Quantcast Determination of Critical Path

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(1) Arrows generally should point to the right so that the job begins
at the left and ends at the right.
(2) Each arrow (step) is joined by circles that are usually lettered
to identify an event, such as the completion of a step or steps, or the
beginning of a step or steps.
(3) Arrows (steps) are numbered to agree with the step number shown
in the step list.  A brief description of the work involved may also be placed
on the arrow.
(4) Arrows are joined in their logical sequence of work and the work
represented by one arrow must be completed before the work represented by the
next arrow can start; for example, in Figure A-4, arrow number 4 cannot start
until arrow number 2 has been completed.
(5) Arrows with solid stems represent work that is to be
accomplished, or measurable delay periods such as the time required for
procurement of material.  Arrows with dotted stems show the interrelationship
of planned events and, as such, are not steps.  For example, in Figure A-4 the
dotted line arrow between events F and G means that step 11 should not start
until step 9 has been completed.
(6) The numbers of the steps and the letters for the circles will not
necessarily be in sequence from left to right on the complete arrow diagram.
However, the arrows (steps) are placed in their logical sequence of work and
arranged so that the-interrelationships can be seen.  In Figure A-4 steps 2,
4, 8, 9, 10 and 14 are one chain of steps, and steps 2, 5, 7, 12, and 14 are
another chain of steps.  Step 4 can be started as soon as step 2 has been
completed, but step 8 cannot be started until steps 3 and 4 both have been
completed.  Step 11 could be started as soon as step 1 has been completed, but
the job is such that step 11 cannot be started until step 9 has been
completed.  This latter situation is shown on the diagram by a dotted arrow of
zero time value from the circle indicating the completion of step 9, event F,
to the circle representing the start of step 11, event G.
2.  DETERMINATION OF CRITICAL PATH.  When the Master Scheduler is satisfied
that the interrelationship of the job steps on the arrow diagram are truly
represented, the duration time of each step is entered on the diagram.  The
"critical path" will be the chain of arrows (steps that result in the longest
duration time for the job, because the total job cannot possibly be completed
any earlier than the chain of steps with the longest duration time. The
critical path is shown by a double line of arrows.  Only by decreasing the
duration time of one or more of those arrows (steps) on the critical path can
the total job duration time be decreased.  Indicating the duration times on
the steps of the Arrow Diagram and determining the critical path completes its
transition to a Critical Path Diagram.  See Figure A-5 for the initial
critical path for the job described in Figure A-2.  Depending upon the time
required for material procurement, there may be two critical paths, one for
the total job including material procurement, and one for shop forces (or shop
schedule) that covers only the shop labor required.  In Figure A-5 the
critical path for the total job includes steps 2, 4, 8, 9, 10, and 14 while
the shop schedule includes steps 4, 8, 9, 10, and 14.  Note that if step 1
took 360 hours to accomplish, then the critical path for the total job would
be steps 1, 11, and 14.


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