1. The Critical Path Method
The Critical Path Method (CPM) can be used to analyse port operation (including all activities and their relationships) in terms of:
Calculate the start/finish times of each activity
Identifying the critical path within a port
Calculate the slacks of each activity
For a crystal lecture on CPM, see:

2. The Critical Path Method
The earliest start (ES), latest start (LS), earliest finish (EF), and latest finish (LF) of an activity are calculated as follows:
ESi = max(ESi-1 + ti-1) = max(EFi-1)
EFi = ESi + ti
LFi = min(LFi+1 - ti+1)
LSi = LFi - ti
t is the duration and i denotes the activity.
Note:
The “max” and “min” functions are only effective when there is more than one connection to the activity.
The calculation of LFi should start from the last activity backward.
Note: ES and EF MUST always be calculated first. This is call FORWARD PASS calculation.
Only after FORWARD PASS calculation has been completed, LF and then LS for each event will be calculated. This is call BACKWARD PASS calculation

3. The Critical Path Method
There two types of slacks:
Total slack (TS) for an activity is the amount of time it can be delayed without delaying the total operation:
TSi = LSi - ESi = LFi - EFi.
Free slack (FS) for an activity is the amount of time it can be delayed without delaying the early start (ES) of the subsequent activity:
FSi = min(ESi+1 – EFi)
TS is of interest to high-level management as it provides an indication of the total additional time available.
FS is of interest to lower-level management as it allows rescheduling of individual activities.

4. The Critical Path Method
A critical path is defined as the sequence of connected activities from the start to finish without any total or free slack.
The critical path can also be identified by solving the following linear program:
Min: T = (EST - ES0)
Subject to: ESi  ESi-1 + ti-1
The constraint simply means that we cannot start an activity without finishing its predecessor.
Check the linear programming problem.

5. The Critical Path Method
The following table provides an example of port activities with their durations and relationships.
Table 3: Example of port activity durations
Source: Frankel (1987)
NOTE: There are a typo in the table. The immediate predecessor activity for G should be C, not D.

6. The Critical Path Method
Calculated Earliest/Latest Start/Finish and Slacks
Source: Author

7. The Critical Path Method
Figure 18 shows the calculated ES, LS, EF and LF in blocks (e.g. for activity A, ES=0, LS=5, EF=2 and LF=7) with the total slack (TS) and free slack (FS).
The obtained critical
path is:
“Start-B-F-J-Finish”
Figure 18: The CPM Solution
Source: Frankel (1987)

8. Performance Evaluation and Review Technique
The critical path method (CPM) mentioned above is based on fixed activity times.
When activity times are stochastic (random), and their probability distribution functions (PDF) of activity times are known, the corresponding expected activity time and its lower limit (optimistic) and upper limit (pessimistic) can be calculated.
These values can be incorporated into the calculation of early/latest start/finish times similar to CPM. This is known as the performance evaluation and review technique (PERT).

9. References
Australian Logistics Council 2010, Future Supply Chains 2020.
Frankel, E. G. (1987) Port planning and development, Wiley, New York.
Ghiani, G., Laporte, G. and Musmanno, R. 2004, Introduction to Logistics Systems Planning and Control, John Wiley & Sons.
Notteboom, T. & Rodrigue, J.-P. 2008, 'Containerisation, Box Logistics and Global Supply Chains: The Integration of Ports and Liner Shipping Networks', Maritime Economics and Logistics, vol. 10, no. 1-2, pp
Van Der Horst, M. R. & De Langen, P. W. 2008, 'Coordination in Hinterland Transport Chains: A Major Challenge for the Seaport Community', Maritime Econ Logistics, vol. 10, no. 1-2, pp
Veenstra, A., Zuidwijk, R. & van Asperen, E. 2012, 'The extended gate concept for container terminals: Expanding the notion of dry ports', Maritime Econ Logistics, vol. 14, no. 1, pp