# An Integrated Efficiency–Risk Approach in Sustainable Project Control

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## Abstract

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## 1. Introduction and Literature Review

## 2. CCM/BM Method

## 3. EVM/ES Method

- ACWP: Actual cost of work performance
- BCWP: Budget cost of work performance
- BCWS: Budget cost of work schedule
- BAC: Budget at completion
- CPI: Cost performance index
- CV: Cost variance
- CV%: Cost variance percentage
- EAC: Estimate at completion
- SPI: Schedule performance index
- SV: Schedule variance
- SV%: Schedule variance percentage
- TCPI: To complete performance index
- VAC: Variance at completion.

_{t}) for the project. Therefore, the earned schedule can be mathematically defined as adapted in Equation (4).

_{t}) is calculated:

## 4. Integrated Efficiency–Risk Methodology with the Combination of Two EVM and CCM Techniques

- Computing the cost and schedule buffers of the projects;
- The integration of the efficiency-risk control of the projects by managing the schedule and cost buffers;
- Estimating the cost and duration of the project completion with maximum accuracy and efficiency, including: estimating cost at completion (hybrid efficiency–risk approach); and estimating duration at completion (hybrid efficiency–risk approach).

#### 4.1. Computing the Cost and Schedule Buffers of the Projects

#### 4.2. The Integration of the Efficiency-Risk Control of the Projects by Managing the Schedule and Cost Buffers

_{C}) and that of the work done based on cost (W

_{C}) are calculated. The cost status of the project intersection of these two points is shown in Figure 4.

_{T}) and that of the work done based on time (W

_{T}) are calculated using Equations (8) and (9). The duration status of the project intersection of two points is presented in Figure 4.

