Carbon dioxide emissions
Following the evaluation of the design strategies using the primary energy demand parameter, the design strategies were analysed considering their life cycle carbon emissions. Also in this parameter only the design strategies were analysed. The carbon emissions balance is the CO2e saved over the house life cycle through the use of the design strategies (Eq. (5)).
(5) LCO2b= OCO2s -(ECO2+MCO2+DCO2)+ECO2R
where LCO2b is the carbon emissions balance (kgCO2e); OCO2s is the operational carbon emissions saved due to the use of the design strategy (kgCO2e); ECO2 is the embodied carbon emissions in the design strategy (kgCO2e); MCO2 is the maintenance energy due to the design strategy (kgCO2e); DCO2 is the demolition carbon emissions in the design strategy (kgCO2e); ECO2R is the life cycle carbon emissions of the component in the base case that will be replaced by a design strategy.
Cost
The latest parameter is the cost of the design strategy analysed through the LCCA. Through the economic balance it became possible to define the cost for the use of the design strategy during the life cycle of the building. The economy obtained through the reduction on energy consumption during the lifespan of the house was subtracted from the initial costs, maintenance and final demolition costs (Eq. (6)).
(6) LCCb= CS - (CI + CM + CD) + CE
where LCCb is the economic balance (€); CS is the savings on the electricity bill during the operational phase due to the use of the design strategy (€); CI is the initial cost of the design strategy (€); CM is the maintenance cost of the design strategy (€); CD is the demolition cost of the design strategy (€).
The cost of each strategy was obtained through the pricelist of the Camera di Commercio di Milano [48]. The cost of the maintenance material as well as replacement considered the average inflation in the last ten years in Italy, which is 1,34% a year [49].
Multi-criteria decision making
In order to find the best design solution in building, the AHP and multiple criteria decision-making method COmplex PRoportional Assessment (COPRAS) have been applied [24]. The method COPRAS was first introduced in 1994 by Zavadskas and Kaklauskas [25]. It assumes the direct and proportional dependence of the significance and utility degree of the investigated versions on a system of criteria, adequately describing the alternatives, values and weights of the criteria For the assessment of the criteria weights 30 experts, from three different areas (designer, researcher, Administrative and technical) of the construction sector, were selected. The experts have participated in the survey, in order to set the criteria weights and determine their priority. Following the Saaty comparison scale of nine levels [22] they have filled the pair-wise comparison matrix of the following sub-criteria: Indoor comfort hours; Primary energy demand; Cost. The scale of relative importance has the intensity from 1 to 9, where the importance is from equal to extreme importance. In order to ensure the consistence of the comparison matrix, the consistency ratio (CR) must be evaluated and condition CR < 0.1 must be satisfied. The first step to obtain the final decision by the method COPRAS is the formation of the normalized decision-making matrix, where the goal is to get the non dimensional weighted values out of the comparative parameters (Eq.(7)).
(7) \(dij=\frac{xij\cdot qi}{\Sigma\ xij}\ \ i=1,m;\ j=1,n\)
where dij is the non dimensional weighted values; xij is the value, j“ of criteria,, i“ in decision value; m is the number of criteria; n is the number of compared evaluations; qi is the significance of ,,i“ criteria.
Eq. (8) demonstrates how to obtain the sums of minimizing Sej and maximizing Sþj normalized indicators.
(8) \(S_+=\Sigma_{j=1}^nS_{+j}=\Sigma_{i=1}^n\Sigma_{j=1}^md_{+ij}\ \ \ \ S_-=\Sigma_{j=1}^nS_{+j}=\Sigma_{i=1}^n\Sigma_{j=1}^md_{-ij}\)
The relative importance Qj of each alternative aj is evaluated by the following Eq. (9):
(9) \(Q_j=S_{+j}+\frac{S_{-\min}\cdot\Sigma_{j=1}^mS_{-j}}{S_{-j}\cdot\Sigma_{j=1}^m\frac{S_{-\min}}{S_{-j}}}\ j=1,2,3,...m\)
The final stage is calculate the utility degree of each alternative (Eq.(10)).
(10) \(N_{j^=}\frac{Q_j}{Q_{\max}}\cdot100\)%
Through the normalization of the four parameters used in the study it will possible to obtained the relative importance Qj of each design solutions and the utility degree Nj of each alternative.
CASE STUDY
The method was applied in a multi-family social building located in Milan (Fig. 2). A lifespan of 100 years was used for the case study [26]. The Studio Rossi Prodi Associati realized Cenni di Cambiamento in 2013. The building was designed to be highly energy efficient and obtained the level A in the Italian energy certification [27]. Four buildings compose the entire project. In this study, only one building was evaluated. The building has nine stories in contact with the ground. The basement was not evaluated. On each floor there are four apartments of different sizes.