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Analysis of the Cost of a Building’s Life Cycle in a Probabilistic Approach

  • M. Rogalska EMAIL logo and D. Szewczak
Published/Copyright: June 13, 2019
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Open Engineering
From the journal Open Engineering Volume 9 Issue 1

Abstract

In the article the costs of alternative roofing techniques in the life cycle of the building were calculated. The calculations were made in accordance with ISO 15686-5 standard “Buildings and constructed assets – Service life planning – Part 5: Life-cycle costing”, using normative durability periods and minimum period of annual consumption of individual building elements to determine the durability of building components. The normative periods are valid in Poland in relation to the valuation of buildings. Probabilistic costs in the life cycle of ceramic, metal and bituminous coatings were analysed. The probability density distributions were assumed: beta for pricing factors and normal for the interest rate. Calculations were carried out for the periods of 100 years of operation of coverings, taking into account the costs of replacement and utilization. As a result of the calculations, the life cycle costs of alternative coatings with probabilities from 5 to 95% were obtained.

Keywords: LCCA; statistical calculations; simulation-based costing

1 Introduction

Life cycle cost analysis (LCCA) is among others a tool for determining the most cost-effective option among the various competing alternatives. All costs of the user are taken into account in the LCCA of construction projects, starting from the purchase of land through the design process, erection of the building, costs related to the use such as: management costs, periodic inspections, repairs, repairs, replacement of instrumentation and infrastructure related to the object. All costs in the analysis are discounted to the current value known as the net present value (PV). The LCCA analysis uses two approaches: Deterministic (DBC deterministic-based costing) and probabilistic (SBC simulation-based costing). It was observed that all variables used in the calculations are characterized by variability. You can only approximate the scope and cost of the renovation that would take place in 40 years. The article proposes a method for calculating the life cycle costs of a building in the SBC LCCA probabilistic approach. The proposed procedure for calculations is described. Cost-effectiveness plays a key role in any construction project. Life cycle cost analysis (LCCA) is a method of determining the total cost of a construction project in the expected period of use, including operating and maintenance costs. LCCA in the deterministic approach can be improved using alternative modern probabilistic techniques. Probabilistic calculations in which the minimum, average and maximum values are defined with specific distributions are closer to the actual values.

2 Probabilistic Life Cycle Cost Analysis

The choice of building materials when designing a building has a major impact on costs. An analysis of construction and renovation costs has been carried out over a period of 100 years. The SBC LCCA method assumes that all data used for calculations have probabilistic values. It was observed that all data are highly volatile. It was assumed that there are no grounds to claim that the result of life cycle cost calculations of individual building elements, as well as of the entire building, will be a discrete value. The article proposes a method of calculating the life cycle costs of a building in SBC LCCA. The proposed calculation procedure was described. Probabilistic calculations, in which minimum, average and maximum values are defined with specific distributions, are closer to real values. They can form the basis for information on the life cycle costs of a building. The method of SBC LCCA calculations is presented on the example of roofing material selection. Three types of materials in their life cycle were compared: clay roofing tiles, steel roofing tiles and roofing membrane.

3 SBC LCCA calculation

The collection of data needed for calculations is the most important and labour-intensive element of the method. It is necessary to determine the minimum, average, maximum and standard deviations of individual price factors, such as: materials, labour, equipment, indirect costs, material purchase costs and profit. Three valuations are obtained. On the basis of these values the standard deviation can be calculated. The calculated values are summarised in Table 1.

Table 1

Comparison of minimum, average and maximum price

NoPrice-forming factorminimum value PBCminaverage value PBCmedmaximum value PBCmax
1M - materialsin line with price indicators 'Cost estimate value of investments' Price indices, eg SEKOCENBUD in Poland or own analysis
190 PLN/m2200 PLN /m2260 PLN /m2
2R– labor work13,54 PLN /wh15,50 PLN /wh16,72 PLN /wh
3S– equipment work68 PLN/mh72 PLN/mh84 PLN/mh
4Kp(R,S) – indirect cost62 %65%72%
5Km (M)– cost of material purchase7%8%10%
6Z(R, S, Kp, Km) - profit11%12%13%

After analyzing the net costs, we have the minimum PBCmin, average PBCmed and maximum PBCmax values.We can calculate the standard deviation σ net costs (2):

(1)σ=(PBCmin−PBCmed2+PBCmed−PBCmed2+PBCmax−PBCmed2)/31/2

The next step in the calculation is to determine the probability density function for the discount rate and for the price formation factors. It is recommended by ISO 15686-5 to take a normal distribution for the discount rate. With respect to other calculation factors there are no standard recommendations. In scientific studies, different distributions of probability density in relation to price drivers are assumed: [3] triangular, [4] normal and uni, [1] logistical, logarithmic and normal, [5, 7] lognormal, [8] beta. With a large number of data, the correctness of the probability distribution can be tested using the χ2 test according to [2]. Only 3 minimum, mean and maximum values are taken into account in this calculation method. Therefore, the χ2 test cannot be carried out. In the article, the beta distribution was assumed for further calculations, as in [8]. Using the proprietary Beta Pert calculation application in EXCEL, the parameters α PBC and β PBC of beta distribution were calculated. Table 2 and equations (3,4,5) show the generalised data formulas.

