CPA in Precedence networks

Brooke Bicycles has recently moved to new office and manufacturing facilities. A display of historic bicycles is to be assembled in the reception area. The activities to be done have been identified.

First, the display has to be designed following which the selected vintage bikes will be serviced and the building materials bought. The frame of the display can then be assembled.

The backdrop will contain photos of the bikes being serviced. Once the bikes have been serviced and photos taken, the large graphic panels can be produced which are then installed on the completed frame.

The bikes themselves can also be installed when the frame is complete. Once the graphics and bikes have been installed the display is complete.

The activity list is:vintage bicycles

  • Design Display
  • Service Bikes (includes photography)
  • Buy Materials
  • Produce Graphics
  • Build Frame
  • Install Bikes
  • Install Graphics
  • Display Complete


Activity 1

Take a sheet of paper and draw a precedence network from the above information.


  • You might find it easier to write the activity names on small post it notes and arrange these on an A3 sheet before drawing in the links.

  • The network will contain links that cross. Don’t worry too much about producing a sparkling example of draftsmanship, as long as your result is readable.


Click on the graphic to download the sample network. Don’t compare your network to the sample and assume yours is wrong if they aren’t the same.

The chances that our networks look the same are slim. Apart from the fact that we may have arranged the activity boxes differently, we may also have interpreted the text of the case study differently.

Any verbal or text description of how the activities can be performed is likely to be ambiguous and two planners are likely to see different ways of performing the work.

Once the network diagram is drawn, there is no doubt about the sequence of working. A picture speaks a thousand words.

This simple example only uses finish-to-start dependency links but you can use others to model more complex relationships using start-to-start and finish to finish links (see precedence diagram)


Activity 2

Use the example solution from activity 1 to have a go at critical path analysis (including the forward pass, backward pass and float calculations). Mark the critical path on your diagram.

The activity durations (in days) are:

Design Display 


Build Frame


Service Bikes


Install Bikes


Buy Materials


Install Graphics


Produce Graphics  


Display Complete




  • The forward pass calculates earliest start and finish dates which are in the corners of the top row. The backward pass calculates latest start and finish dates which are written in the corners of the bottom row.

  • On the forward pass watch out for activities where two links converge, e.g. Install bikes. Use the higher of the two preceding earliest finish dates.

  • On the backward pass watch out for activities where two links converge e.g. Build frame. Use the lower of the two succeeding latest start dates.


Click on the graphic to download the answer. This time, your calculations should be the same as those in the answer.

A final thing to note on the completed network is the float on 'Produce graphics'. The total float is calculated as 3 days.

However, while 'Produce graphics' could finish as early as 7, it's succeeding activity 'Install graphics' cannot start any earlier than 9.


This means that 'Produce graphics has 2 days of 'free float', i.e. it could be delayed by 2 days without having any impact on any succeeding activities.


What next?

Worked example for Gantt Charts

This will enable you to see how the numbers in this CPA calculation are converted to dates to represent a real world schedule.


Further reading

Schedule calculations

A pdf article that provides more detail on a wider range of network calculations.

No logic required

An article warning of the dangers of schedules not based on logic.

What makes a good project schedule

An overview of the factors that make a schedule 'usable'

Float - is it real?

The concept of ‘float’ is less than 60 years old. The key question posed by this post is if schedule float did not exist before 1957, how real is it today?







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