# Economic–Environmental Sustainability in Building Projects: Introducing Risk and Uncertainty in LCCE and LCCA

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Background

- Deterministic techniques through which it is possible to evaluate the influence on project results by altering one significant value or an array of values at a time;
- Quantitative techniques, which can be distinguished in statistical approaches (that integrate into economic performance measures, for example, Net Present Value (NPV) factors such as standard deviation and variance) and probabilistic approaches (that use probabilistic distribution functions and simulation techniques);
- Qualitative techniques solved through subjective and non-numerical evaluation criteria. These are often used to obtain general information about the risk associated with a project, but subsequently, it may be necessary to undertake a more specific and detailed quantitative analysis where risk has been identified as particularly important.

## 3. Methodological Background

_{G}(τ) stands for the Global Cost (referred to starting year τ

_{0}) [€]; C

_{I}stands for the initial investment costs; Ca,i (j) stands for the annual cost during year i of component j, which includes the annual running costs (energy costs, operational costs, maintenance costs) and periodic replacement costs; R

_{d}(i) stands for the discount rate during the year i; V

_{f,τ}(j) stands for the residual value of the component j at the end of the calculation period, referred to the starting year.

_{G}= C

_{I}+ ∑ (C

_{m}+ C

_{r})/(1 + r)

^{t}+ (C

_{dm}+ C

_{dp}− V

_{r})/(1 + r)

^{N}

_{G}is the Life-Cycle Cost [€]; C

_{I}is the investment costs; C

_{m}is the maintenance cost; C

_{r}is the replacement cost; C

_{dm}is the dismantling cost; and C

_{dp}is the disposal cost; V

_{r}is the residual value; t is the year in which the cost occurred; N is the number of years of the entire period considered for the analysis; and r is the discount rate.

_{GEnEc}= C

_{I}+ C

_{EE}+ C

_{EC}+ ∑ (C

_{m}+ C

_{r})/(1 + r)

^{t}+ (C

_{dm}+ C

_{dp}− V

_{r})/(1 + r)

^{N}

_{GEnEc}is the life-cycle cost including environmental and economic indicators [€]; C

_{I}is the investment costs; C

_{EE}is the costs related to Embodied Energy; C

_{EC}is the costs related to Embodied Carbon; C

_{m}is the maintenance cost; C

_{r}is the replacement cost; C

_{dm}is the dismantling cost; C

_{dp}is the disposal cost; V

_{r}is the residual value; t is the year in which the cost occurred; N is the number of years of the entire period considered for the analysis; and r is the discount rate.

_{GEnEC}is the Life-Cycle Cost, including environmental and economic indicators [€] expressed in stochastic terms; Ĉ

_{I}is the stochastic investment costs; Ĉ

_{EE}is the stochastic costs related to Embodied Energy; Ĉ

_{EC}is the stochastic costs related to the Embodied Carbon; Ĉ

_{m}is the stochastic maintenance cost, Ĉ

_{r}is the stochastic replacement cost; Ĉ

_{dm}is the stochastic dismantling cost; Ĉ

_{dp}is the stochastic disposal cost; Vr is the residual value; t is the year in which the cost occurred; N is the number of years of the entire period considered for the analysis; and $\u0213$ is the stochastic discount rate.

_{r}is expressed as a deterministic input. In fact, being the residual value directly linked to the duration of the service life of each component, in other words, to the time, it would be necessary to switch from stochastic variables to stochastic processes. In this work, as the first experiment, an empirical modality was adopted by setting three alternative scenarios with three different associated lifespans. We assume that the different lifespans fixed the time horizon for the evaluation and gave origin to three different residual values, modeling the possible temporal variability of the components, or even simplifying them.

- (1)
- identification of each LCCE and, from among these, the selection of the relevant cost drivers (risky or uncertain input cost items);
- (2)
- for each relevant cost driver, the identification of the potential range of variability to the point estimate;
- (3)
- calculation of the overall range associated to the estimate, according to two different approaches: the deterministic one (variability range defined according to a minimum and maximum point estimates) and the probabilistic one (variability range expressed through probability distribution functions, calculated with the analytic approach or through simulation).

