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Learning in Setups: Analysis, Minimal Forecast Horizons, and Algorithms

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  • Michal Tzur

    (Industrial Engineering Department, Tel Aviv University, Tel Aviv 69978, Israel)

Abstract

We analyze the dynamic lot-sizing model in which the cost of a setup depends on the number of setups that have occurred prior to it. This arises, for example, when there exist learning effects in setups. Our model is more general than most learning models in the literature since it allows the total setup cost to be a general nondecreasing (but not necessarily concave) function of the number of setups. We explore tight relationships between our model and special cases of the classical dynamic lot-sizing model. On the basis of these we find minimal forecast and planning horizons for our model, which determine the first decision when the model is solved on a rolling horizon basis. When a forecast horizon cannot be found, we provide guidelines regarding the optimal first decision. We also provide an algorithm to solve the finite horizon problem, which uses as sub-problems variations of the classical dynamic lot-sizing problem. The advantage of this approach is the ability to use the extensive literature available on the latter, to generalize the results of this paper. As many of our results are qualitative in nature, they provide insights which can be useful for other models with a similar setup cost behavior.

Suggested Citation

  • Michal Tzur, 1996. "Learning in Setups: Analysis, Minimal Forecast Horizons, and Algorithms," Management Science, INFORMS, vol. 42(12), pages 1732-1743, December.
    • Handle: RePEc:inm:ormnsc:v:42:y:1996:i:12:p:1732-1743
    DOI: 10.1287/mnsc.42.12.1732
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    Citations

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    Cited by:

    1. Fuying Jing & Zirui Lan, 2017. "Forecast horizon of multi-item dynamic lot size model with perishable inventory," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-15, November.
    2. Chiu, Huan Neng & Chen, Hsin Min, 2005. "An optimal algorithm for solving the dynamic lot-sizing model with learning and forgetting in setups and production," International Journal of Production Economics, Elsevier, vol. 95(2), pages 179-193, February.
    3. Bradley R. Staats & Francesca Gino, 2012. "Specialization and Variety in Repetitive Tasks: Evidence from a Japanese Bank," Management Science, INFORMS, vol. 58(6), pages 1141-1159, June.
    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. Mazzola, Joseph B. & Neebe, Alan W. & Rump, Christopher M., 1998. "Multiproduct production planning in the presence of work-force learning," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 336-356, April.
    6. Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    7. 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.
    8. Sunantha Teyarachakul & Suresh Chand & Michal Tzur, 2016. "Lot sizing with learning and forgetting in setups: Analytical results and insights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 93-108, March.

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