# Critical Path Analysis. Why Is CPA Important? CPA is arguably the piece of maths used most often, outside of basic arithmetic. Important not only in commerce.

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Critical Path Analysis

Why Is CPA Important? CPA is arguably the piece of maths used most often, outside of basic arithmetic. Important not only in commerce and industry, but also in our own lives. Can be used to ensure the efficient running of any Project!

Project A Project can be defined as any activity with: A defined purpose A clear start and finish

Other Considerations Other types of dependencies –Planned delays – e.g. plaster drying –Start – Start dependencies Delays on Critical Path, e.g. –Goods not delivered –Weather delays

Activities of a particular project are usually set out in a precedent / dependent table. This table shows the activities which cannot start until a previous activity has been completed. An example is as follows: ACTIVITYDEPENDS ON A- B- CA, B DB EB FC GC, D HE

The common method to establish the general shape of an Activity Network, is to use an Activity on Arc method. Terminology; Arc; denoted by a straight line which shows the activity. Node; denoted by a circle to signify the end of an activity. Each node in numbered from 0 to n. Node 0 is called the source node. The final node is called the sink node. Dummy; A dummy arc is required if a particular activity requires two or more activities to finish prior to the new activity starting

Using our example dependent table. 0 1 2 3 4 5 6 A B C D E F G H

An Alternative Approach......

WORKED EXAMPLE ABC Manufacturing Ltd construct luxury sofas by hand on an order by order basis. The sofa consists of various tasks which must be completed in order. The activities are as follows: A; Build a Wooden Frame B; Cut out material for cushions C; Stitch and fill cushions D; Attach springs to wooden frame E; Cover Frame F; Complete Assembly G; Inspect H; Wrap

The information is supplied in a Dependency table ActivityDependent onTime of Activity (hrs) A-6 B-2 CB3 DA4 ED2 FC, D4 GF2 HG1

Your task is to create an activity network from the information given, (hint – you will require 1 dummy arcs).

0 1 2 3 A B C E 0 D 4 7 F 5 6 G H

Carrying out the algorithm

Step One: Draw an Activity-On-Arc Network

Step Two: The forward Pass In the Left hand box, we write the EARLIEST TIME that you can move onto the next task 6

6 2 10 This is 10 and not 5 because we have to have done D as well as C before we can move onto F. We have to pick the latest. 14 16 17

Step Three: The backward Pass In the Right Hand box we write the latest the next activity needs to start in order to finish on time. We go backwards. The first one is always the same as the forward pass. 17 16

6 0 2 10 17 14 16 17 161410 6 7 0 The box after D says 10 and not 15 because we have to get F,G and H done. Activity E doesnt have to start until 12, but we must write down the lower number. The box after B says 7 because in order to be done by 10, C doesnt have to start until 7.

6 0 2 10 17 14 16 17 161410 6 7 0 If the latest an activity must have finished by take away the earliest it can start is the length of the activity, then the activity is CRITICAL. The CRITICAL PATH is the list of activities that are CRITICAL. If an activity isnt critical, it has FLOAT. E is not critical because 17- 10 > 2. E has a float of 5. E can start any time between 10 and 15.

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