6.1Example facility

For the statistical investigation of operating costs of real estate, a data sample of 253 operated facilities is analysed. Based on the data, multiple statistical models are developed and validated. The models intend to reveal the causal interrelationships between operating costs and various candidate predictor variables. Furthermore, the models aim to give an accurate estimation of operating costs. Therefore, linear and non-linear regression models, artificial neural network models, and binary classification tree models are stepwise developed. Furthermore, median values of categorised cost indicators for the purpose of cost estimation are introduced for all analysed cost groups of the standard DIN 18960:2008-02. The evaluation of the performance of the methods reveals the most accurate cost estimation for non-linear regression models (8 cost groups), binary classification tree models (4 cost groups), and median values of categorised cost indicators (3 cost groups). The current chapter provides a step-by-step presentation of the implementation of these statistical methods based on the example of an independent example facility. The practical applicability of the methods and the respective amount of facility related information required for a cost estimation is considered.

The practical application of the presented statistical methods is presented by three implementation examples employing a operated municipal facility as example. An overview of the facility with the observation number 192 is presented in Figure 6.1 including a summary of essential information and simplified floor plans. The building was built in 1922 and has a gross external floor area GEFA of 3,448 m2 allocated on 4 floors. The usable floor area UFA of 2,372 m2 with approximately 70 workplaces is located mainly on the first and second level floors of the building. Furthermore, the facility includes a non-built site area of 2,401 m2 with paved, planted, and green areas. The facility is owned and operated by a municipality in the German state of Baden-Wuerttemberg and is used as an office building by the building management department for school facilities.

The available data contain all relevant information including further quantities, characteristics, utilisation, location, and the management strategies. With an exception of the third level cost group 355 and the second level cost group 360, the cost data of the facility is available for all analysed cost groups of the cost structure of the standard DIN 18960:2008-02. The example facility with the observation number 192 is not included in the development of the statistical models or used for the introduction of the categorised cost indicators. Therefore, independent and unbiased conclusions can be drawn about the practical applicability of the developed statistical methods.

6.2Regression model

As summarised in Chapter 5, the highest performance and the lowest estimation error is indicated for the non-linear regression models NLR for 8 of the total 15 analysed cost groups of DIN 18960:2008-02. The developed non-linear regression models employ cost indicators as response variables. For the introduction of cost indicators, adequate reference quantities are determined by an evaluation of absolute cost models that contain the available candidate reference quantities as predictor variables. The development of the non-linear regression models for the estimation of cost indicators is based on a transformation of the underlying predictor and response variables. The correction of non-normality in the data distribution by transformation results in a significant improvement of the regression models. The practical application of the nonlinear regression models is demonstrated subsequently in an implementation based on the presented example facility.

The implementation of the non-linear regression models is illustrated on the example of the model NLR(ind)310 for the estimation of CG 310 utility cost indicators as presented in Section 4.2 in detail. By an evaluation of absolute cost models of CG 310, the gross internal floor area GIFA is determined as adequate reference quantity and corresponding cost indicators are introduced. Employing the utility cost indicators as response variable, the non-linear regression model NLR(ind)310 offers the best compliance to the underlying data with the lowest mean absolute percentage error MAPE of 15.6 %for the total sample of 206 observations. The model is introduced with transformations of both predictor and response variables. The respective lambdas (λ) range from a natural logarithm transformation (λ=0) to square (λ=2) and square root (λ=0.5) transformations of the variables. Under consideration of a 95% confidence interval, significant relationships are identified between the CG 310 cost indicators and 6 predictor variables. As presented in detail in Section 4.2, the following equation describes the developed non-linear regression model NLR(ind)310:

where

$\widehat{Y}$ is the response variable CG 310 utility cost indicators in Euro/m2 GIFA*year,

β0 is the regression constant,

β1, β2, β3, β4, β5, and β6 are the coefficients of the regression,

X1 is the quantitative variable share of heatable GIFA in %,

X2 is the quantitative variable share of ventilated and air-conditioned GIFA in %,

X3 is the quantitative variable share of defective envelope in %,

X4 is the quantitative variable share of defective heat supply systems in %,

X5 is the qualitative variable type of heating energy source, and

X6 is the qualitative variable type of facility.

Under consideration of the observed characteristics, the equation of the model NLR(ind)310 is employed to estimate the CG 310 indicator for the observation 192. With the determined regression constant and the regression coefficients of

β0 = 2.610,

β1 = 0.451,

β2 = 0.236,

β3 = 0.353,

β4 = 0.219,

β5 = 0.000 (complies with district heating),

β6 = −0.494 (complies with municipal facility),

and the observed characteristics for the predictor variables of

X1 = 67.6% (share of heatable GIFA),

X2 = 0.0% (share of ventilated and air-conditioned GIFA),

X3 = 19.9% (share of defective envelope),

X4 = 7.8% (share of defective heat supply systems),

X5 = 1 (type of heating energy source in combination with β5),

X6 = 1 (type of facility in combination with β6),

the equation of non-linear regression model NLR(ind)310 solves as follows and the annual CG 310 utility cost indicator for the observation 192 is estimated to be:

