An Integrated Efficiency-Risk Approach in Sustainable Project Control

The most important result of the hybrid efficiency–risk approach, with a combination of CCM/BM and EVM/ES in project control, is the estimated duration and cost at completion of the project considering maximum efficiency and reliability. By using the CCM technique in scheduling, the concepts of the EVM formulas to estimate cost at completion, the ES formulas to estimate the duration at completion, schedule buffer, and cost buffer, we offer new formulas to estimate the cost at completion and duration at completion of the project with maximum accuracy and efficiency return. The process is described below.

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

Using the formulas provided in the EVM/ES and the buffers calculated in the previous section, the new formula estimate cost at completion with or without the cost buffer (hybrid efficiency-risk approach) is provided. Note that the EVM technique in project cost-control works with complete accuracy. Through the formulas and concepts of the CCM/BM technique, new formulas are provided at this stage.

• 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.
• BCAC₀: Budget cost at completion, regardless of the cost buffer for the project, is the sum of BPV_ifor all the planned activities at the baseline plan, which is calculated using Equation (10):

$\begin{aligned} &B C A C_{0}=\sum\nolimits_{i=1}^{N} B P V_{i} \\ &\text { where } \\ &N=\text { quantity of activity }\end{aligned}$                 (10)

• BCAC: Budget cost at completion with regard to the cost buffer (combination of performance and risk parameters), which is calculated using Equation (11):

$\begin{aligned} &B C A C=B C A C_{0}+C B \\ &\text { where } \\ &C B=\text { Cost } B u f f e r \end{aligned}$                   (11)

• B_C: Cost buffer percent of BCAC₀, which is calculated using Equation (12):

$B_{C}=\frac{C B}{B C A C_{0}}$               (12)

• 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 BCAC₀, 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:

$\begin{aligned} &C V=B C W P-A C W P=E V-A C W P \\ &C P I=\frac{B C W P}{A C W P}=\frac{E V}{A C W P}=\frac{E V}{E V-C V}=\frac{W_{C}{ }^{*} B C A C_{0}}{W_{C}{ }^{*} B C A C_{0}-P_{C}{ }^{*} C B} \end{aligned}$                (13)

• ECAC₀: 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 BCAC₀is estimated, which is the same as ECAC₀. Equation (14) calculates this value:

$E C A C_{0}=B C A C_{0}+B C A C_{0} * P_{C}=B C A C_{0}\left(1+P_{C}\right)$                 (14)

• 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).

$\ \begin{aligned} &C B_{A}=C C B+R C B_{A}  \\ &C B_{A}=C B^{*} P_{C}+\frac{C B^{*}\left(1-P_{C}\right)}{C P I} \\  &C B_{A}=C B^{*} P_{C}+\frac{C B^{*}\left(1-P_{C}\right)}{\frac{W_{C}^{*} B C A C_{0}}{W_{C}^{* B C A C_{0}-P_{C}^{*} C B}}} \\ &C B_{A}=C B^{*} P_{C}+C B^{*}\left(1-P_{C}\right) *\left(1-\frac{P_{C}^{*} C B}{W_{C} ^{ \, \, *} B C A C_{0}}\right) \\ &C B_{A}=B_{C} * B C A C_{0} * P_{C}+B_{C} * B C A C_{0} *\left(1-P_{C}\right) *\left(1-\frac{P_{C}{ }^{*} B_{C}}{W_{C}}\right) \\ &\text { where } \\ &C C B=\text { Consumed Cost Buffer } \\ &R C B_{A}=\text { Re mained Cost Buffer of Adjusted } \end{aligned}$                (15)

ECAC: Estimated cost at completion, with regard to cost buffers (combination of performance and risk parameters), is calculated using Equation (16):

$\begin{aligned} &E C A C=E C A C_{0}+C B_{A} \\ &E C A C=B C A C_{0}\left(1+P_{C}\right)+C B^{*} P_{C}+C B^{*}\left(1-P_{C}\right) *\left(1-\frac{P_{C} * C B}{W_{C}^{*} B C A C_{0}}\right) \\ &E C A C=B C A C_{0}\left(1+P_{C}\right)+B_{C} * B C A C_{0} * P_{C}+B_{C} * B C A C_{0} *\left(1-P_{C}\right) *\left(1-\frac{P_{C}^{*} B_{C}}{W_{C}}\right) \end{aligned}$           (16)

