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8/13/2019 PERT sample question

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Review problems and solutions

1. For the Project network shown answer the following questions based on the dataprovided. You can use Excel to assist you in solving the proble! but you stillneed to show your work pretending you solve by hand.

"ctivity Expected tie#weeks$ %tandard deviation

" & .&' ( .)* + (.,- 1 .(E 1.,F / .(0 ) ./ 1 .12 & &3 ) 1.,4 .

#a$ 5hat is the critical path6#b$ 5hat is the probability of eeting a desired ( weeks copletion tie6#c$ %everal activities can be expedited for a cost. %pecifically! activity - expected

tie could be reduced by 1,7 for a cost of 8),,! or by (,7 for a cost of 8(,,,.2f the project is not copleted in ( weeks a penalty of 81,,!,,, will be paid.5hat is your recoendation regarding expediting activity -6 "ssue thestandard deviations don9t change.

%olution:o solve with Excel enter the data to the PE;:


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#c$ 5e apply the expected value criterion>#i$ Iot reducing the copletion tie of activity ->

E#*ost$A,P#?@($H1,,!,,,P#?J($A1,,!,,,#.K+/1$AK+/1,

#ii$ ;educing the expected copletion tie of activity - by 1,7. IewtieA.. Fro the teplate we have P#?@($A.((& soP#?J($A.KK/.E#*ost$A,P#?@($H1,,!,,,P#?J($H),,A1,,!,,,#.KK/$H),,AK+1/,

#iii$ ;educing the expected copletion tie of activity - by (,7. IewtieA.+. Fro Excel we have P#?@($A.(&1) so P#?J($A.K+).E#*ost$A,P#?@($H1,,!,,,P#?J($H(,,,A1,,!,,,#.K+)$H(,,,AK++),

*onclusion> "llocate 8),, to expedite activity - by 1,7.

(. :he following data pertains to a certain project>2ediate Ioral Ioral *rash *rash

"ctivity Predecessor. :ie#weeks$ *ost :ie#weeks$ *ost" LL 1, &, + K,' " + 1(, 1),

* ' 1, 1,, K 1,- " K /, ),E - 1, ), + K)F *! E & , 1 )

#a$ %how the project network#b$ "ssue the copany wants to coplete the project in (+ weeks. %hould any

activity be crashed6 Explain.#c$ 5hich activities should be crashed! by how uch! and at what total crashing

cost! if the objective is to iniiMe the total crashing costs! while eeting thedeadline of (+ weeks6

#d$ "ssuing there is a penalty of (, paid for each week the project is notcopleted beyond the deadline of (+ weeks. 5hat is the optial crash planthat iniiMes total costs6

%olution>#b$ 5e run Excel and realiMe that the project needs to be crash since the noral

project copletion tie is &1 weeks.#c$ Fro the Excel printout we have>

"ctivity ' is crashed by 1 week and activity F is crashed by ( weeks.#d$ 5e need to forulate this proble as a linear prograing odel! because the

PE;:=iniiMe *rash cost H penalties A(,Y"H1)Y'H(,Y*H1,Y-H1(.)YEH1K.)YFH(,#-elta$%.:.-elta A ?FH&


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?-?"H1,


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