#### 4.3. Estimating the Cost and Duration of Project Completion with Maximum Accuracy and Efficiency

#### 4.3.1. Estimate Cost at Completion (Hybrid Efficiency-Risk Approach)

- BPV
_{i}: Baseline planned value of the scheduled activity i, and the authorized budget assigned to the work to be accomplished for activity i. BPV_{i}is independent of the status date. Some may refer to it the baseline cost for activity i. - BCAC
_{0}: Budget cost at completion, regardless of the cost buffer for the project, is the sum of BPV_{i}for all the planned activities at the baseline plan, which is calculated using Equation (10):$$\begin{array}{l}BCA{C}_{0}={\displaystyle {\sum}_{i=1}^{N}BP{V}_{i}}\\ where\\ N=quantity\text{}of\text{}activity\end{array}$$ - BCAC: Budget cost at completion with regard to the cost buffer (combination of performance and risk parameters), which is calculated using Equation (11):$$\begin{array}{l}BCAC=BCA{C}_{0}+CB\\ where\\ CB=Cost\text{}Buffer\end{array}$$
- B
_{C}: Cost buffer percent of BCAC_{0}, which is calculated using Equation (12):$${B}_{C}=\frac{CB}{BCA{C}_{0}}$$ - P
_{C}: The percentage of the cost buffer is calculated with the help of the Equation (6). - W
_{C}: The percentage of work done based on cost, which is calculated using Equation (7). - CPI: Based on parameters BCAC
_{0}, W_{C}, P_{C}, cost buffer, and formulas presented in Section 3 (EVM/ES), the cost performance index can be calculated as Equation (13). The index is used to update the remainder of the cost buffer:$$\begin{array}{l}CV=BCWP-ACWP=EV-ACWP\\ CPI=\frac{BCWP}{ACWP}=\frac{EV}{ACWP}=\frac{EV}{EV-CV}=\frac{{W}_{C}*BCA{C}_{0}}{{W}_{C}*BCA{C}_{0}-{P}_{C}*CB}\end{array}$$ - ECAC
_{0}: In the phases of project control, estimated cost at completion, regardless of the cost buffer, and only after the control of the project buffer usage is done. In other words, with the help of the cost buffer usage, the adjusted BCAC_{0}is estimated, which is the same as ECAC_{0}. Equation (14) calculates this value:$$ECA{C}_{0}=BCA{C}_{0}+BCA{C}_{0}*{P}_{C}=BCA{C}_{0}(1+{P}_{C})$$ - CB
_{A}: Cost buffer, which is adjusted during the phases of project control, with the help of the percentages of the cost buffer (P_{C}) and cost performance index (CPI) parameters for calculating the adjusted cost buffer, using Equation (15).$$\begin{array}{l}C{B}_{A}=CCB+RC{B}_{A}\\ C{B}_{A}=CB*{P}_{C}+\frac{CB*(1-{P}_{C})}{CPI}\\ C{B}_{A}=CB*{P}_{C}+\frac{CB*(1-{P}_{C})}{\frac{{W}_{C}*BCA{C}_{0}}{{W}_{C}*BCA{C}_{0}-{P}_{C}*CB}}\\ C{B}_{A}=CB*{P}_{C}+CB*(1-{P}_{C})*(1-\frac{{P}_{C}*CB}{{W}_{C}*BCA{C}_{0}})\\ C{B}_{A}={B}_{C}*BCA{C}_{0}*{P}_{C}+{B}_{C}*BCA{C}_{0}*(1-{P}_{C})*(1-\frac{{P}_{C}*{B}_{C}}{{W}_{C}})\\ where\\ CCB=Consumed\text{}Cost\text{}Buffer\\ RC{B}_{A}=\mathrm{Re}\text{}mained\text{}Cost\text{}Buffer\text{}of\text{}Adjusted\end{array}$$ - ECAC: Estimated cost at completion, with regard to cost buffers (combination of performance and risk parameters), is calculated using Equation (16):$$\begin{array}{l}ECAC=ECA{C}_{0}+C{B}_{A}\\ ECAC=BCA{C}_{0}(1+{P}_{C})+CB*{P}_{C}+CB*(1-{P}_{C})*(1-\frac{{P}_{C}*CB}{{W}_{C}*BCA{C}_{0}})\\ ECAC=BCA{C}_{0}(1+{P}_{C})+{B}_{C}*BCA{C}_{0}*{P}_{C}+{B}_{C}*BCA{C}_{0}*(1-{P}_{C})*(1-\frac{{P}_{C}*{B}_{C}}{{W}_{C}})\end{array}$$

