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Article Dans Une Revue European Journal of Operational Research Année : 2024

Quadratic regularization of bilevel pricing problems and application to electricity retail markets

Quentin Jacquet
  • Fonction : Auteur
Wim van Ackooij
  • Fonction : Auteur
Clémence Alasseur
  • Fonction : Auteur
Stéphane Gaubert

Résumé

We consider the profit-maximization problem solved by an electricity retailer who aims at designing a menu of contracts. This is an extension of the unit-demand envy-free pricing problem: customers aim to choose a contract maximizing their utility based on a reservation bill and multiple price coefficients (attributes). A basic approach supposes that the customers have deterministic utilities; then, the response of each customer is highly sensitive to price since it concentrates on the best offer. A second classical approach is to consider logit model to add a probabilistic behavior in the customers’ choices. To circumvent the intrinsic instability of the former and the resolution difficulties of the latter, we introduce a quadratically regularized model of customer’s response, which leads to a quadratic program under complementarity constraints (QPCC). This allows to robustify the deterministic model, while keeping a strong geometrical structure. In particular, we show that the customer’s response is governed by a polyhedral complex, in which every polyhedral cell determines a set of contracts which is effectively chosen. Moreover, the deterministic model is recovered as a limit case of the regularized one. We exploit these geometrical properties to develop a pivoting heuristic, which we compare with implicit or non-linear methods from bilevel programming, showing the effectiveness of the approach. Throughout the paper, the electricity retailer problem is our guideline, and we present a numerical study on this application case.

Dates et versions

hal-03504874 , version 1 (29-12-2021)

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Identifiants

Citer

Quentin Jacquet, Wim van Ackooij, Clémence Alasseur, Stéphane Gaubert. Quadratic regularization of bilevel pricing problems and application to electricity retail markets. European Journal of Operational Research, 2024, 313 (3), pp.841-857. ⟨10.1016/j.ejor.2023.05.006⟩. ⟨hal-03504874⟩
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