Abstract
We introduce a two-level stochastic capacitated lot-sizing problem with random demand and service level constraints under the static and static-dynamic uncertainty strategy. While the static strategy determines setup periods and lot-sizes at the beginning of the planning horizon, the static-dynamic strategy allows adjustments of lot-sizes during the planning horizon. We present a model formulation of the demand difference adaptation policy for a multi-stage production system. Thereby, lot-size adaptations depend on demand differences between the realized and expected demand. We evaluate 144 test instances with different parameter settings to quantify the economic efficiency of the uncertainty strategies for the multilevel lot-sizing problem. The computational study demonstrates that additional costs of semifinished goods and scarcity of storage capacity on upstream precesses reduce the cost saving potential of lot-size adaptations.
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References
Bookbinder, J. H., & Tan, J. Y. (1988). Strategies for the probabilistic lot-sizing problem with service-level constraints. Management Science, 34(9), 1096-1108. https://doi.org/10.1287/mnsc.34.9.1096
Mickein, M., & Haase, K. (2022). A novel demand difference adaptation policy for applying the static-dynamic uncertainty stratgey for the lot-sizing problem. Working Paper.
Helber, S., Sahling, F., & Schimmelpfeng, K. (2013). Dynamic capacitated lot sizing with random demand and dynamic safety stocks. OR Spectrum, 35(1), 75-105. https://doi.org/10.1007/s00291-012-0283-6
Mickein, M., & Haase, K. (2022). Technical summary: Scenario generation and solution approach for scenario-approximated problems. Preprint. https://doi.org/10.25592/uhhfdm.10799
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Mickein, M., Haase, K. (2023). The Lot-Size Adaptation Approach for the Two-Level Stochastic Capacitated Lot-Sizing Problem. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_79
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DOI: https://doi.org/10.1007/978-3-031-24907-5_79
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