#### 4.3.2. Estimate Duration at Completion (Hybrid Efficiency–Risk Approach)

- BPD
_{0}: The baseline planned duration, regardless of the schedule buffer, of the project is the authorized duration assigned to the scheduled work to be accomplished for the entire project irrespective of the status date. - BPD: Total baseline planned duration, with regard to the schedule buffer (combination of performance and risk parameters), which is calculated using Equation (17):$$\begin{array}{l}BPD=BP{D}_{0}+SB\\ where\\ SB=Schedule\text{}Buffer\end{array}$$
- B
_{T}: Schedule buffer percent of BPD_{0}, which is calculated using Equation (18):$${B}_{T}=\frac{SB}{BP{D}_{0}}$$ - P
_{T}: The percentage of the schedule buffer is calculated with the help of Equation (19):$$\begin{array}{l}E{S}_{T}=T+\frac{EV-P{V}_{T}}{P{V}_{T+1}-P{V}_{T}}\\ S{V}_{T}=E{S}_{T}-AT\\ {P}_{T}=\frac{S{V}_{T}}{SB}\end{array}$$ - W
_{T}: The percentage of work done based on time, which is calculated using Equation (20):$${W}_{T}=\frac{E{S}_{T}}{BP{D}_{0}}$$ - SPI
_{T}: With the help of the parameters of BPD_{0}, W_{T}, P_{T}, Schedule Buffer, and formulas presented in EVM/ES, the schedule performance index can be calculated as follows: The SPI_{T}is used to update the remaining schedule buffer, which can be seen in Equation (21):$$\begin{array}{l}S{V}_{T}=E{S}_{T}-AT\\ SP{I}_{T}=\frac{E{S}_{T}}{AT}=\frac{E{S}_{T}}{E{S}_{T}-S{V}_{T}}=\frac{{W}_{T}*BP{D}_{0}}{{W}_{T}*BP{D}_{0}-{P}_{T}*SB}\end{array}$$ - EDAC
_{0}: Within the phases of project control, the estimated duration at completion, regardless of the schedule buffer, and only after the control of project buffer usage is done. In other words, with the help of schedule buffer usage, the adjusted BPD_{0}is estimated, which is the same as EDAC_{0}. Equation (22) calculates this value:$$EDA{C}_{0}=BP{D}_{0}+BP{D}_{0}*{P}_{T}=BP{D}_{0}(1+{P}_{T}^{})$$ - SB
_{A}: Adjusted schedule buffer; during the phases of project control, with the help of the percentage of the schedule buffer (P_{T}) and the schedule performance index (SPI) parameters, the calculation of the adjusted schedule buffer uses Equation (23):$$\begin{array}{l}S{B}_{A}=CSB+RS{B}_{A}\\ S{B}_{A}=SB*{P}_{T}+\frac{SB*(1-{P}_{T})}{SP{I}_{T}}\\ S{B}_{A}=SB*{P}_{T}+\frac{SB*(1-{P}_{T})}{\frac{{W}_{T}*BP{D}_{0}}{{W}_{T}*BP{D}_{0}-{P}_{T}*SB}}\\ S{B}_{A}=SB*{P}_{T}+SB*(1-{P}_{T})*(1-\frac{{P}_{T}*SB}{{W}_{T}*BP{D}_{0}})\\ S{B}_{A}={B}_{T}*BP{D}_{0}*{P}_{T}+{B}_{T}*BP{D}_{0}*(1-{P}_{T})*(1-\frac{{P}_{T}*{B}_{T}}{{W}_{T}})\\ where\\ CSB=Consumed\text{}Schedule\text{}Buffer\\ RS{B}_{A}=\mathrm{Re}\text{}mained\text{}Schedule\text{}Buffer\text{}of\text{}Adjusted\end{array}$$ - EDAC: Estimated duration at completion, with regard to schedule buffers (the combination of performance and risk parameters), which is calculated using Equation (24).$$\begin{array}{l}EDAC=EDA{C}_{0}+S{B}_{A}\\ EAC=BP{D}_{0}(1+{P}_{T})+SB*{P}_{T}+SB*(1-{P}_{T})*(1-\frac{{P}_{T}*SB}{{W}_{T}*BP{D}_{0}})\\ EAC=BP{D}_{0}(1+{P}_{T})+{B}_{T}*BP{D}_{0}*{P}_{T}+{B}_{T}*BP{D}_{0}*(1-{P}_{T})*(1-\frac{{P}_{T}*{B}_{T}}{{W}_{T}})\\ \end{array}$$

## 5. Case Study

_{0}) is estimated to be equal to 48 days, and the budget cost at completion regardless of the buffer cost (BAC

_{0}) is calculated using Equation (25):

