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Construction Management – Decision Support / Network Techniques MPMCalculationExample-ForProjector.pdf

BUTE Department of Construction Technology & Management / Engineering Programs In English / 2000- Dr. Zoltán András Vattai

Do perform the time-analysis of the MPM network below

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1.0 Substituting (exchanging) CR1 relation-pair by the dominant

relation: SS1

( )SS1

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1.1 Identifying the starting point („Source”) and assigning „0”

time-potential to it

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1.2 „If I knew the start time-potential of an activity of fixed

duration, then I do know the finish of it too …”

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1.3 Progressing on like „rolling-up” in „by-arrow” direction

SS1( )

FS0

For progressing we have to chose an activity pointed at by arrows only originated

from activities at which the early time-potentials have already been calculated.

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SS1( )

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SS1( )

For progressing we have to chose an activity pointed at by arrows only

originated from activities at which the early time-potentials have already been

calculated. The minimum („earliest”) time-potential to be assigned must fit all

„preceeding” relative boundaries (time-potential limitations).

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1.6 „If I knew the finish time-potential of an activity of fixed

duration, then I do know the start of it too …”

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1.7 Progressing – temporarily – not considering any related

maximum-typed relations involved in any loop (cycle)

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1.13 Checking validity of maximum-typed relation involved in

the loop and had been – temporarily – not considered.

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1.15 Checking validity of all the limitations (relations, „arrows”)

involved in the loop (cycle)

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2.1 „Let the latest finish time-potential of the finishing (closing)

activity be equal to its early finish time-potential”

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2.3 Progressing – temporarily – not considering any related

maximum-typed relations involved in any loop (cycle)

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1711

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2.5 Progressing on like „rolling-up” in „counter-arrow” direction

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2.7 Checking validity of maximum-typed relation involved in

the loop and had been – temporarily – not considered.

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For progressing we have to chose an activity pointing its arrows at activities

only at which the late time-potentials have already been calculated.

The maximum („latest”) time-potential to be assigned must fit all „succeeding”

relative boundaries (time-potential limitations).

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3.1 Calculating total floats and identifying the critical activities

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By definition: all activities having no any float are considered as critical ones

( Total float equals to zero )

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3.2 Identifying critical relations (limitations, „arrows”)

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By definition: relations (limitations) between critical activities, having been

satisfied on limit value (by equivalence) are considered as critical ones

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3.3 Identifying (dominance-) types of critical activities

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+ -

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Type of dominance of critical activities (likely effect of modifying their duration

by one unit) is determined by the entering and leaving points (start or finish) of

related critical relations („arrows”) along „The Critical Path”.

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3.4 Restoring original relation: CR1

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+ -

+ + 0(F)

THE END

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Analogy (The Dual Problem): The Longest Path in a Weighted DiGraph

AS AF

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|LP(DS,CF)| = 5+0+4-2-2+3+7+2 = 17 |L(CF,FS,FF,BS,BF)| = -10+5-5+7+2 = -1 ≤ 0

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