In order to calculate a estimation of absolute costs, the determined cost indicator is multiplied with the observed reference quantity of the observation 192. With a gross internal floor area GIFA (reference quantity REFQ for CG 310) of 2,875 m2, the annual absolute CG 310 utility costs for the observation 192 are estimated to be:

In accordance with the presented procedure for the exemplary calculation of the utility costs of the second level cost group 310 as defined in the standard DIN 18960:2008-02, operating costs can be estimated for all first, second, and third level cost groups presented in the current study. Nevertheless, the practical application of the introduced regression models requires usually the availability of detailed information like quantities, characteristics, utilisations, locations, and management strategies of the facilities. For a rough estimation of operating costs, the categorised median values of cost indicators as presented in the implementation example in Section 6.4 may offer an alternative estimation method with less input data required.

6.3Binary classification tree model

Binary classification tree models BCT may have the advantage to reveal and describe the causal interrelationships between the response variable and predictor variables transparently as described by Curram and Mingers (1994). According to the performance evaluation as summarised in Chapter 5, the developed BCT models show the most accurate cost estimation for 4 of the total 15 analysed cost groups defined in the standard DIN 18960:2008-02. For the other cost groups, the estimation performance of the BCT models does not deviate significantly from the results achieved by the nonlinear regression models NLR. The predictor variables identified by the BCT models correspond generally with the predictors identified by the NLR models and indicate therefore a correct specification of both statistical methods. Like the non-linear regression models, the binary classification tree models employ cost indicators as response variable. The respective reference quantities are determined by the evaluation of absolute cost regression models.

The practical application of the BCT models is demonstrated subsequently on the example of the model BCT(ind)350 estimating the CG 350 operation, inspection and maintenance cost indicator for the observation 192. The gross external floor area GEFA is employed as the reference quantity for the compilation of cost indicators. With a mean absolute percentage error MAPE of 32.8 %for the analysed sample of 244 observations, the model BCT(ind)350 offers the best compliance to the underlying cost data of CG 350 compared with the other developed statistical models. With a tree depth of 6 layers, the developed classification tree model includes 25 nodes in total whereof 13 are terminal nodes with stop rules. The following 5 variables are identified as predictors influencing the CG 350 cost indicators: The qualitative variables type of facility, protected structure, and standard of building automation and the quantitative variables share of defective construction and share of defective technical installations. As presented in detail in Section 4.9 of the current study, the developed tree structure of the BCT(ind)350 model is illustrated in Figure 6.2.

In order to estimate the CG 350 cost indicator for the observation 192, the following observed characteristics are employed to conduct the classification according to the classification tree model BCT(ind)350:

According to the classification tree structure of the model BCT(ind)350 and as highlighted in Figure 6.2, the classification is conducted as follows:

With the terminal node on the fourth layer of the model BCT(ind)350, the annual CG 350 operation, inspection and maintenance cost indicator for the observation 192 is estimated to be:

In order to calculate a estimation of absolute costs, the determined cost indicator is multiplied with the observed reference quantity of the observation 192. With a gross external floor area GEFA (reference quantity REFQ for CG 350) of 3,448 m2, the annual absolute CG 350 operation, inspection and maintenance costs for the observation 192 are estimated to be:

As presented in the procedure for the estimation of the costs of second level cost group 350, the operating costs can be estimated for all first, second, and third level cost groups of the standard DIN 18960:2008-02 that are analysed and presented in the current study. As already described in the example for the implementation of the developed regression models in Section 6.2, the practical application of the introduced binary classification tree models requires likewise the availability of detailed information like for example quantities, characteristics, utilisations, locations, and management strategies of the facilities. With less input data required, the categorised median values of cost indicators as presented in the subsequent implementation example may offer an alternative estimation method for a rough estimation of costs.

6.4Categorised cost indicators

Besides various statistical models, median values of categorised cost indicators MV are introduced in the current study in order to estimate operating costs. The presented cost indicators can likewise be employed for the purpose of benchmarking as described in Section 2.3.5. The cost indicators are presented with a categorisation based on the predictor variables identified by the statistical models. According to the performance evaluation as summarised in Chapter 5, the introduced median values of categorised cost indicators MV show the most accurate cost estimation for 3 of the total 15 analysed cost groups defined in the standard DIN 18960:2008-02. With values of the mean absolute percentage error MAPE of between 17.2% (third level cost estimation) and 22.7 % (first level cost estimation) for the total sample, the median values of categorised cost indicators MV reveal a lower performance and a less accurate cost estimation compared with the non-linear regression models NLR or the binary classification tree models BCT.

