Identifying Fair Solutions in the Optimal Design of Integrated Residential Complexes

This paper presents an optimization framework to design an intensified and integrated residential complex that involves satisfying demands and using wastes. The problem is addressed by evaluating distinct allocation schemes (social welfare, Rawlsian welfare, Nash, and Rawlsian-Nash allocation) to identify solutions when the objective functions are considered as stakeholders of the system. To find the optimal design of the complex with the minimum amount of resources, the minimization of the total cost, the freshwater consumption, and the generated emissions are included as objective functions. To fulfill demands (water, electricity, heating, and cooling) and treat the generated wastes, distinct alternatives are considered, such as rainwater harvesting, water treatment and recycling, cogeneration, gasification of solid wastes, and algae cultivation. The resulting formulations are mixed-integer linear and mixed-integer nonlinear programming models. The applicability of the formulation was demonstrated through a case study of a residential complex in Mexico. Results show several optimal solutions that favor distinct stakeholders depending on the evaluated scheme. We also find that the only scheme that gives preference to two objectives is the Nash formulation. When specific weights for the objectives were included, alternative allocations guided simultaneously by the weighting factor and the scheme are found as well.