  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.
