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Lot sizing with storage losses under demand uncertainty

Lot sizing with storage losses under demand uncertainty
Lot sizing with storage losses under demand uncertainty
We address a variant of the single item lot sizing problem affected by proportional storage (or inventory) losses and uncertainty in the product demand. The problem has applications in, among others, the energy sector, where storage losses (or storage deteriorations) are often unavoidable and, due to the need for planning ahead, the demands can be largely uncertain. We first propose a two-stage robust optimization approach with second-stage storage variables, showing how the arising robust problem can be solved as an instance of the deterministic one. We then consider a two-stage approach where not only the storage but also the production variables are determined in the second stage. After showing that, in the general case, solutions to this problem can suffer from acausality (or anticipativity), we introduce a flexible affine rule approach which, albeit restricting the solution set, allows for causal production plans. A hybrid robust-stochastic approach where the objective function is optimized in expectation, as opposed to in the worst-case, while retaining robust optimization guarantees of feasibility in the worst-case, is also discussed. We conclude with an application to heat production, in the context of which we compare the different approaches via computational experiments on real-world data.
763-788
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Koster, Arie
22c70cb3-4f20-4721-9694-1a45a623c2f8
Spiekermann, Nils
b770add8-31f6-4fa2-9cf8-d0fdf3b7fbc7
Coniglio, Stefano
03838248-2ce4-4dbc-a6f4-e010d6fdac67
Koster, Arie
22c70cb3-4f20-4721-9694-1a45a623c2f8
Spiekermann, Nils
b770add8-31f6-4fa2-9cf8-d0fdf3b7fbc7

Coniglio, Stefano, Koster, Arie and Spiekermann, Nils (2018) Lot sizing with storage losses under demand uncertainty. Journal of Combinatorial Optimization, 36, 763-788. (doi:10.1007/s10878-017-0147-8).

Record type: Article

Abstract

We address a variant of the single item lot sizing problem affected by proportional storage (or inventory) losses and uncertainty in the product demand. The problem has applications in, among others, the energy sector, where storage losses (or storage deteriorations) are often unavoidable and, due to the need for planning ahead, the demands can be largely uncertain. We first propose a two-stage robust optimization approach with second-stage storage variables, showing how the arising robust problem can be solved as an instance of the deterministic one. We then consider a two-stage approach where not only the storage but also the production variables are determined in the second stage. After showing that, in the general case, solutions to this problem can suffer from acausality (or anticipativity), we introduce a flexible affine rule approach which, albeit restricting the solution set, allows for causal production plans. A hybrid robust-stochastic approach where the objective function is optimized in expectation, as opposed to in the worst-case, while retaining robust optimization guarantees of feasibility in the worst-case, is also discussed. We conclude with an application to heat production, in the context of which we compare the different approaches via computational experiments on real-world data.

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Accepted/In Press date: 16 June 2017
e-pub ahead of print date: 4 July 2017
Published date: 1 October 2018

Identifiers

Local EPrints ID: 414901
URI: http://eprints.soton.ac.uk/id/eprint/414901
PURE UUID: 5476783a-6a13-4c2e-b060-a52c9f690c66
ORCID for Stefano Coniglio: ORCID iD orcid.org/0000-0001-9568-4385

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Date deposited: 13 Oct 2017 16:30
Last modified: 16 Mar 2024 04:24

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Contributors

Author: Arie Koster
Author: Nils Spiekermann

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