Table 2

Comparison of generalized data

LpPrice-forming factorSymbolQuantity surveyThe unit PBC price
1MaterialsMiYmiMi(normal; Mimin, Mimed, Mimax,σMi) lub
Mi(beta; Mimin, Mimed, Mimax,σMi,αMi,βMi)
2Labor workRiYRiRi(normal; Rmin, Rmed, Rmax,σRi) lub
Ri(beta; Rimin, Rimed, Rimax,σRi,αRi,βRi)
3Equipment workSiYSiSi(normal; Simin, Simed, Simax,σRi) lub
Si(beta;Simin, Simed, Simax,σSi,αSi,βSi)
4Indirect costKpi=f(Ri,Si)%Kpi(normal, Kpmin, Kpmed, Kpmax,σKp) lub
Kpi(beta, Kpimin, Kpimed, Kpimax,σKp, αKpi,βKpi)
5Cost of material purchaseKzi=g(Mi)%Kz((normal; Kzmin, Kzmed, Kzmax,σKzi) lub
Kzi(beta;Kzimin, Kzimed, Kzimax,σKzi, αKzi,βKzi)
6ProfitZ=h(Ri,Si,Kp)%Zi(normal; Zmin, Zmed, Zmax,σZi) lub
Zi(beta; Zimin, Zimed, Zimax,σZi, αZi,βZi)

Where:

(2)PBCn=∑i=1n(Mi(normal;Mimin,Mimed,Mimax,σMi)+Ri(normal;Rmin,Rmed,Rmax,σRi)+Si(normal;Simin,Simed,Simax,σSi)+Kpi(normal,Kpmin,Kpmed,Kpmax,σKp)+Kz(normal;Kzmin,Kzmed,Kzmax,σKZi)+Zi(normal;Zmin,Zmed,Zmax,σZi))

or

(3)PBCn=∑i=1n(Mi(beta;Mimin,Mimed,Mimax,σMi,αMi,βMi)+Ri(beta;Rmin,Rmed,Rmax,σRi,αRi,βRi)+Si(beta;Simin,Simed,Simax,σSi,αSi,βSi)+Kpi(beta,Kpmin,Kpmed,Kpmax,σKp,αKp,βKp)+Kz(btea;Kzmin,Kzmed,Kzmax,σKZi,αKZi,βKzi)+Zi(beta;Zmin,Zmed,Zmax,σZi,αZi,βZi))

or

(4)PBCn=∑i=1n(Mi(beta;Mimin,Mimed,Mimax,σMi,αMi,βMi)+Ri(beta;Rmin,Rmed,Rmax,σRi,αRi,βRi)+Si(beta;Simin,Simed,Simax,σSi,αSi,βSi)+Kpi(normal,Kpmin,Kpmed,Kpmax,σKp)+Kz(normal;Kzmin,Kzmed,Kzmax,σKZi)+Zi(normal;Zmin,Zmed,Zmax,σZi))

A calculation analysis is presented below. The calculation was performed using the @Risk add-on to Microsoft Excel, which enables risk analysis by means of Monte Carlo simulation. @RISK shows practically all possible results for each situation and informs about the probability of their occurrence. The calculations were carried out on the assumption that the probability distribution of pricing factors is beta and normal in relation to the inflation coefficient. The results are compared with deterministic calculations, table 3.

Table 3

The results of calculations for beta distribution and deterministic data for ceramic tile

NameMinMeanMax5%95%
beta distribution primary instalation100,25118,15148,52102,72139,89
deterministic primary instalation59,5374,73105,88

All calculations were carried out with reference to the present value PV (6.7.8).

(5)PVPBC=PBC1+rm
(6)PVPBC=PBC/1++rbetal;rmin,rmed,rmax,σrmbetal;mmin,mmed,mmax,σm
(7)PVPBCm=1/1++rnormal;rmin,rmed,rmax,σrmnormal;mmin,mmed,mmax,σm+∑i=1n(Mi(beta;Mimin,Mimed,Mimax,σMi,αMi,βMi)+Ri(beta;Rimin,Rimed,Rimax,σRi,αRi,βRi)+Si(beta;Simin,Simed,Simax,σsi,αSi,βSi)+Kpi(normal;Kpmin,Kpmed,Kpmax,σKp)+Kz(normal;Kzmin,Kzmed,Kzmax,σKzi)+Zi(normal;Zmin,Zmed,Zmax,σZi))

Where:

PVPBC – present value,

PBC – the future amount of money, r– interest rate (is given as a percentage, but expressed as a decimal in this formula), r(beta;rmin,rmed,rmax, σr) m – is the number of compounding years between the present date and the date where the sum is worth PBC, m(normal;mmin,mmed,mmax, σm)

The cost LCCA of building can be accout (9):

(8)PVPBCtotal=∑m=1100PVPBCm

Calculations were carried out using the Monte Carlo method in the @Risk Excel program. The results were obtained in a probabilistic form. The results are summarized in Table 5 and presented on figure 1.