- identification of the set of “relevant cost drivers”, or critical inputs, to be expressed as stochastic variables. Costs are subject to different degrees of uncertainty, also in relation to the time. For this reason, it is suggestable to define different confidence levels of the estimates, or “expected accuracy ranges” [37], in relation to the different cost items. Since the costs refer to the life-cycle of the components, the “expected accuracy ranges” can be appropriately expressed in terms of life-cycle cost estimates—LCCEs;
- assignment of the Probability Distribution Function (PDF) to each stochastic input variable, and the identification of the relative probability distribution parameters. As said before, the triangular distribution can be considered the most used PDF to represent the uncertain variables present in the real estate investments (Figure 1) [40,41,42]. Therefore, this step is devoted to the assignment of minimum, maximum, and point estimate values for each variable;
- definition of alternative scenarios with different lifespans in order to simulate different residual values for the components considered in the analysis. In this step, the aim is introducing uncertainty in the duration of the components. The duration is expressed through the variation of the residual values, being uncertain the lifespan of the components themselves;
- Iteration and sampling resolved through MCM. For the simulation, it is necessary to define the number of iterations and the sampling modality, in our case the Latin Hypercube Sampling (LHS);
- running the simulation and production of the regression analysis in order to quantify the effect of the input variables on the output value, expressed in terms of marginal coefficients of the dependent variables against the independent variable (Global Cost). This step is supported by the production of graphics (tornado graphs and spider graphs). Operatively, this step is solved according to the following passages:
- -
- Multiple regression analysis application (usually, sensitivity analysis according to the simulation approach is solved through multiple regression analysis. Formally, the regression model applied for the simulation can be approximated by the following Equation (see Kleijnen, J.P.C., Verification and validation of simulation models, European Journal of Operation Research, 1995, 82, 145–162, p. 156):$${y}_{i}={\beta}_{0}+{\displaystyle \sum}_{k=1}^{K}{\beta}_{k}{x}_{ik}+{\displaystyle \sum}_{k=1}^{K-1}{\displaystyle \sum}_{{k}^{\prime}=k=1}^{K}{\beta}_{k{k}^{\prime}}{x}_{ik}{x}_{i{k}^{\prime}}+{e}_{i}$$
_{i}represents the results of the simulation in the i combination (or run) of the simulation inputs k, for i = 1, …n (where n represents the total number of simulation runs); x_{ik}stands for the value of the simulation input, k, in the i combination; β_{k}is the first order effect of input k; β_{kk}is the interaction between the k and k’ inputs; and e_{i}stands for the approximation or best-fit error in the i run.) The sampled values of the input variables are regressed against the output variable through multivariate stepwise regression analysis. In LCCA, if the global cost is taken as the dependent variable in the regression equation, then the marginal coefficient calculated for each input variable measures the sensitivity of the output variable with respect to each of them; - -
- Degree of correlation calculation. This is expressed by coefficients of correlation between the output values and each set of input value samples. Operatively, this step is solved through the rank correlation analysis, calculating Spearman’s correlation coefficients in order to determine the correlation between the global cost and the samples for each input distribution;

- output calculation in terms of the Probability Distribution Functions and statistics (minimum value, maximum value, standard deviation, skewness, kurtosis, and so forth) calculated for each alternative option.

## 4. Case Study

^{2}, a total glazing area of 1426 m

^{2}, and a glazing ratio of the external walls of 90%.

## 5. Application and Results

#### 5.1. Risk and Uncertainty in Model Input

#### 5.2. Risk and Uncertainty in Model Output: Stochastic Simulation Through the Monte Carlo Method

_{CEnEc}, as defined in the methodology section.

_{GcEnEc}, the related Probability Density Function, and the statistics calculated for the two alternative frames, higher costs emerge for the timber frame, as expected from being in the presence of higher initial and periodic maintenance cost amounts.

- for every scenario, the discount rate is the variable that produces the largest perturbation on the output. In fact, considering the range of values assumed for this variable, the effects on the output are relevant;
- cost items regarding preemptive maintenance, light maintenance work, and the main and elements costs are relatively significant, while the other items have a small influence on the results;
- the relative influence of Embodied Energy is particularly significant in differentiating the aluminum frame and the timber frame;
- the substantial effect of the residual value and the related uncertainty on components lifespans in differentiating the output results in favor of the aluminum frame technological solution.

#### 5.3. Results and Final Considerations

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Probability distribution function: the triangular distribution described by the minimum, most likely, and maximum values.

**Scheme 2.**Comparison between the consolidated and the proposed life-cycle cost (LCC) with risk analysis workflows.

**Figure 2.**The case study: (

**a**) the whole building project, named the Red Ring Office; (

**b**) an isometric view of the building.

**Figure 4.**The output probability distribution function, probability density function, and statistics for the timber/aluminum frame scenarios for the 25-year lifespan option; Monte Carlo simulation output.

**Figure 5.**The inputs ranked by the effect on the output mean, the timber/aluminum frame scenarios, the 25/20/15-years lifespans. The Monte Carlo simulation output.

**Figure 6.**The Spearman correlation coefficients for the timber/aluminum frame scenarios, for the 25/20/15-year lifespan options. The Monte Carlo simulation output.

**Figure 7.**The spider graphs for the timber/aluminum frame scenarios for the 25/20/15-year lifespan options. The Monte Carlo simulation output.

