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Critical Path Analysis.

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In projects made up of various activities where ‘time is of the essence’, the duration of each activity needs to be managed.  Certain activities run simultaneously and some must precede others.  If all activities are listed with their duration and preceding activities these can be networked visually.  Earliest and  latest times for each event (starting and finishing times for activities) can be established till the last activity. This saves time making the project as efficient as possible.   Certain activities when delayed will increase the time of the entire project.  These form a path known as the ‘critical path’ and show those ‘critical activities’ that have no spare time.  All these steps make up the Critical Path Analysis.

After analysis of the network a cascade chart can be formed with a corresponding resource histogram showing the number of workers throughout the project.  The floats can be re-arranged to produce a levelled histogram where the number of workers are levelled out throughout the project.

These are helpful in mall projects like cooking where they may only be two cooks to carry out the whole project ranging to large-scale projects like constructing a shopping centre.

I am required to cook a meal consisting of 21 activities.

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The critical activities are activities that cannot be delayed in order for the network to finish on time (at 79 minutes).  For example, a delay in ‘cook pasta shells’ will delay the ‘drain pasta’ as it must start at 14.5 minutes.  This will have a knock-on effect on the rest of the critical path. The last activity, ‘eat and clean away’ will be delayed at the same amount of time as the original activity ‘cook pasta shells’ was delayed.

Critical activities can be established when:

earliest finishing time (lj) - the latest starting time (ei) = the duration of the activity.

Independent and Interfering Activities

The five independent activities are ‘preheat oven’ ‘get pan’, ‘boil water in kettle’, ‘put layer of tomato sauce on dish’ and ‘prepare boiled sweet corn’.  These activities have spare time known as floats.  This means they can be delayed for however long their float is without delaying the entire project duration.  Floats occur when:

earliest finishing time (lj) - the latest starting time (ei) > the duration of the activity.

For example, ‘boil water in kettle’ starting from 0 minutes takes 2 minutes to finish.   Its latest finishing time is 5 minutes so can be delayed by upto 3 minutes.  If ‘boil water in kettle’ finishes after

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 When independent or interfering activities are delayed by their float duration they will not affect the rest of the project.  In independent activities the float of an activity only relates to that particular activity.  For example, when preparing boiled sweet corn with chillies it has 40.5 minutes to spare if it begins on time. This cannot be shared with its receding or succeeding activities, as they are critical.  Instead, we can use this extra time to finish putting water in a pan, cooking the pasta and draining the pasta.  After this we can then boil the sweet corn with chillies, as there has only been a delay of 10.5 minutes, still leaving enough float.

The three interfering floats precede each other.  They share a spare time of 7.5 minutes.  This float unlike the independent float can be shared at anyhow among the three.  So, for example, I could spend this float by 2 ½ minutes extra in placing the broccoli and herbs in the processor, 2 ½ minutes extra in seasoning with Tabasco and salt and 2 ½ minutes extra in processing to a cream.  As an alternative I could spend this 7 ½ minutes float on just one of these activities like processing to a cream.  When cooking I would then have to ensure I do not take extra duration in placing the broccoli and herbs in the processor and seasoning with Tabasco and salt.

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