Table 4

The input data for calculations

LpPrice-forming factorType of materialminimum value PBCmin

[PLN]		average value PBC med

[PLN]		maximum value PBCmax

[PLN]		standard deviation

[PLN]		αPBC

Beta		βPBC

Beta
primary installation
1M –materials*ceramic tile39,6052,5280,9217,261,252,75
steel tile22,9128,9937,905,441,602,40
bitumen membrane25,6434,5639,85,842,521,48
2R - laborall13,5415,516,721,312,471,53
ceramic tile7,919,069,770,942,471,53
steel tile4,625,295,700,552,471,53
bitumen membrane8,399,6110,370,992,471,53
3S - equipment workall5,507,7410,22,351,912,09
ceramic tile0,290,410,540,121,912,09
steel tile0,040,530,690,161,912,09
bitumen membrane0,370,530,690,011,912,09
4Kp( R,S) – indirect costs [%]all6265724,191,22,8
ceramic tile5,876,166,824,191,22,8
steel tile3,613,784,194,191,22,8
bitumen membrane6,296,597,304,191,22,8
5Km (M)– costs of material purchase [%]all7%8%10%1,251,352,65
ceramic tile3,684,205,251,251,352,65
steel tile0,040,530,690,161,912,09
bitumen membrane0,370,530,690,011,912,09
6Z(R, S, Kp, Km) – profit[%]the same11%12%13%0,8222
ceramic tile2,182,382,580,202,002,00
steel tile1,311,431,550,822,002,00
bitumen membrane2,103,482,480,822,002,00
demolition works
7R - laborR total13,5415,516,721,312,471,53
ceramic tile7,919,069,770,942,471,53
steel tile4,625,295,70,552,471,53
bitumen membrane8,399,6110,370,992,471,53
8S - equipment workextract total5,57,7410,22,351,912,09
ceramic tile0,290,410,540,121,912,09
steel tile0,040,530,690,161,912,09
bitumen membrane0,370,530,690,011,912,09
truck total6175,8791,9315,471,932,07
ceramic tile29,8937,1845,0415,471,932,07
steel tile5,496,838,271,391,932,07
bitumen membrane5,797,218,731,471,932,07
9Kp( R,S) – indirect costs [%]the same78101,251,352,65
ceramic tile28,9230,3233,592,391,22,8
steel tile7,848,229,110,651,22,8
bitumen membrane7,848,229,110,651,22,8
10Z(R, S, Kp, Km) – profit[%]the same1112130,8222
ceramic tile8,479,2410,012,3922
steel tile2,302,502,710,6522
bitumen membrane2,302,502,710,6522
Table 5

The output data of calculation

NameMaterialMinMeanMaxprobability 5%probability 95%
primary instalationceramic tile132,33146,99170,54134,58162,90
in totalceramic tile300,08415,07579,14332,78504,62
primary instalationsteel tile41,8142,1142,6541,8442,46
in totalsteel tile101,13132,84184,37105,21166,49
primary instalationbitumen membrane44,1651,0860,9245,0958,24
in totalbitumen membrane429,21569,30723,70472,26681,59
Figure 1 The cost of installing and using roof coverings over a 100-year period
Figure 1

The cost of installing and using roof coverings over a 100-year period

As can be seen in Figure 2, the cost of the original roofing with a steel tile and a bituminous membrane is almost three times lower than that of ceramic roof tiles.When con-sidering PLCCA over 100 years of use (shelf life of 25 years for a bituminous membrane, 10 years of steel roofing, 100 years of ceramic roof tiles), the cost of a ceramic roof tile is the lowest. Assuming the cost of LCCA bituminos membrane as 100%, the cost of a steel roof tile is 64% and ceramic tile only 26%. The probability of the cost of roof usage in 100 years has been analyzed. The results are presented on Figure 2.

