Critical Path Method

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The method of the critical path (also called activity arrow representation ; English critical path method , CPM ) represents the activity arrow network plans, a special network plan technique . It was founded in 1956/57 by the American chemical company DuPont in cooperation with the ADV specialist Remington Rand Corp. developed and implemented on a UNIVAC I in order to systematically plan and monitor large investment projects and maintenance work in chemical plants.

Basics

The critical path method uses the task arrow representation. With CPM plans, the processes are shown as arrows, the events as nodes and the relationships as arrows. The prerequisite for being able to work meaningfully with a network plan is that all processes in the project with the respective individual duration are correctly related to one another.

Creation

The following CPM rules must be observed:

  1. An activity cannot begin until all previous activities (predecessors) have been completed. The start event coincides with the end event of the previous process (exception first process).
  2. If several processes have to be finished before a following process (successor) can begin, they end in the initial event of the successor.
  3. If several successors can begin after a predecessor has ended, they begin in the predecessor's end event.
  4. If two or more processes have common start and end events, they must be clearly identified by inserting dummy processes. Apparent processes should be shown as a dashed arrow for the sake of clarity.
  5. If several processes begin and end in an event, which are not all dependent on one another, clarity must also be achieved by means of apparent processes.
  6. Any number of dummy activities can be inserted in a sequence of activities. They serve the logical connection and can increase the overview. Sham processes should be viewed as a necessary evil and therefore generally used sparingly.
  7. If a process can begin before the predecessor is completely finished, the predecessor must be subdivided. This rule does not necessarily increase the clarity of the network plan.
  8. Each process may only run once, there may be no loops.

Example of a CPM network plan

Critical thread method.jpg

Mathematical representation

If the required information about duration , dates and relationships (term see network plan technology ) is available, the critical path can be calculated independently of the graphic representation. The times for the individual processes and the resulting buffer times are calculated . Every event and every process has an earliest (possible) and a latest (permitted) situation in terms of time.

The calculation takes place in two steps:

  1. First of all, there is forward scheduling , in which, based on the planned earliest start time of the project , all processes are calculated one after the other into the future. This results in the earliest start and end times for all processes.
  2. The reverse procedure is used for backward scheduling; the time of the planned end of the project is now calculated towards the present. The latest start and end times of the individual processes result.

If there is a difference between the result of the forward and backward calculation for an operation, there is a buffer time . A task that has a slack time can be postponed by this slack time between the earliest start date and its latest finish date without adversely affecting the project duration. A path through the network plan from the start to the destination node in which no event has buffer times is called a critical path. A delay in one of the events on the critical path always results in a delay in the end date.

Advantages and disadvantages of network plan technology in general

Advantages:

  • Compulsion to think through the project flow exactly
  • clear presentation of the dependencies
  • Possibility of minimizing the project duration
  • greater security in meeting deadlines
  • clear highlighting of project bottlenecks
  • Timely recognition of possible delays and assessment of the consequences

Disadvantage:

  • Uncertainty in timing
  • Different (subjective) views on the project process
  • Buffer times are quickly used up by bloating the individual activities

Advantages and disadvantages of the process arrow network plans (CPM network plan technique)

Advantages:

  • Simple calculation rules and therefore simple programming

Disadvantage:

  • Modeling difficult because there are few possibilities to simply describe complicated dependencies between different processes. See in particular rules 4 to 7. Because of this disadvantage, process arrow networks are rarely used today in practice, but only process node network plans.

literature

  • Manfred Schulte-Zurhausen : Organization . 3. Edition. Verlag Franz Vahlen, Munich 2002, ISBN 3-8006-2825-2
  • Jürgen Zimmermann, Christoph Stark and Julia Rieck: Project planning - models, methods, management . Springer, Berlin 2006
  • Edmund Heinen: Industrial operations teaching - decisions in industrial operations . 9th edition, Gabler 1991 (p. 548 ff)