# Cost Calculation of Construction Projects Including Sustainability Factors Using the Case Based Reasoning (CBR) Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Cost Calculations Method Based on Case Based Reasoning with Sustainability Criterion

- Case
_{i}—i-th case from the database, - GEO
_{i}—graphical representation of the construction elements for the i-th case, - SoP
_{i}—solution of problem, - DoC
_{i}—description of construction, - Ad—data for adaptation process such date, localization of construction, and
- n—number of old cases in the database.

- w
_{N}—value of the explanatory variable for the new case, - w
_{j}—value of the explanatory variable for the j-th old case, and - w
_{max}, w_{min}—minimum and maximum values for all the old cases included in the database.

- n(w
_{N}), n(w_{j})—place in an ordered array of values n(w) = 1, 2, …, n, - M—number of values.

- sim(A
_{NC}, B_{Ci})—similarity between fuzzy numbers, - A
_{NC}—fuzzy number for the new case, - B
_{Ci}—fuzzy number for the old case taken from the database, and - a
_{i}, b_{i}—characteristic points for fuzzy numbers A_{NC}= (a_{1}, a_{2}, a_{3}, a_{4}) and B_{Ci}= (b_{1}, b_{2}, b_{3}, b_{4}).

_{NC}= (a

_{1}, a

_{2}, a

_{3}, a

_{4}) and B

_{Ci}= (b

_{1}, b

_{2}, b

_{3}, b

_{4}). The characteristic points allow for describing the limit values for the shape of the membership function that accepts the values 0 and 1. This allows for describing the fuzzy number using the four real numbers, which allows for the quick execution of actions using only these characteristic point values. When adopting other forms of membership functions, other calculation formulas should be used.

- w
_{N}—an explanatory variable for the new case and - w
_{S}—an explanatory variable for the old case.

- ω
_{i}—weight of the i-th explanatory variable, - SIM(V
_{N},V_{Sj})—global similarity between the old V_{j}and the new case V_{N}, and - sim
_{i}(V_{Ni},V_{Sji})—local similarity for the i-th explanatory variable between the old V_{j}and the new case V_{N}.

- old cases with the highest global similarity SIM(V
_{N}, V_{j}) are selected. The minimum number of cases entering the selected set of cases is 3. This assumption is to limit the possibility of choosing an accidental solution—if three solutions are chosen, then the possible extreme solution is rejected to limit the possibility of overestimating or underestimating the price of works; - the minimum value of global similarity for cases included in the set of solutions must be greater than 70%;
- the resulting value of similarities is given as a percentage and is a natural number; and,
- cases from the set of selected cases are rejected as extreme when the difference between the selected cases is greater than 50%.

## 4. An Example of Supporting Cost Calculation with the Use of the CBR Method, Taking into Account the Factors of Sustainable Construction

- Quantitative variables (type of information—GEO)intended use of the field (five types of fields)surface area of the field (variables range: 275–8714 m
^{2})surface area of the access paths and routes (variables range: 0–1753 m^{2})green surface area (variables range: 0–6017 m^{2})surface area of the ball containment netting (variables range: 0–2212 m^{2})fence length (variables range: 0–602.5 m) - Qualitative variables (type of information—DoC)type of the material for sports surface (six types of materials)type of the material for access routes (five types of materials)type of the fence (five types of fences)type of sports equipment—handball (yes or no)type of sports equipment—volleyball (yes or no)type of sports equipment—basketball (yes or no)type of sports equipment—football (yes or no)type of sports equipment—tennis (yes or no)impact of the construction on the environment (rating 1–5)impact on the surroundings (rating 1–5)

_{n}{GEO = (intended use of the field, surface area of the field, surface area of the access paths and routes, green surface area, surface area of the ball containment netting, fence length); DoC = (type of the material for sports surface, type of the material for access paths, type of the fence, type of sports equipment—handball, type of sports equipment—volleyball, type of sports equipment—basketball, type of sports equipment—football, type of sports equipment—tennis, impact of the construction on the environment, impact on the surroundings); SoP = (unit price of the field surface area); and, Ad = (location, date of the bid)}

- impact of the construction on the environment (for instance, energy demand, use of renewable energy, efficiency of energy systems);
- materials (for instance, materials with low environmental impact, materials with low risk of health hazard, recyclable materials): type of the material for sports surface and type of the material for access routes; and,
- impact on the surroundings (such as air pollution, noise, vibration, wind effects and shading of the area, the effect of the thermal island)

- r = 0 no correlation,
- 0 < r < 0.1 barely perceptible correlation,
- 0.1 < r < 0.3 poor correlation,
- 0.3 < r < 0.5 average correlation,
- 0.5 < r < 0.7 high correlation,
- 0.7 < r < 0.9 very high correlation,
- 0.9 < r < 1 almost full correlation, and
- r = 1 full correlation.

