, product aggregation, and partitioning of the planning horizon) for the uncapacitated dynamic lot size problem. We propose two managerially oriented heuristics and show that they have a relative wont case error bound equal to two, and develop similar analyses for methods known as the least cost per unit heuristic, the part period balancing heuristic, and an economic order quantity heuristic (expressed in terms of a time supply of demand). We also show how errors introduced by partitioning of the planning horizon in multi-product multi-facility problems are bounded by product set-up costs, and how errors introduced by product aggregation are bounded by set-up costs, holding costs, and demands. The latter results suggest methods for product aggregation that minimize the worst case error bounds.

Suggested Citation

  • Gabriel R. Bitran & Thomas L. Magnanti & Horacio H. Yanasse, 1984. "Approximation Methods for the Uncapacitated Dynamic Lot Size Problem," Management Science, INFORMS, vol. 30(9), pages 1121-1140, September.
  • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:9:p:1121-1140

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    Cited by:

    1. van den Heuvel, W.J. & Wagelmans, A.P.M., 2008. "A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters," Econometric Institute Research Papers EI 2008-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Chung-Yee Lee & Sila Çetinkaya & Albert P. M. Wagelmans, 2001. "A Dynamic Lot-Sizing Model with Demand Time Windows," Management Science, INFORMS, vol. 47(10), pages 1384-1395, October.
    4. Chung-Yee Lee & Sila Çetinkaya & Albert P.M. Wagelmans, 1999. "A Dynamic Lot-Sizing Model with Demand Time Windows," Tinbergen Institute Discussion Papers 99-095/4, Tinbergen Institute.
    5. Ganas, Ioannis S. & Papachristos, Sotirios, 1997. "Analytical evaluation of heuristics performance for the single-level lot-sizing problem for products with constant demand," International Journal of Production Economics, Elsevier, vol. 48(2), pages 129-139, January.
    6. Hiroshi Konno & Takaaki Egawa & Rei Yamamoto, 2009. "Comparative studies on dynamic programming and integer programming approaches for concave cost production/inventory control problems," Computational Management Science, Springer, vol. 6(4), pages 447-457, October.
    7. 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.
    8. Massonnet, G. & Gayon, J.-P. & Rapine, C., 2014. "Approximation algorithms for deterministic continuous-review inventory lot-sizing problems with time-varying demand," European Journal of Operational Research, Elsevier, vol. 234(3), pages 641-649.
    9. Lee, C.Y. & Cetinkaya, S. & Wagelmans, A.P.M., 1999. "A dynamic lot-sizing model with demand time windows," Econometric Institute Research Papers EI 9948-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.

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    inventory/production: lot sizing;


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