TY - GEN
T1 - A Quantization Procedure for Nonlinear Pricing with an Application to Electricity Markets
AU - Jacquet, Quentin
AU - Van Ackooij, Wim
AU - Alasseur, Clémence
AU - Gaubert, Stéphane
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - We consider a revenue maximization model, in which a company aims at designing a menu of contracts, given a population of customers. A standard approach consists in constructing an incentive-compatible continuum of contracts, i.e., a menu composed of an infinite number of contracts, where each contract is especially adapted to an infinitesimal customer, taking his type into account. Nonetheless, in many applications, the company is constrained to offering a limited number of contracts. We show that this question reduces to an optimal quantization problem, similar to McEneaney's pruning problem that appeared in the max-plus based numerical methods in optimal control. We develop a new quantization algorithm, which, given an initial menu of contracts, iteratively prunes the less important contracts, to construct an implementable menu of the desired cardinality, while minimizing the revenue loss. We apply this algorithm to solve a pricing problem with price-elastic demand, originating from the electricity retail market. Numerical results show an improved performance by comparison with earlier pruning algorithms.
AB - We consider a revenue maximization model, in which a company aims at designing a menu of contracts, given a population of customers. A standard approach consists in constructing an incentive-compatible continuum of contracts, i.e., a menu composed of an infinite number of contracts, where each contract is especially adapted to an infinitesimal customer, taking his type into account. Nonetheless, in many applications, the company is constrained to offering a limited number of contracts. We show that this question reduces to an optimal quantization problem, similar to McEneaney's pruning problem that appeared in the max-plus based numerical methods in optimal control. We develop a new quantization algorithm, which, given an initial menu of contracts, iteratively prunes the less important contracts, to construct an implementable menu of the desired cardinality, while minimizing the revenue loss. We apply this algorithm to solve a pricing problem with price-elastic demand, originating from the electricity retail market. Numerical results show an improved performance by comparison with earlier pruning algorithms.
U2 - 10.1109/CDC49753.2023.10384010
DO - 10.1109/CDC49753.2023.10384010
M3 - Conference contribution
AN - SCOPUS:85184820739
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2270
EP - 2277
BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 62nd IEEE Conference on Decision and Control, CDC 2023
Y2 - 13 December 2023 through 15 December 2023
ER -