Operations Management: Processes and Supply Chains, 12th Edition

Key Equations

Developing the Project Schedule

1. 1. Start and finish times:

   $$\begin{array}{lll}\hfill t& =\hfill & \text{estimated time duration of the activity}\hfill \\ \hfill \text{ES}& =\hfill & \text{latest of the EF times of all activities immediately preceding activity}\hfill \\ \hfill \text{EF}& =\hfill & \text{ES}+t\hfill \\ \hfill \text{LF}& =\hfill & \text{earliest of the LS times of all activities immediately following activity}\hfill \\ \hfill \text{LS}& =\hfill & \text{LF}-t\hfill \end{array}$$

2. 2. Activity slack:

   $$\text{S}=\text{LS}-\text{ES or S}=\text{LF}-\text{EF}$$

Analyzing Cost–Time Trade-offs

1. 3. Project costs:

   $$\begin{array}{ll}\text{Crash cost per period}\hfill & =\frac{\text{Crash cost}-\text{Normal cost}}{\text{Normal time}-\text{Crash time}}\hfill \\ =\frac{\text{CC}-\text{NC}}{\text{NT}-\text{CT}}\hfill \end{array}$$

Assessing and Analyzing Risks

1. 4. Activity time statistics:

   $$\begin{array}{lll}\hfill t_e& =\hfill & \text{mean of an activity's beta distribution}\hfill \\ \hfill t_e& =\hfill & \frac{a+4m+b}{6}\hfill \\ \hfill {\sigma }^2& =\hfill & \text{variance of the activity time}\hfill \\ \hfill {\sigma }^2& =\hfill & {\left(\frac{b-a}{6}\right)}^2\hfill \end{array}$$

2. 5. z-transformation formula:

   $$z=\frac{T-T_E}{{\sigma }_P}$$

   where

   $$\begin{array}{lll}\hfill T& =\hfill & \text{due date for the project}\hfill \\ \hfill T_E& =\hfill & \sum \left(\text{expected activity times on the critical path}\right)\hfill \\ =\hfill & \text{mean of normal distribution of critical path time ...}\hfill \end{array}$$