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# Dynamic capacitated lot sizing with random demand and dynamic safety stocks

## Author

Listed:
• Helber, Stefan
• Sahling, Florian
• Schimmelpfeng, Katja

## Abstract

We present a stochastic version of the single-level, multi-product dynamic lotsizing problem subject to a capacity constraint. A production schedule has to be determined for random demand so that expected costs are minimized and a constraint based on a new backlog-oriented $\delta$-service-level measure is met. This leads to a non-linear model that is approximated by two different linear models. In the first approximation, a scenario approach based on random samples is used. In the second approximation model, the expected values of physical inventory and backlog as functions of the cumulated production are approximated by piecewise linear functions. Both models can be solved to determine efficient, robust and stable production schedules in the presence of uncertain and dynamic demand. They lead to dynamic safety stocks that are endogenously coordinated with the production quantities. A numerical analysis based on a set of (artificial) problem instances is used to evaluate the relative performance of the two different approximation approaches. We furthermore show under which conditions precise demand forecasts are particularly useful from a production-scheduling perspective.

## Suggested Citation

• Helber, Stefan & Sahling, Florian & Schimmelpfeng, Katja, 2011. "Dynamic capacitated lot sizing with random demand and dynamic safety stocks," Hannover Economic Papers (HEP) dp-465, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
• Handle: RePEc:han:dpaper:dp-465
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File URL: http://diskussionspapiere.wiwi.uni-hannover.de/pdf_bib/dp-465.pdf

## Citations

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Cited by:

1. Timo Hilger & Florian Sahling & Horst Tempelmeier, 2016. "Capacitated dynamic production and remanufacturing planning under demand and return uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 849-876, October.
2. Koca, Esra & Yaman, Hande & Selim Aktürk, M., 2015. "Stochastic lot sizing problem with controllable processing times," Omega, Elsevier, vol. 53(C), pages 1-10.
3. Rafiei, Rezvan & Nourelfath, Mustapha & Gaudreault, Jonathan & De Santa-Eulalia, Luis Antonio & Bouchard, Mathieu, 2015. "Dynamic safety stock in co-production demand-driven wood remanufacturing mills: A case study," International Journal of Production Economics, Elsevier, vol. 165(C), pages 90-99.
4. Löhndorf, Nils & Riel, Manuel & Minner, Stefan, 2014. "Simulation optimization for the stochastic economic lot scheduling problem with sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 157(C), pages 170-176.
5. 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.

### Keywords

lot sizing; random demand; dynamic safety stocks;

### JEL classification:

• C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

### NEP fields

This paper has been announced in the following NEP Reports:

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