## 2 Materials and Methods
### Mathematical Procedures  
#### 2.3.1 Life Cycle Costing (LCC)  
The economic estimations in this work were undertaken based on the life cycle costing analysis method [21]. This method includes all of the discounted expenses that originated during a specified time horizon of the facility's operation, and has been used to analyze the feasibility of renewable energy solutions, as shown by [PERSON] et al. [22]. The total discounted expenses are defined below as the net present cost (NPC; depending on the case study, i.e. any of the considered actions described in Section 2.5, this variable may refer to one single unit or to the combination of all units of the Logistics Center) of the project:  
\[NPC=I_{0}+CF_{a}.PWF \tag{1}\]  
where \(I_{0}\) (this variable may take the value of zero in the case that no investment is required) is the capital investment at the start of the project (Equation (2)). The investment capital (\(I_{0}\)) in this study is present only in Action 3 (see Section 2.5.3) when photovoltaic panels have to be purchased. \(I_{0}\) is defined as follows:  
\[I_{0}=n_{PV}.P_{PV}\text{-}C_{PV} \tag{2}\]  
In Equation (2), \(n_{PV}\) is the number of installed photovoltaic panels; \(P_{PV}\) is the power supplied per panel in \(\text{Wp}/\text{panel}\); and \(C_{PV}\) is the PV price in \(\xi\)/\(\text{Wp}\). The \(\text{CF}_{a}\) is the annual net cash flow detailed in Equation (3); The annual net cash flow (\(C_{E}\)), as defined in Equation (3), includes the annual costs of purchased energy (\(C_{E}\)) and power (\(C_{P}\)) (depending on the case study, i.e., any of the considered actions described in Section 2.5, these variables may refer to one single unit or to the combination of all units of the Logistics Center.) in Euro (Equations (5) and (6)), and the annual cost of maintenance (\(C_{M}\)) (this variable may take the value of zero in the case that no investment is required). The maintenance costs are considered only for Action 3 (see Section 2.5.3). \[CF_{a}=C_{E}+C_{P}+C_{M} \tag{3}\]  
The _PWF_ (mentioned in Equation (1)) is the present worth factor, which reflects the time value of money. The _PWF_ detailed in Equation (4) is the present worth of one Euro paid periodically in the future, where the nominal discount rate (\(d\)) and the time horizon of the analysis (\(N\)), in years, are considered. \[PWF=\frac{1}{d}\left(1-\left[\frac{1}{1+d}\right]^{N}\right) \tag{4}\]  
The annual energy costs are obtained, as shown in Equation (5), where \(E\) (also this variable may refer to one single unit or to the combination of all units of the Logistics Center) is the annually consumed energy in kWh and \(C_{E}\) is the energy price in \(\xi\)/kWh (see Figure 5). Both \(E\) and \(C_{E}\) vary depending on the index (\(i\)), which represents one of the charging periods of the 3.0A tariff specified in Figure 5.  
\[C_{E}=\sum_{i}E_{(i)}.c_{E(i)}\ \forall i\in\{P1,P2,P3\} \tag{5}\]  
The annual power costs are calculated in Equation (6). There, \(D\) represents the cardinal number of days in a specific month \(m\); \(P_{ch}\) (also this variable may refer to one single unit or to the combination of all units of the Logistics Center) is the monthly charged power in kW; and \(C_{P}\) is the power price in \(\epsilon\)/kW/day. As in the previous equation, \(P_{ch}\) and \(C_{P}\) vary depending on the charging periods of the 3.0A tariff (Figure 5) and the charged power may also vary from month to month. \[C_{P}=\sum_{i}\sum_{m}D_{(m)}\cdot P_{ch(m,i)}\cdot c_{P(i)}\ \forall i\in\{P1,P2,P3\}\ \text{and}\ \text{m}\in\{12\ \text{months of a year}\} \tag{6}\]  
A piecewise function in Equation (7) defines the charged power (\(P_{ch}\)3). This function is split in ranges depending on where the maximum demanded power of a specific month (\(P_{d}\textsuperscript{max}\) ) falls concerning the contracted power (\(P_{c}\) ). \[P_{ch}=