- w
_{N}equals 458 and determines the size of the access surface for the New Case—458 m^{2}, - w
_{j}equals 295, which means the access surface for Old Case 7 equal 295 m^{2}, - w
_{max}equals 5569, which means the maximum access area for the whole set of cases is equal 5569 m^{2}, and - w
_{min}is equal 0, which means the minimum access space for the whole set of cases is equal 0 m^{2}(some orders for the implementation of sports fields did not include the implementation of access routes).

- n(w
_{N}) is equal 5 and determines the value given to the material which is the polyurethane from which the New Case surface is planned to be made, - n(w
_{j}) is equal 5, which means the value given to the material which is the polyurethane from which the Old Case 7 surface was made, and - M = 6, which results from the specification of six types of materials used for sports surfaces found in the database (natural grass; surface from natural dried wood chips—technologically softened along fibers with 5–50 mm fraction; artificial grass; brick flour; polyurethane surface; asphalt surface).

_{Test case 1}, V

_{Case 7}); Case 23—SIM(V

_{Test case 1}, V

_{Case 23}); and, Case 83—SIM(V

_{Test case 1}, V

_{Case 83}).

^{2}it is necessary to specify the value of the works. For this purpose, the unit price was multiplied by the number of the works representing the construction works consisting in the performance of the sports field, namely the area of the pitch.

^{2}] × 1200 [m

^{2}] = 98 844.00 €.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References and Notes

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**Figure 2.**The distribution of the Mean Absolute Estimate Error (MAEE) error with the cost calculation broken down into percentage ranges.

Variables | Correlation Coefficient: |
---|---|

Surface area of the fields | −0.192 |

Surface area of the access paths | 0.232 |

Green surface area | 0.079 |

Fence length | 0.249 |

Surface area of the ball containment netting | 0.056 |

Intended use | −0.472 |

Material for sport surface | −0.299 |

Material for access paths | −0.283 |

Type of sports equipment—Handball | 0.244 |

Type of sports equipment—Basketball | 0.477 |

Type of sports equipment—Volleyball | 0.363 |

Type of sports equipment—Football | −0.289 |

Type of sports equipment—Tennis | −0.071 |

Fence type | −0.045 |

Impact of the construction on the environment | 0.095 |

Impact on the surroundings | −0.640 |

Variables | Weights ω_{i} |
---|---|

Surface area of the fields | 6.2% |

Surface area of the access paths | 7.5% |

Fence length | 8.0% |

Intended use | 15.2% |

Material for sport surface | 9.7% |

Material for access paths | 9.1% |

Type of sports equipment—Handball | 7.9% |

Type of sports equipment—Basketball | 15.4% |

Type of sports equipment—Volleyball | 11.7% |

Type of sports equipment—Football | 9.3% |

Variables | Local Similarities | ||
---|---|---|---|

Case 7 | Case 8 | Case 9 | |

Surface area of the fields | 94% | 88% | 94% |

Surface area of the access paths | 97% | 87% | 92% |

Fence length | 86% | 79% | 79% |

Intended use | 86% | 0% | 100% |

Material for sport surface | 100% | 0% | 100% |

Material for access paths | 100% | 100% | 0% |

Type of sports equipment—Handball | 100% | 100% | 100% |

Type of sports equipment—Basketball | 100% | 0% | 100% |

Type of sports equipment—Volleyball | 100% | 0% | 100% |

Type of sports equipment—Football | 100% | 100% | 100% |

Global similarities | 98% | 45% | 88% |

Case | Case 7 | Case 23 | Case 83 |
---|---|---|---|

Unit price | 80.25 € | 84.23 € | 79.34 € |

Regional factor | 1.028 | 0.960 | 1.028 |

Indexation factor | 100.1% | 101.3% | 101.3% |

Adjusted price | 82.58 € | 81.91 € | 82.62 € |

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**MDPI and ACS Style**

Leśniak, A.; Zima, K.
Cost Calculation of Construction Projects Including Sustainability Factors Using the Case Based Reasoning (CBR) Method. *Sustainability* **2018**, *10*, 1608.
https://doi.org/10.3390/su10051608

**AMA Style**

Leśniak A, Zima K.
Cost Calculation of Construction Projects Including Sustainability Factors Using the Case Based Reasoning (CBR) Method. *Sustainability*. 2018; 10(5):1608.
https://doi.org/10.3390/su10051608

**Chicago/Turabian Style**

Leśniak, Agnieszka, and Krzysztof Zima.
2018. "Cost Calculation of Construction Projects Including Sustainability Factors Using the Case Based Reasoning (CBR) Method" *Sustainability* 10, no. 5: 1608.
https://doi.org/10.3390/su10051608