PERT/CPM Problems

 

1.  For the following data, draw the network diagram, and then crash the activities to find the time-cost trade-off points that the company should want to consider.  Start with the plan that has the longest duration.

 

Activity

Preceding       Activity

            Time(weeks)

  Normal                Crash

 Program             Program

           Cost ($000s)

 Normal               Crash

Program             Program

A

-

      2                         2

      5                         5

B

A

      5                         3

    11                       21

C

A

      2                         1

      7                       16

D

B, C

      4                         2

      8                       22

E

B

      3                         2

      9                       18

F

D, E

      3                         3

      9                         9

 

 

2.  Draw the network diagram for the following problem and indicate a sequence of plans that the company should want to consider in making a time-cost tradeoff.  The company is not interested in reducing the project duration below 29 days.  Start with the plan that has the longest duration. 

 

Activity

Preceding       Activity

             Time(days)

  Regular                Crash

 Program             Program

             Cost ($)

 Regular               Crash

Program             Program

A

-

     10                        9

  5,000                  5,200

B

-

     14                      11

  3,500                  3,950

C

A

       8                        7

  4,000                  4,100

D

A

       7                        2

  2,100                  3,600

E

B

       5                        3

  2,500                  3,000

F

B

     10                        7

  2,250                  3,750

G

C

       9                        9

  5,000                  5,000

H

D, E

     11                        9

  3,850                  5,250

I

G, H

       5                        3

  2,375                  3,575

 

 

3.  For the following data, draw the network diagram, and then crash the activities to find the time-cost trade-off points that the company should want to consider.  Start with the plan that has the longest duration.

 

Activity

Preceding       Activity

            Time(weeks)

  Normal                Crash

 Program             Program

           Cost ($)

 Normal               Crash

Program             Program

A

-

      2                         1

 20,000                20,700       

B

-

      3                         1

 29,000                33,000   

C

A

      2                         1

 25,000                26,100      

D

B

      4                         3

 47,000                47,750     

E

C

      4                         2

 55,000                57,000      

F

C

      3                         2

 29,000                29,500        

G

D, E

      5                         3

 79,000                80,800

H

F, G

      2                         1

 15,000                17,900

 

 

Answers:

1.  The plan with the longest duration takes 14 weeks at a cost of $49,000.  The one with the shortest duration takes 10 weeks at a cost of $82,000

 

2.  Beginning plan takes 35 days at a cost of $30,575.  Completing the project in 29 days increases the project cost to $32,975

 

3.  The plan with the longest duration takes 15 weeks and has a cost of $299,000.  The one with the shortest duration takes 8 weeks and has a cost of $312,250