- BCAC: Budget cost at completion with regard to the cost buffer (combination of performance and risk parameters), which is calculated using Equation (30):$$BCAC=BCA{C}_{0}+CB=143000+37766=\$180766$$
- B
_{C}: Cost buffer percentage of BCAC_{0}, which is calculated using Equation (31):$${B}_{C}=\frac{CB}{BCA{C}_{0}}=\frac{37766}{143000}=26.4\%$$ - ECAC
_{0}: During the phases of project control, estimated cost at completion, regardless of the cost buffer, and only after control of project buffer usage is done. In other words, with the help of cost buffer usage, the adjusted BCAC_{0}is estimated, which is the same as ECAC_{0}. Equation (32) calculates this value:$$ECA{C}_{0}=BCA{C}_{0}+BCA{C}_{0}*{P}_{C}=BCA{C}_{0}(1+{P}_{C})=\$16588\text{}for\text{}period1\text{}and\text{}\$198770\text{}for\text{}period2$$ - ECAC: Estimated cost at completion with regard to cost buffers (combination of performance and risk parameters), which is calculated using Equation (33);$$ECAC=BCA{C}_{0}(1+{P}_{C})+{B}_{C}*BCA{C}_{0}*{P}_{C}+{B}_{C}*BCA{C}_{0}*(1-{P}_{C})*(1-\frac{{P}_{C}*{B}_{C}}{{W}_{C}})==\$200841\text{}for\text{}period1\text{}and\text{}\$232983\text{}for\text{}period2$$
- BPD: Total baseline planned duration, with regard to the schedule buffer (combination of performance and risk parameters), which is calculated using Equation (34):$$BPD=BP{D}_{0}+SB=48+12.6=60.6\text{}days$$
- B
_{T}: Schedule buffer percentage of BPD_{0}which is calculated using Equation (35):$${\mathrm{B}}_{\mathrm{T}}=\frac{\mathrm{SB}}{\mathrm{B}P{D}_{0}}=26.2\%$$ - EDAC
_{0}: Within the phases of project control, the estimated duration at completion, regardless of the buffer, and only after control of project buffer usage is done. In other words, with the help of schedule buffer usage, the adjusted BPD_{0}is estimated, which is the same as EDAC_{0}. Equation (36) calculates this value:$$EDA{C}_{0}=BP{D}_{0}+BP{D}_{0}*{P}_{T}=BP{D}_{0}(1+{P}_{T}^{})=48\text{}days\text{}for\text{}period1\text{}and\text{}82\text{}days\text{}for\text{}period2$$ - EDAC: Estimated duration at completion with regard to schedule buffers (the combination of performance and risk parameters), which is calculated using Equation (37):$$EDAC=BP{D}_{0}(1+{P}_{T})+{B}_{T}*BP{D}_{0}*{P}_{T}+{B}_{T}*BP{D}_{0}*(1-{P}_{T})*(1-\frac{{P}_{T}*{B}_{T}}{{W}_{T}})=61\text{}days\text{}for\text{}period1\text{}and\text{}93\text{}days\text{}for\text{}period2$$

## 6. Results and Conclusions

- Taking full advantages of CCM/BM (allocating precaution time to the whole project and not to each individual activity, preventing the occurrence of Student Syndrome and parallel activities) and EVM/ES (concurrent control on time and cost, thereby drawing equations for ECAC and EDAC);
- Integrated control on the efficiency (time and cost) and risk of projects;
- Calculation of time and cost buffers to deal with cost and time risks;
- Providing a tight control (fast and accurate) on time, cost, and related risks with the help of developed buffers;
- Giving an estimation on EDAC and ECAC with respect to the percentage of project progress, as well as the consumed time–cost buffers;
- Providing an applied procedure to implement the methodology in practice.

## Data Availability Statements

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Method of calculation of budget at completion (BAC) and estimate at completion (EAC) values [36].

**Figure 3.**Method of calculating the earned schedule [15].

**Figure 4.**Project control charts based on project progress (schedule or cost) and the buffer usage percent (schedule or cost).

**Figure 6.**Case study project status based on project progress and the buffer usage percent (cost and schedule).

**Table 1.**Research taxonomy of control project methods based on the critical chain method (CCM) and earned value management (EVM).