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

Using the formulas in EVM/ES for calculating the buffers in the previous section, a new formula to estimate duration at completion that considers the buffers (hybrid efficiency-risk approach) is presented. As the EVM techniques in the project control duration does not work with complete accuracy, new formulas are developed using the ES techniques and CCM/BM concepts at this stage.

• BPD₀: 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):

$\begin{aligned} &B P D=B P D_{0}+S B \\ &\text { where } \\ &S B=\text { Schedule Buffer } \end{aligned}$               (17)

• B_T: Schedule buffer percent of BPD₀, which is calculated using Equation (18):

$B_{T}=\frac{S B}{B P D_{0}}$                (18)

• P_T: The percentage of the schedule buffer is calculated with the help of Equation (19):

$\begin{aligned} &E S_{T}=T+\frac{E V-P V_{T}}{P V_{T+1}-P V_{T}} \\ &S V_{T}=E S_{T}-A T \\ &P_{T}=\frac{S V_{T}}{S B} \end{aligned}$                (19)

• W_T: The percentage of work done based on time, which is calculated using Equation (20):

$W_{T}=\frac{E S_{T}}{B P D_{0}}$            (20)

• SPI_T: With the help of the parameters of BPD₀, 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):

$\begin{aligned} &S V_{T}=E S_{T}-A T \\ &S P I_{T}=\frac{E S_{T}}{A T}=\frac{E S_{T}}{E S_{T}-S V_{T}}=\frac{W_{T}^{*} B P D_{0}}{W_{T}^{* B P D_{0}-P_{T}^{*} S B}} \end{aligned}$               (21)

• EDAC₀: 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 BPD₀is estimated, which is the same as EDAC₀. Equation (22) calculates this value:

$E D A C_{0}=B P D_{0}+B P D_{0} * P_{T}=B P D_{0}\left(1+P_{T}\right)$                  (22)

• 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):

$\begin{aligned} &S B_{A}=C S B+R S B_{A} \\ &S B_{A}=S B^{*} P_{T}+\frac{S B^{*}\left(1-P_{T}\right)}{S P I_{T}} \\ &S B_{A}=S B^{*} P_{T}+\frac{S B^{*}\left(1-P_{T}\right)}{\frac{W_{T}^{*} B P D_{0}}{W_{T}^{*} B P D_{0}-P_{T}^{*} S B}} \\ &S B_{A}=S B^{*} P_{T}+S B^{*}\left(1-P_{T}\right) *\left(1-\frac{P_{T}^{*} S B}{W_{T}^{*} B P D_{0}}\right) \\ &S B_{A}=B_{T} * B P D_{0} * P_{T}+B_{T} * B P D_{0} *\left(1-P_{T}\right) *\left(1-\frac{P_{T}^{*} B_{T}}{W_{T}}\right) \\ &where \\ &C S B= Consumed \, Schedule Buffer \\ &R S B_{A}= Re mained \, Schedule \, Buffer \, of \, Adjusted \end{aligned}$               (23)

• EDAC: Estimated duration at completion, with regard to schedule buffers (the combination of performance and risk parameters), which is calculated using Equation (24).

$\begin{aligned} &E D A C=E D A C_{0}+S B_{A} \\ &E A C=B P D_{0}\left(1+P_{T}\right)+S B^{*} P_{T}+S B *\left(1-P_{T}\right) *\left(1-\frac{P_{T} * S B}{W_{T}^{*} B P D_{0}}\right) \\ &E A C=B P D_{0}\left(1+P_{T}\right)+B_{T} * B P D_{0} * P_{T}+B_{T} * B P D_{0} *\left(1-P_{T}\right) *\left(1-\frac{P_{T} * B_{T}}{W_{T}}\right) \end{aligned}$              (24)