**Table 1.**The categorization of risk management techniques in building investments (Source: Boussabaine, 2004, p. 57).

Deterministic Approaches | Quantitative Approaches | Qualitative Approaches |
---|---|---|

Conservative benefit and cost estimating | Input estimates using probability distribution | Risk matrix |

Breakeven analysis | Mean-variance criterion | Risk registers coefficient of variation |

Risk-adjusted discount rate | Decision tree analysis | Event tree |

Certainty equivalent technique | Monte Carlo simulation | SWOT analysis |

Sensitivity analysis | Analytical technique | Risk scoring |

Variance and standard deviation | Artificial intelligence | Brainstorming sessions |

Net present value | Fuzzy sets theory | Likelihood/consequence assessment |

Event tree (quantitative) |

Indicator | Unit of Measurement | Timber Frame | Aluminum Frame |
---|---|---|---|

Initial investment cost | € | 363,027.50 | 272,852.50 |

Embodied Energy | MJ | 2,333,539.78 | 5,881,721.38 |

Embodied Carbon | kg CO_{2} eq (100 years) | 665,485 | 1,100,860 |

Cost Driver | Expected Accuracy Range | |
---|---|---|

Low | High | |

Initial investment costs (elements costs) | −5% | +10% |

Annual running and replacement costs: | ||

- Inspection | −5% | +10% |

- Preemptive maintenance | −5% | +10% |

- Maintenance work (light) | −5% | +10% |

- Maintenance work (main) | −10% | +20% |

- Replacement | −10% | +20% |

Dismantling cost | −10% | +20% |

Disposal cost | −10% | +20% |

**Table 4.**The cost drivers and relative probability distribution parameters in the timber frame case.

Timber Frame | ||||
---|---|---|---|---|

Cost Driver | Unit | Low Range | Point Estimate | High Range |

Initial investment costs (elements costs) | €/m^{2} | 218.06 | 229.53 | 252.49 |

Annual running and replacement costs: | ||||

- Inspection | € per year | 6220.05 | 6547.43 | 7202.17 |

- Preemptive maintenance | € per year | 15,550.13 | 16,368.56 | 18,005.42 |

- Maintenance work (light) | € every 3 years | 62,200.54 | 65,474.25 | 72,021.68 |

- Maintenance work (main) | € every 7 years | 117,853.65 | 130,948.50 | 157,138.20 |

- Replacement | € | 339,561.00 | 377,290.00 | 452,748.00 |

Dismantling cost | €/m^{2} | 29.70 | 33.00 | 39.60 |

Disposal cost | €/ton | 49.50 | 55.00 | 66.00 |

**Table 5.**The cost drivers and relative probability distribution parameters in the aluminum frame case.

Aluminum Frame | ||||
---|---|---|---|---|

Cost Driver | Unit | Low Range | Point Estimate | High Range |

Initial investment costs (elements costs) | €/m^{2} | 157.99 | 166.31 | 182.94 |

Annual running and replacement costs: | ||||

- Inspection | € per year | 2253.36 | 2371.96 | 2609.16 |

- Preemptive maintenance | € per year | 11,266.82 | 11,859.81 | 13,045.79 |

- Maintenance work (light) | € every 5 years | 45,067.29 | 47,439.25 | 52,183.18 |

- Maintenance work (main) | € every 10 years | 74,716.82 | 83,018.69 | 99,622.00 |

- Replacement | € | 258,403.50 | 287,115.00 | 344,538.00 |

Dismantling cost | €/m^{2} | 29.70 | 33.00 | 39.60 |

Disposal cost | €/ton | −640.00 | −800.00 | −880.00 |

**Table 6.**The financial assumptions and environmental cost items: probability distribution parameters.

Timber/Aluminum Frame | ||||
---|---|---|---|---|

Finacial Assumptions and Environmental Cost Items | Unit | Low Range | Point Estimate | High Range |

Discount rate | % | 1.25 | 1.39 | 2.50 |

Embodied Energy—Cost for electricity | €/Kwh | 0.145 | 0.153 | 0.168 |

Embodied Carbon—Carbon Tax EU | €/ton | 13.50 | 22.25 | 33.00 |

**Table 7.**The cost drivers and probability distribution values in the 25-year lifespan scenario; Monte Carlo simulation output.

