Pomes, A. orcid.org/0009-0009-6087-5363, Diglio, A. orcid.org/0000-0002-9775-3927, Nickel, S. orcid.org/0000-0002-8339-0117 et al. (1 more author) (2025) Multi-stage stochastic districting: optimization models and solution algorithms. Annals of Operations Research. ISSN 0254-5330
Abstract
This paper investigates a Multi-Stage Stochastic Districting Problem (MSSDP). The goal is to devise a districting plan (i.e., clusters of Territorial Units—TUs) accounting for uncertain parameters changing over a discrete multi-period planning horizon. The problem is cast as a multi-stage stochastic programming problem. It is assumed that uncertainty can be captured by a finite set of scenarios, which induces a scenario tree. Each node in the tree corresponds to the realization of all the stochastic parameters from the root node—the state of nature—up to that node. A mathematical programming model is proposed that embeds redistricting recourse decisions and other recourse actions to ensure that the districts are balanced regarding their activity. The model is tested on instances generated using literature data containing real geographical data. The results demonstrate the relevance of hedging against uncertainty in multi-period districting. Since the model is challenging to tackle using a general-purpose solver, a heuristic algorithm is proposed based on a restricted model. The computational results obtained give evidence that the approximate algorithm can produce high-quality feasible solutions within acceptable computation times.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2025. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Applied Mathematics; Information and Computing Sciences; Mathematical Sciences |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Social Sciences (Sheffield) > Management School (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Jan 2025 17:09 |
Last Modified: | 30 Jan 2025 17:09 |
Status: | Published online |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10479-024-06459-7 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:222540 |