Estimated Cost at Completion | Estimated Duration at Completion | CCM Advantages | Capability Uncertainty | Performance in Schedule Control | Performance in Cost Control | Method Name | Publication |
---|---|---|---|---|---|---|---|

√ | − | − | − | − | √ | Earned value project management | Vanhoucke and Vandevoorde (2007) [3] |

√ | − | − | √ | − | √ | Fuzzy approach for earned value management | Naeni et al. (2011) [9] |

√ | − | − | √ | − | √ | A graphical framework for EVM | Acebes et al., 2013 [11] |

− | − | √ | √ | √ | − | Improved critical chain project management | Ma et al., 2014 [21] |

√ | √ | − | − | √ | √ | Earned duration management | Khamooshi and Golafshani (2014) [15] |

− | − | √ | √ | √ | − | Critical chain based on comprehensive resource tightness | Zhang et al., 2016 [29] |

√ | √ | √ | √ | √ | √ | Efficiency–risk approach | Current study |

Cost Buffer | ||||
---|---|---|---|---|

Green | Yellow | Red | ||

Follow schedule more quickly even if it leads to spending more cost. | Without extra cost, increase speed of project implementation by using of new techniques. | Follows more quickly and do non-critical activities in a cost saving manner. | Red | Schedule Buffer |

Attention should be paid to the control of the project duration and it is not necessary to make corrective actions. | At remaining of project, continue same status of time and cost. | Keep speed in implementation of work with saving cost on noncritical activities. | Yellow | |

Do not need to make corrective actions. | Attention should be paid to the control of the project cost and it is not necessary to make corrective actions. | As far as possible, the value of the project is preserved and the costs are saved. | Green |

ID | Activity Name | Expected Duration | Expected Cost | ||||
---|---|---|---|---|---|---|---|

Description | Min Duration (days) | Most Likely (days) | Max Duration (days) | Min Cost ($) | Most Likely Cost ($) | Max Cost ($) | |

0010 | Project of assembled product | 116,250 | 143,000 | 233,060 | |||

0020 | Part No. 1 | 52,000 | 65,000 | 104,000 | |||

0025 | Start project | Milestone | - | ||||

0030 | Design | 8 | 10 | 16 | 8000 | 10,000 | 16,000 |

0040 | Civil | 8 | 10 | 16 | 40,000 | 50,000 | 80,000 |

0050 | Test | 8 | 10 | 16 | 4000 | 5000 | 8000 |

0060 | Part No. 2 | 20,250 | 27,000 | 47,250 | |||

0070 | Design | 6 | 8 | 14 | 3000 | 4000 | 7000 |

0080 | Civil | 6 | 8 | 14 | 15,000 | 20,000 | 35,000 |

0090 | Test | 6 | 8 | 14 | 2250 | 3000 | 5250 |

0100 | Part No. 3 | 20,000 | 24,000 | 39,860 | |||

0110 | Design | 5 | 6 | 10 | 2500 | 3000 | 5000 |

0120 | Civil | 5 | 6 | 10 | 12,500 | 15,000 | 24,900 |

0130 | Test | 5 | 6 | 10 | 5000 | 6000 | 9960 |

0140 | Product Assembly | 24,000 | 27,000 | 41,950 | |||

0150 | Assembly | 8 | 9 | 14 | 16,000 | 18,000 | 28,000 |

0160 | Product test | 5 | 6 | 10 | 8000 | 9000 | 13,950 |

0170 | Project completion | Milestone | - |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ghazvini, M.S.; Ghezavati, V.; Raissi, S.; Makui, A.
An Integrated Efficiency–Risk Approach in Sustainable Project Control. *Sustainability* **2017**, *9*, 1575.
https://doi.org/10.3390/su9091575

**AMA Style**

Ghazvini MS, Ghezavati V, Raissi S, Makui A.
An Integrated Efficiency–Risk Approach in Sustainable Project Control. *Sustainability*. 2017; 9(9):1575.
https://doi.org/10.3390/su9091575

**Chicago/Turabian Style**

Ghazvini, Mohammadreza Sharifi, Vahidreza Ghezavati, Sadigh Raissi, and Ahmad Makui.
2017. "An Integrated Efficiency–Risk Approach in Sustainable Project Control" *Sustainability* 9, no. 9: 1575.
https://doi.org/10.3390/su9091575