## 2 Method
### Local Sensitivity Analysis--OAT
Moreover, some of those fees are fixed while others are added concerning the building heating system and demand. For example, a general charge of 88.4 ore/kWh is added to the electricity price. If the building is heated by electricity, an additional 25.9 ore/kWh is owed by each client (building owner) [38]. Moreover, a variable \"PSO (Public service obligation)\" is added when forming the final electricity price. As all of those price elements are highly variable and continuously evolving, they are thereby excluded from the calculations along with VAT, taxes, and fees. In addition to all taxes and fees, electricity price is also dependent on the annual amount of purchased electricity by the \"client\" of the energy providers, e.g., apartment tenants or building owners. Clients of a supply company are classified into categories (usage intervals) from small (single-family homes) to large (industrial clients). Naturally, the unit cost for large clients is lower than that for small clients. As the baseline considers a multi-family building, the baseline value was selected considering medium-size client (usage interval from 2.5 < 5 MWh) and determined as the average of available annual cost data for 2009-2018 [33]. It should be pointed out that the analysis presented in [28] and those presented in this paper account for the purchase of electricity for the whole building globally (e.g., building operation and private use in apartments are analyzed as inputs). In reality, the building owner and each tenant would be individual clients of the electricity provider. Thus, tenants would be categorized/charged according to costs with respect to low usage intervals, while the building owner would likely be categorized as a client in the higher usage intervals with lower unit costs. The range applied in OAT analysis represents the minimum and maximum annual values for electricity costs of different usage intervals to investigate the effect of this simplification. * Gas--unit costs for gas are also differentiated by client type (household or industry) and by the amount of purchased energy. A breakdown of household gas prices is provided monthly for the period from 2009-2018. Each aspect contributing to the total gas price is represented individually. Given that the gas price has been rather stable [33] for the period from 2009-2018, the baseline value was determined by average cost, while the OAT range was determined as the minimum and maximum values for the whole period and excluding VAT. Gas prices are also available as annual values for different usage intervals (client sizes). In a scenario where gas is the source for centralized heating and DHW supply, the energy demand of the building would be a determining factor for the unit cost of gas. However, just as for electricity, governmental taxes and local subscription tariffs are also major determining factors for the total cost. Those are included in the OAT variation, as the baseline adapts average, minimum, and maximum values from 2007-2018, excluding VAT but including government taxes and levies. Furthermore, baseline values were selected based on the smallest available usage interval (<20 GJ gas). Ranges for implementation, maintenance, and lifetime of the energy systems are referenced in Table 1 TDC [34; 35]. The variation ranges for energy efficiency improvementsare determined as \(\pm\)20% variation from the baseline due to the lack of a better source. The same \(\pm\)20% are applied to the quantity of the different material inputs. These variations, for instance, could result from false quantity estimations related to different renovated building parts or insufficient documentation, leading to uncertain assumptions. Once all variations are computed with their respective minimum and maximum values, the sensitivity index of each parameter is determined by Equation (2). The parameters are sorted in ascending order with respect to the calculated sensitivity index.