| 1) LOB calculationsThis step consists of (at least) four (sub)steps. First is to draw a unit network (of repetitive activities for single work unit); second is to estimate the crew size for each activity; third is to establish a target rate of output (this (sub)step can be further divided into smaller steps); fourth is to derive the LOB diagram. |
1) Initial equationsThe execution of PSM starts with describing all activities in the Macaulay bracket notation (e.g., singularity functions). However, no links are considered for the initial equations (one equation for each activity). |
1) Activity listBased on available technical documentation, devise the list of linear activities of the projects, along with their parameters of work quantity and work group productivity (average). Work quantity is spread through work units using linear interpolation to make every activity continuous. Their sequence must be established unambiguously. |
| 2) Calculating activity durationOverlapping activities are generalized to represent repetitive activities. For this generalization to be possible, the duration is assumed constant in all units of a repetitive activity. |
2) Buffer equationsIn the second step, the singularity functions for buffers are set up (one equation for each buffer). |
2) Calculating activity durations and slopesCalculate durations and unit production rates (e.g., slopes) for every linear continuous activity. |
| 3) Specifying logical relationships using overlapping activities (buffer time)To specify relationships, the actual progress rate of each activity is compared with that of its successors. Three scenarios can be encountered: diverging, converging, and parallel activities. Based on the scenario, the buffer time is placed on the first or the last unit. |
3) Initial stackingIn the third step, the initial activity and buffer equations are stacked up in the order of precedence with the set of singularity functions (one equation for each activity). |
3) Using the newly developed algorithm for determination of buffers between activitiesPair of activities can converge, can diverge, or be parallel depending on the relation of production rates of two adjacent activities. Depending on this relation, the equation for every buffer y is determined, and calculation of the buffer is performed. |
| 4) Time scheduling1. Forward pass – the early timings (belong to the first and last units only) are determined for each activity. 2. Backward pass – the late timings (belong to the first and last units only) are determined for each activity. |
4) Minimum differencesIn the fourth step, the differences between neighboring predecessor buffer equations and successor equations are taken and the minima of these difference equations are determined across all positive values of x (one equation for each activity–buffer link). |
4) Using the newly developed algorithm for calculation of project durationBased on the determined buffer times, the project duration is calculated as the sum of the buffers and the duration of the last activity. |
| 5) Criticality analysis |
5) DifferentiationDifferences are differentiated using equations to confirm the nature of the vertices (set of equations) |
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6) Final consolidationIn the sixth step, the vertex distances between a neighboring predecessor buffer equation and successor equation are compared to identify the overall minimum distance (set of equations). |
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7) Criticality analysisThe equivalent of a critical path from CPM is calculated (set of equations). |
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