BUS606: Operations and Supply Chain Management

Mobarakeh Steel Co. is a leading Iranian company that produces steel sheets. This company is committed to playing a central role in the industrial, economic, and social development of the country, to improving its technologies in the steel industry, and to acting as an international organization that produces about 50% of the country's steel for use in industries, such as automobiles, energy, heavy steel, fluid transfer tubes, packaging, electricity, profile, and tube. This company comprises seven industrial complexes distributed across the country and has more than 20,000 employees in its different departments. One of the projects related to this plant is the development of a custom product, which is used as a case study for applying the proposed approach of integrated risk–efficiency methodology. The Primavera Risk Analysis software version 8.7 (Oracle Corporation, Redwood City, CA, USA) is used for the application. The project is composed of three parts, with each part built separately and then assembled. The project activities, activity duration, and costs required are extracted, as shown in Table 3. Cut and paste, error root square, and Monte Carlo simulation are used to calculate the schedule and cost buffer of the projects. The duration and costs are estimated as a probability (triangular probability distribution).

Table 3. Activity list, duration, and budget cost of project.

After scheduling the project, the baseline planned duration (BPD₀) is estimated to be equal to 48 days, and the budget cost at completion regardless of the buffer cost (BAC₀) is calculated using Equation (25):

$\begin{aligned} &B C A C_{0}=\sum\nolimits_{i=1}^{N} B P V_{i}=\$ 143000 \\ &\text { where } \\ &N=\text { quantity of activity } \end{aligned}$            (25)

The results of the deterministic scheduling are illustrated in Figure 5.

Figure 5. Deterministic scheduling.

Based on the equations in Section 2, the schedule and cost buffer are calculated by cut and paste, error root square, and Monte Carlo simulation as Equations (26) and (27). Based on the calculations, the results of the error root square are obtained:

$\begin{aligned} &For \, Schedule \, Buffer \\ & B_{C-P} =.5 \times \sum\nolimits_{i=1}^{N}\left(T_{p}-T_{m}\right)=14 \text { days } \\ & B_{r s e} =\sqrt{\sum\nolimits_{i=1}^{N}\left(T_{p}-T_{m}\right)^{2}}=12.6 \text { days } \\ & B_{m c s} =B P D_{\% 90}-B P D_{d}=12 \text { days } \end{aligned}$         (26)

$\begin{aligned} & For \, Cost \, Buffer \\  &B_{C-P}=.5 \times \sum\nolimits_{i=1}^{N}\left(C_{p}-C_{m}\right)=\$ 90060 \\ &B_{r s e}=\sqrt{\sum\nolimits_{i=1}^{N}\left(C_{p}-C_{m}\right)^{2}}=\$ 37766 \\ &B_{m c s}=B C A C_{\%} 90-B C A C_{d}=\$ 37750 \\ &\text { where } \\ &N=\text { equal quantity of activity } \\ &C_{p}=\text { pessimestic cost of activity } \\ &C_{m}=\text { most likely cost of activity } \\ &B C A C_{d}=\text { deterministic Budget Cost At Completion of project } \\ &B C A C_{\%} 90=\text { Budget Cost At Completion of project with a probability of 90%} \end{aligned}$         (27)

The project in two control periods of 15 and 30 days is updated and monitored. In the mentioned periods all activities, except no. 130 (related to the test activity of part 3), are conducted based on a scheduling plan. Using the proposed methodology of integrated risk–efficiency methodology, the duration progress, cost progress, usage percentage of the schedule, and cost buffer are calculated using Equations (28) and (29):

The duration and cost at completion of the project in the two control periods of 15 and 30 days are also estimated using the proposed methodology.

• BCAC: Budget cost at completion with regard to the cost buffer (combination of performance and risk parameters), which is calculated using Equation (30):

$B C A C=B C A C_{0}+C B=143000+37766=\$ 180766$              (30)

• B_C: Cost buffer percentage of BCAC₀, which is calculated using Equation (31):

$B_{C}=\frac{C B}{B C A C_{0}}=\frac{37766}{143000}=26.4 \%$              (31)

• ECAC₀: 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 BCAC₀is estimated, which is the same as ECAC₀. Equation (32) calculates this value:

$E C A C_{0}=B C A C_{0}+B C A C_{0} * P_{C}=B C A C_{0}\left(1+P_{C}\right)=\text{\$16588 for period 1 and \$198770 for period 2}$            (32)

• ECAC: Estimated cost at completion with regard to cost buffers (combination of performance and risk parameters), which is calculated using Equation (33);

$E C A C=B C A C_{0}\left(1+P_{C}\right)+B_{C} * B C A C_{0} * P_{C}+B_{C} * B C A C_{0} *\left(1-P_{C}\right) *\left(1-\frac{P_{C} * B_{C}}{W_{C}}\right)==\text{\$200841 for period 1 and \$232983 for period 2}$              (33)

• BPD: Total baseline planned duration, with regard to the schedule buffer (combination of performance and risk parameters), which is calculated using Equation (34):

$B P D=B P D_{0}+S B=48+12.6=60.6 \text { days }$              (34)

• B_T: Schedule buffer percentage of BPD₀which is calculated using Equation (35):

$\mathrm{B}_{\mathrm{T}}=\frac{\mathrm{SB}}{\mathrm{BPD}_{0}}=26.2 \%$            (35)

• EDAC₀: 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 BPD₀is estimated, which is the same as EDAC₀. Equation (36) calculates this value:

$\begin{align}E D A C_{0}=B P D_{0}+B P D_{0} * P_{T}=B P D_{0}\left(1+P_{T}\right)=48 \text { days for period } 1 \text { and } 82 \text { days for period } 2 \end{align}$            (36)

• EDAC: Estimated duration at completion with regard to schedule buffers (the combination of performance and risk parameters), which is calculated using Equation (37):

\begin{align} E D 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)= 61 \text { days for period } 1 \text { and } 93 \text { days for period } 2 \end{align}         (37)