The main motivation of this work is to provide an optimization-based tool for an aggregator involved in residential demand response (DR) programs. The proposed tool comply with the following requirements, which are widely accepted by the residential DR literature: (i) the aggregated consumption should be optimized under a particular utility's target, such as the minimization of the Peak-to-Average Ratio, (ii) incentives can be used to retain prosumers in the DR program, (iii) the participants' profit/cost should not be worse off due to their enrollment in the program and (iv) prosumers' comfort and privacy must be preserved. To that end, an existing optimization framework involving two phases is revisited. First, by taking into account both the limitations of their smart-home components and their comfort preferences, each prosumer optimizes their self-generation and household consumption. Then, in a subsequent phase, the aggregator coordinates all prosumers responses by solving a mixed-integer linear programming problem. As a salient feature, new constraints based on the concept of the Shapley Value are devised for their incorporation into the problem, yielding a fair allocation of the aggregator's incentives while respecting the above DR requirements. The resulting problem is solved in a decentralized fashion by applying Dantzig-Wolfe decomposition, which is embedded in the proposed solution methodology to accommodate a large number of prosumers and their specific characteristics and needs. Computational results highlight the advantages of the proposed tool in terms of the Peak-to-Average-Ratio, fairness of the incentives' allocation and scalability.