In this work, an operation strategy for a biomass-fired combined cooling, heating and power system, composed of a cogeneration unit, an absorption chiller, and a thermal energy storage system, is formulated in order to satisfy time-varying energy demands of an Italian cluster of residential multi-apartment buildings. This operation strategy is adopted for performing the economical optimization of the design of two of the devices composing the combined cooling, heating and power system, namely the absorption chiller and the storage system. A sensitivity analysis is carried out in order to evaluate the impact of the incentive for the electricity generation on the optimized results, and also to evaluate, separately, the effects of the variation of the absorption chiller size, and the effects of the variation of the thermal energy storage system size on the system performance. In addition, the inclusion into the system of a cold thermal energy storage system is analyzed, as well, assuming different possible values for the cold storage system cost. The results of the sensitivity analysis indicate that the most influencing factors from the economical point of view are represented by the incentive for the electricity generation and the absorption chiller power. Results also show that the combined use of a thermal energy storage and of a cold thermal energy storage during the hot season could represent a viable solution from the economical point of view.