Figure 2 The cost of installing and using roof coverings over a 100-year period as a probability function from 0% to 100%
Figure 2

The cost of installing and using roof coverings over a 100-year period as a probability function from 0% to 100%

4 Summary and conclusions

Reilly (2004) indicates that the construction of the line London’s Jubilee subway has been delayed by two years, and the cost of implementation exceeded the planned costs by 67% (ie 1.4 billion pounds); tunnel under the channel La Manche exceeded the planned budget by 80%, the bridge over the Great Belt in Denmark is 54% of the overrun costs (Połoński 2010). Such examples can be found in literature more. However, only research carried out under the direction of Flyvbjerg (Flyvbjerg 2002) have been carried out on a large, representative statistical sample of 258 objects. The results of these tests will be unequivocally confirmed - that the problem of underestimating planned investments - is common and affects almost 9 out of 10 respondents investment, with the average analytical overrun - planned costs was 28%. Farr et al. (2016) indicate that simulation-based costing should be replaced by the traditional cost estimate. Advanced analytical tools are needed to incorporate risk and provide more defensible cost estimates. The cost calculation applies not only to the embedding process but also to the cost of use in the life cycle of the building. The article presents a probabilistic method of calculating costs in the lifecycle of a building, on the example of roof coverings. It is very important to take into account costs not only in the first phase of embedding, but also costs of demolition, repairs and replacements. The proposed method is new and has not been used so far.

References

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Received: 2018-04-16
Accepted: 2018-03-07
Published Online: 2019-06-13

© 2019 M. Rogalska and D. Szewczak, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/eng-2019-0015
Keywords for this article
LCCA; statistical calculations; simulation-based costing
Creative Commons
BY 4.0

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  49. Evaluation the effect of lime on the plastic and hardened properties of cement mortar and quantified using Vipulanandan model
  50. Uplift and Settlement Prediction Model of Marine Clay Soil e Integrated with Polyurethane Foam
  51. IoT Applications in Wind Energy Conversion Systems
  52. A new method for graph stream summarization based on both the structure and concepts
  53. “Zhores” — Petaflops supercomputer for data-driven modeling, machine learning and artificial intelligence installed in Skolkovo Institute of Science and Technology
  54. Economic Disposal Quantity of Leftovers kept in storage: a Monte Carlo simulation method
  55. Computer technology of the thermal stress state and fatigue life analysis of turbine engine exhaust support frames
  56. Statistical model used to assessment the sulphate resistance of mortars with fly ashes
  57. Application of organization goal-oriented requirement engineering (OGORE) methods in erp-based company business processes
  58. Influence of Sand Size on Mechanical Properties of Fiber Reinforced Polymer Concrete
  59. Architecture For Automation System Metrics Collection, Visualization and Data Engineering – HAMK Sheet Metal Center Building Automation Case Study
  60. Optimization of shape memory alloy braces for concentrically braced steel braced frames
  61. Topical Issue Modern Manufacturing Technologies
  62. Feasibility Study of Microneedle Fabrication from a thin Nitinol Wire Using a CW Single-Mode Fiber Laser
  63. Topical Issue: Progress in area of the flow machines and devices
  64. Analysis of the influence of a stator type modification on the performance of a pump with a hole impeller
  65. Investigations of drilled and multi-piped impellers cavitation performance
  66. The novel solution of ball valve with replaceable orifice. Numerical and field tests
  67. The flow deteriorations in course of the partial load operation of the middle specific speed Francis turbine
  68. Numerical analysis of temperature distribution in a brush seal with thermo-regulating bimetal elements
  69. A new solution of the semi-metallic gasket increasing tightness level
  70. Design and analysis of the flange-bolted joint with respect to required tightness and strength
  71. Special Issue: Actual trends in logistics and industrial engineering
  72. Intelligent programming of robotic flange production by means of CAM programming
  73. Static testing evaluation of pipe conveyor belt for different tensioning forces
  74. Design of clamping structure for material flow monitor of pipe conveyors
  75. Risk Minimisation in Integrated Supply Chains
  76. Use of simulation model for measurement of MilkRun system performance
  77. A simulation model for the need for intra-plant transport operation planning by AGV
  78. Operative production planning utilising quantitative forecasting and Monte Carlo simulations
  79. Monitoring bulk material pressure on bottom of storage using DEM
  80. Calibration of Transducers and of a Coil Compression Spring Constant on the Testing Equipment Simulating the Process of a Pallet Positioning in a Rack Cell
  81. Design of evaluation tool used to improve the production process
  82. Planning of Optimal Capacity for the Middle-Sized Storage Using a Mathematical Model
  83. Experimental assessment of the static stiffness of machine parts and structures by changing the magnitude of the hysteresis as a function of loading
  84. The evaluation of the production of the shaped part using the workshop programming method on the two-spindle multi-axis CTX alpha 500 lathe
  85. Numerical Modeling of p-v-T Rheological Equation Coefficients for Polypropylene with Variable Chalk Content
  86. Current options in the life cycle assessment of additive manufacturing products
  87. Ideal mathematical model of shock compression and shock expansion
  88. Use of simulation by modelling of conveyor belt contact forces
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