The implementation of the median values of categorised cost indicators MV is illustrated subsequently on the example of statutory charges and contributions (CG 370) for the observation 192. With a mean absolute percentage error MAPE of 36.8 %for the total sample of 208 observations, the MV(ind)370 cost indicators offer the best performance for the estimation of CG 370 costs. As determined by the evaluation of absolute cost regression models, the gross external floor area GEFA is employed as reference quantity for the compilation of the cost indicators. The categorisation of the cost indicators is determined according to the predictor variables with the largest effect on the costs of the cost group. Therefore, the CG 370 indicators are categorised according to the qualitative variable type of facility as described in detail in Section 4.15. The introduced categorised cost indicators MV(ind)370 for the estimation of statutory charges and contributions are presented in Table 6.1.

Table 6.1. Implementation of categorised CG 370 cost indicators

[a]CG370 cost indicators (Euro/m2 GEFA*year), 1st quarter 2016 prices including VAT.

[b]Total sample size: 191 observations.

With the type of facility observed as a municipal facility, the annual cost indicator for statutory charges and contributions of CG 370 is estimated to be:

In order to calculate an estimation of absolute costs, the determined cost indicator is multiplied with the observed reference quantity of the observation 192. With a gross external floor area GEFA (reference quantity REFQ for CG 370) of 3,448 m2, the annual absolute costs for statutory charges and contributions of CG 370 for the observation 192 are estimated to be:

As presented in the exemplary procedure for the estimation of the costs of second level cost group 370, the operating costs can be estimated for all first, second, and third level cost groups of the standard DIN 18960:2008-02 that are analysed and presented in the current study. For most of the analysed cost groups, the estimation accuracy is lower compared to the estimation with the developed statistical models. Nevertheless, the cost estimation with cost indicators may offer an alternative estimation method with less input data required. Likewise, the presented cost indicators can be employed as benchmarks for the monitoring and assessment of operating costs of operated facilities.

6.5Implementation summary

Under consideration of the practical applicability, the previous Sections provide a step-by-step presentation of the implementation of the most accurate cost estimation methods based on an independent example facility. A summary of the observed and estimated absolute costs and cost indicators of the observation 192 for all analysed cost groups of DIN 18960:2008-02 is presented in Table 6.2.

Table 6.2. Observed and estimated values for observation 192

[a]Cost indicators (Euro/m2 REFQ*year) and absolute costs (Euro/year), 1st quarter 2016 prices including VAT.

The summary contains the observed annual absolute costs and the observed annual cost indicators for all cost groups where costs for observation 192 are available. The cost indicators are compiled with the identified reference quantities for the respective cost groups. The cost estimation for all cost groups is conducted according to the respective estimation method with the best performance and the highest accuracy as determined in Chapter 4 of the study. The percentage error PE compares the respective value to the observation to the estimated value and is defined as follows:

where

PEi is the percentage error PE of the observation i,

OBSi is the observed value of the observation i, and

ESTi is the estimated value of the observation i.

On the example of the cost indicators of cost group 300, the percentage error of observation 192 is calculated as:

A summary of the estimation performance for the observation 192 throughout all analysed cost groups is presented in Table 6.3 including a comparison with the estimation performance of the total sample as described in detail in Section 5.3. The results are presented as aggregated MAPE values for a cost estimation on the 3 estimation levels according to the structure of DIN 18960:2008-02. The calculations of the aggregated percentage errors PE for the observation 192 and the mean absolute percentage errors MAPE for the total sample are conducted by a comparison of the sum of the estimated values with the sum of the observed values for the costs groups included in the respective estimation level.

Table 6.3. PE values for 1st, 2nd, and 3rd level cost estimation for observation 192

[a]Cost group 300.

[b]Cost groups 310, 320, 330, 340, 350, 360, and 370.

[c]Cost groups 311, 312-316, 316, 320, 330, 340, 352, 353, 354, 355, 360, and 370.

The aggregated percentage error PE(aggr.) is calculated as follows:

where

PE (aggr.)i is the aggregated percentage error in % of the observation i,

OBSi is the observed value of the observation i for the cost group c, and

ESTi is the estimated value of the observation i for the cost group c.

On the example of the second level cost estimation for the observation 192, the aggregated costs include the second level cost groups 310 (utilities), 320 (disposal), 330 (cleaning and care of buildings), 340 (cleaning and care of outdoor facilities), 350 (operation, inspection and maintenance), 360 (security and surveillance), and 370 (statutory charges and contributions) according to DIN 18960:2008-02. The respective cost groups that are included in the determination of the estimation performance on the 3 estimation levels are presented in the footnote of Table 6.3. The example of the aggregated second level cost estimation of the observation 192 solves as follows:

The mean absolute percentage errors MAPE presented throughout the study are calculated as presented in the exemplary procedure for the calculation of the percentage error PE and the aggregated percentage error PE (aggr.) for the observation 192. As illustrated in Table 6.3, the cost estimation for observation 192 on the second level of DIN 18960:2008-02 can offer a significant improvement of accuracy compared with the first level cost estimation. On the most detailed third level of cost estimation, a percentage error PE of 8.4% is achieved for observation 192. As already observed for the mean absolute percentage errors MAPE of the total sample, an improvement of estimation accuracy can generally be achieved by an estimation of costs on the more detailed second and third levels of cost estimation according to DIN 18960:2008-02.