A Catalog of Formulations for the Network Pricing Problem
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916665219874816 |
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| author | Bui, Quang Minh Gendron, Bernard Carvalho, Margarida |
| author_facet | Bui, Quang Minh Gendron, Bernard Carvalho, Margarida |
| contents | We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest paths to travel. Many distinct single-level reformulations to this bilevel optimization program have been proposed, however, their relationship has not been established. In this paper, we aim to build a connection between those reformulations and explore the combination of the path representation with various modeling options, allowing us to generate 12 different reformulations of the problem. Moreover, we propose a new path enumeration scheme, path-based preprocessing, and hybrid framework to further improve performance and robustness when solving the final model. We provide numerical results, comparing all the derived reformulations and confirming the efficiency of the novel dimensionality reduction procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_03887 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Catalog of Formulations for the Network Pricing Problem Bui, Quang Minh Gendron, Bernard Carvalho, Margarida Optimization and Control Computer Science and Game Theory 90C35 G.1.6 We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest paths to travel. Many distinct single-level reformulations to this bilevel optimization program have been proposed, however, their relationship has not been established. In this paper, we aim to build a connection between those reformulations and explore the combination of the path representation with various modeling options, allowing us to generate 12 different reformulations of the problem. Moreover, we propose a new path enumeration scheme, path-based preprocessing, and hybrid framework to further improve performance and robustness when solving the final model. We provide numerical results, comparing all the derived reformulations and confirming the efficiency of the novel dimensionality reduction procedures. |
| title | A Catalog of Formulations for the Network Pricing Problem |
| topic | Optimization and Control Computer Science and Game Theory 90C35 G.1.6 |
| url | https://arxiv.org/abs/2106.03887 |