Scheduling Projects - Critical Path Method

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One of the most critical aspects in Project Management is for the Project Managers to arrive at a Project Schedule.  This Project Schedule has to be based on highly accurate estimates and often requires a visual Network Diagram to depict the Schedules. Of the various tools and techniques available to Develop the Project Schedule, Critical Path Method remains the favourite across Project Managers.

The Critical Path Method was developed in the early 1950s by DuPont.  This simplistic design was initially used by various industries for scheduling their Plant and Machinery Maintenance Projects.  Over the years the Critical path Method has been adapted by Project Managers to arrive at their Project Schedules in almost all verticals. The popularity of the Critical Path Method stems from its design which allows Project Managers to

a.       Estimate the minimum Project Duration

b.      Identify critical activities in the Project; where any delay will cause a Delay for the Project.

c.       Calculate Early Start and Early Finish Dates for each activity

d.      Calculate the late Start and Late Finish Date for each activity without compromising on the overall Schedule

e.      Calculate the amount of scheduling flexibility on the logical network path of the Project Schedule

f.        Provide a graphical view of the Project.

Analysis of the Critical Path Method, thus allows the Project Manager to focus on critical path activities. Eg. If resources are to be added to a Project with a view to shorten the Schedule, it makes more sense to add the resources on the critical activities rather than the non-critical activities.

Elaborate descriptions of the various terms used in the Critical Path Method are as under

Critical Path        -              The Critical Path is that path in the Network Schedule Diagram, where the total duration of all the activities lying in the path is longer than that of any other path of the network.    

Critical Activity   -              All activities lying on the Critical Path are Critical Activities.

Float or Slack      -              Float on an activity is the amount of time it can slip without causing any delay in the overall Project Schedule. Hence, by definition, float for any activity on the critical path will be zero.

Early Time          -              This is the earliest time the activity can start.

Early Finish        -              This is the earliest time the activity can finish.

Late Start            -              This is the latest time the activity can start without affecting the Schedule

Late Finish          -              This is the latest time the activity can finish without affecting the Schedule

The steps for calculating the Critical Path are as under

1.       Put the activity diagram in place

a.       Organize a table of activities, their dependencies and their durations as depicted in the figure below.

b.      Translate the inputs from the table created into a Network Diagram. A network diagram derived from the above table is illustrated below.

c.       Calculate the durations for each path. 

Path1.   Start – A – D – E – F – Finish        =             10

Path2.   Start – A – B – C – Finish              =             18

Path3.   Start – A – B – J – Finish                =            13

Path4.   Start – G – H – I – J – Finish          =             11

2.       Locate the critical path

By definition of the critical Path, the Path with the highest sum total duration is the Critical Path. In the above illustration, Path2 viz Start – A – B – C – Finish becomes the Critical Path and all the activities A, B and C become critical activities.

3.       Estimate the Early Start and Finish days

For calculating Early Start (ES) and Finish (EF) days in the critical Path method, we go through a Forward Pass of the Schedule Network Diagram.  The Early Start and Finish Days for the above example are depicted below.

The ES for the first Activity in the Path is always 1.

The EF for any activity is calculated as EF = ES + duration of the activity -1.

The ES for all other activities (not the first activity) is calculated as ES = EF of predecessor activity +1

For activities which have more than 1 predecessor, the greatest EF among the predecessors is used for calculating ES. Refer Activity J in Fig 3.1. The ES for J = EF of B (10) + 1 = 11.

4.       Estimate the Late Start and Finish days

For calculating Late Start (LS) and Late Finish (LF) days in the Critical Path Method, we go through a backward Pass of the Schedule Network Diagram. The Late Start and Finish Days for the same example are depicted below.

                       

We start at the end of the path. All activities at the end will have LF =18, which is the duration of the Schedule (Refer Step 1, Critical Path Duration is 18). Hence activities F, C and J have LF = 18.

The LS for the activities = LF-duration+1.

The LF for all other activities (not the last activity) = LS of the successor activity -1.

For activities having more than 1 successor, the least LF among the successors is used to calculate LF. Refer activity B in fig 4.1.  The LF for B = LS of C -1 = 10.

5.       Calculate float on each activity.

Float is the flexibility you have in the Project schedule. All activities in the critical path have a float of 0. Hence, for activities A, B and C the float is 0.

We then proceed to the next longest path in the Network. In the illustrated example as calculate in Step1, the Path3 is the next longest path.

Float for activities is = Critical Path duration – Current path duration. In this case it is 18-13 = 5. Hence for activities on this path (except for A and B where Float is already calculated) i.e  J float is 5

We next proceed to the next longest path i.e Path 4. In this case Float = 18-11 = 7. Hence activities G, H and I have a float of 7.

We then proceed on the last path i.e Path 1. In this case Float = 18-10 = 8. Hence activities D,E and F have a Float of 8.

Float can also be calculated as LS – ES OR LF – EF.

Another of the advantages of the Critical Path Method is that algorithms can easily be devised to derive Critical Path using Computer Applications.  Hence deriving the Critical Path is no more an elaborate manual effort but most of the Project Management Information Systems like MS Project etc, provide Project Managers with a facility of calculating Critical Paths. 

As is evident from the above, the Critical Path Method for working out Project Schedules will give best results when estimated activity durations have minimal variations. In situations where the activity durations are highly uncertain, within complex Schedule Network Models, the Critical Path Method may come up with incorrect Schedules.

Yogeeta Deshmukh   BE, ITIL, PMP