Abstract
We consider a variant of the single item lot sizing problem where the product, when stored, suffers from a proportional loss, and in which the product demand is affected by uncertainty. This setting is particularly relevant in the energy sector, where the demands must be satisfied in a timely manner and storage losses are, often, unavoidable. We propose a two-stage robust optimization approach to tackle the problem with second stage storage variables. We first show that, in the case of uncertain demands, the robust problem can be solved as an instance of the deterministic one. We then address an application of robust lot sizing arising in the context of heat and power cogeneration and show that, even in this case, we can solve the problem as an instance of the deterministic lot sizing problem. Computational experiments are reported and illustrated.
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Notes
- 1.
In case of backlogging, shortages in the inventory are allowed—or, said differently, unmet demand can be postponed, at a cost, to the future.
- 2.
When applied to the lot sizing problem, the idea of \(\varGamma \)-robustness is of assuming that the uncertain parameters, i.e., the demand at different time steps, belong to symmetric intervals and that, given an integer \(\varGamma \), the total number of time steps in which the uncertain demand deviates from its nominal value to either of the extremes of its intervals is bounded by \(\varGamma \) in any constraint of the problem. See [BS03, BS04].
- 3.
Although “electrical energy” would be more precise, we will refer to “power” in the following. Due to the hourly time scale, this quantity is, indeed, a measure of power.
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Acknowledgement
This work is supported by the German Federal Ministry for Economic Affairs and Energy, BMWi, grant 03ET7528B.
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Coniglio, S., Koster, A., Spiekermann, N. (2016). On Robust Lot Sizing Problems with Storage Deterioration, with Applications to Heat and Power Cogeneration. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_3
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DOI: https://doi.org/10.1007/978-3-319-45587-7_3
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