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Motivated by real challenges on energy management faced by industrial firms, we propose a novel way to reduce production costs by including the pricing of electricity in a multi-product lot-sizing problem. In incentive-based programs, when electric utilities face power consumption peaks, they request electricity-consuming firms to curtail their electric load, rewarding the industrial firms with incentives if they comply with the curtailment requests. Otherwise, industrial firms must pay financial penalties for an excessive electricity consumption. A two-stage stochastic formulation is presented to cover the case where a manufacturer wants to satisfy any curtailment request. A chance-constrained formulation is also proposed, and its relevance in practice is discussed. Finally, computational studies are conducted to compare mathematical models and highlight critical parameters and show potential savings when subscribing incentive-based programs. We show that the setup cost ratio, the capacity utilisation rate, the number of products and the timing of curtailment requests are critical parameters for manufacturers. [ABSTRACT FROM AUTHOR]