J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

Network analysis - summary


Network analysis is nowadays very widely used so it might be profitable to consider the benefits that using network analysis can bring to a project.

Forming the list of activities, precedence relationships and activity completion times structures thought about the project and clearly indicates the separate activities that we are going to have to undertake, their relationship to one another and how long each activity will take. Hence network analysis is useful at the planning stage of the project.

Once the project has started then the basic idea is that we focus management attention on the critical activities (since if these are delayed the entire project is likely to be delayed).

In addition, for the non-critical activities, we have a natural ranking in terms of their slack (float) time, or in terms of their slack fraction = (slack time)/(completion time). Plainly activities with a smaller slack time or slack fraction require more attention than those with a larger slack time/fraction.

It is relatively easy to update the network, at regular intervals, with details of any activities that have been finished, revised activity completion times, new activities added to the network, changes in precedence relationships, etc and recalculate the overall project completion time. This gives us an important management tool for managing (controlling) the project.

Plainly it is also possible to ask (and answer) "what if" questions relatively easily e.g. what if a particular activity takes twice as long as expected - how will this affect the overall project completion time?

The ability to tackle resource constraints and resource smoothing is also a great help in making efficient use of the resources available to the project manager.

It is also possible to identify activities that, at the start of the project, were non-critical but which, as the project progresses, approach the status of being critical. This enables the project manager to "head off" any crisis that might be caused by suddenly finding that a previously neglected activity has gone critical.

State of the art

Computer packages, such as Microsoft Project are widely available for network analysis. Typically such packages will:

Problems involving thousands of activities can be easily handled on a pc but be aware that the computational burden can grow considerably if you have resource smoothing/resource constrained problems to solve.

The primary characteristics for distinguishing between packages (apart from cost) are ease of use, graphical facilities, and the ability to tackle resource problems effectively. In particular note that whilst all packages will give an identical minimum project completion time not all packages will be equally effective in dealing with resource problems, i.e. the solutions to such problems produced by different packages will be different.