Cost Driver | Graph | Min | Mean | Max | 5% | 95% |
---|---|---|---|---|---|---|

Disposal cost_glass | 72.04174 | 82.66666 | 95.9882 | 75.09819 | 91.6178 | |

Disposal cost_timber | 49.52516 | 56.83334 | 65.97852 | 51.63001 | 62.98751 | |

Disposal cost_aluminum | 640.3812 | 773.3333 | 879.7273 | 683.8148 | 849.0135 | |

Dismantling cost | 29.70633 | 34.1 | 39.59618 | 30.97808 | 37.7925 | |

Discount rate | 1.25% | 1.71% | 2.50% | 1.34% | 2.24% | |

Embodied Energy_cost of electricity | 0.1453121 | 0.1555333 | 0.1682803 | 0.1482755 | 0.1641051 | |

Embodied Carbon_Carbon Tax mean EU | 13.51154 | 22.91667 | 32.9786 | 16.42056 | 29.7623 | |

Fixture Elements Cost: | ||||||

Fixture elements cost/Timber | 218.0984 | 233.3584 | 252.466 | 222.5009 | 246.2 | |

Fixture elements cost/Aluminum | 157.9929 | 169.0794 | 182.8887 | 161.2125 | 178.3837 | |

Inspection: | ||||||

Inspection/Timber | 6221.259 | 6656.549 | 7200.021 | 6346.84 | 7022.841 | |

Inspection/Aluminum | 2253.682 | 2411.495 | 2608.782 | 2299.294 | 2544.194 | |

Maintenance Work (Light): | ||||||

Maintenance work (light)/Timber | 62,215.12 | 66,565.48 | 71,997.41 | 63,468.33 | 70,228.49 | |

Maintenance work (light)/Aluminum | 45,079.43 | 48,229.91 | 52,172.09 | 45,985.94 | 50,883.93 | |

Maintenance Work (Main): | ||||||

Maintenance work (main)/Timber | 117,859.3 | 135,313.5 | 157,064.5 | 122,924.9 | 149,965.5 | |

Maintenance work (main)/Aluminum | 74,738.78 | 85,785.84 | 99,568.09 | 77,931.94 | 95,074.59 | |

Preemptive Maintenance: | ||||||

Preemptive aintenance/Timber | 15,553.31 | 16,641.37 | 18,002.42 | 15,867.11 | 17,557.11 | |

Preemptive maintenance/Aluminum | 11,269.82 | 12,057.48 | 13,043.91 | 11,496.46 | 12,720.99 | |

Replacement: | ||||||

Replacement/Timber | 339,753 | 389,866.3 | 452,551.2 | 354,172.4 | 432,081.8 | |

Replacement/Aluminum | 258,436.4 | 296,685.5 | 344,450.6 | 269,523.2 | 328,811.6 |

**Table 8.**The output values of Gc

_{EnEc}for the timber/aluminum frames: the probability distribution function and statistics for the 25-year lifespan option. The Monte Carlo simulation output.

Output | Graph | Min | Mean | Max | 5% | 95% |
---|---|---|---|---|---|---|

GcEnEc Timber | €1,623,874.00 | €1,826,083.00 | €2,005,719.00 | €1,718,837.00 | €1,919,279.00 | |

GcEnEc Aluminum | €1,108,475.00 | €1,222,942.00 | €1,332,700.00 | €1,164,164.00 | €1,274,020.00 |

**Table 9.**The output values of Gc

_{EnEc}for the timber/aluminum frames: the probability distribution function and statistics for the 20-year lifespan option. The Monte Carlo simulation output.

Output | Graph | Min | Mean | Max | 5% | 95% |
---|---|---|---|---|---|---|

GcEnEc Timber | €1,664,037.00 | €1,889,592.00 | €2,093,332.00 | €1,774,911.00 | €1,988,238.00 | |

GcEnEc Aluminum | €1,210,552.00 | €1,353,980.00 | €1,492,126.00 | €1,278,157.00 | €1,419,990.00 |

**Table 10.**The output values of Gc

_{EnEc}for the timber/aluminum Frames: the probability distribution function and statistics for the 15-year lifespan option. The Monte Carlo simulation output.

Output | Graph | Min | Mean | Max | 5% | 95% |
---|---|---|---|---|---|---|

GcEnEc Timber | €1,768,091.00 | €2,012,776.00 | €2,250,914.00 | €1,889,712.00 | €2,119,987.00 | |

GcEnEc Aluminum | €1,232,633.00 | €1,395,225.00 | €1,547,834.00 | €1,320,232.00 | €1,461,350.00 |

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**MDPI and ACS Style**

Fregonara, E.; Ferrando, D.G.; Pattono, S.
Economic–Environmental Sustainability in Building Projects: Introducing Risk and Uncertainty in LCCE and LCCA. *Sustainability* **2018**, *10*, 1901.
https://doi.org/10.3390/su10061901

**AMA Style**

Fregonara E, Ferrando DG, Pattono S.
Economic–Environmental Sustainability in Building Projects: Introducing Risk and Uncertainty in LCCE and LCCA. *Sustainability*. 2018; 10(6):1901.
https://doi.org/10.3390/su10061901

**Chicago/Turabian Style**

Fregonara, Elena, Diego Giuseppe Ferrando, and Sara Pattono.
2018. "Economic–Environmental Sustainability in Building Projects: Introducing Risk and Uncertainty in LCCE and LCCA" *Sustainability* 10, no. 6: 1901.
https://doi.org/10.3390/su10061901