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					                       Solution to CPM Practice

                                                         F
           1                                     4       5


                          E                                   5
               A          20
               5                                 C
                                                 7       D
                                                         10

                   2              B
                                  5
                                                     3


1. The total number of paths in this network is ___
       a. 1
       b. 2
       c. 3
       d. 4
       e. 5


2. The early start time for activity C is ____
       a. 0
       b. 5
       c. 10
       d. 15
       e. 20
   3. The early finish time for activity D is ____
          a. 5
          b. 10
          c. 15
          d. 20
          e. 25


   4. The late finish time for activity B is ____
          a. 5
          b. 10
          c. 15
          d. 20
          e. 25


   5. Slack time for activity D is ____
          a. 0
          b. 5
          c. 7
          d. 8
          e. 10


   6. The critical path of the network consists of activities
          a. A-B-C-F.
          b. A-B-D-F.
          c. A-B-E-F.
          d. A-E-F
          e. A-B-C-D-E-F.


   7. The length of the critical path is
          a. 20
          b. 22
          c. 25
          d. 30
          e. 52



Competitive Advantage from Operations          2                Professor Juran
   8. (New problem, not related to Problems 1-7) If the pessimistic duration of an activity
      is 10 and the optimistic duration is 4, what is the variance for the activity time when
      using CPM analysis?
          a. 1
          b. 2.333
          c. 4.777
          d. 10.4
          e. 12
                 Estimated Activity Variance       2
                                                                                    2
                                                        Pessimistic  Optimistic
                                                   
                                                                               
                                                                   6           
                                                                   2
                                                        10  4 
                                                   
                                                              
                                                         6 
                                                   1

Below are the data for a Time-Cost CPM Scheduling analysis. The time is in days and the
costs include both direct and indirect costs.
                            Immediate     Normal Crash Normal Crash
                 Activity Predecessor       Time Time     Cost      Cost
                    A          None           3    2      $200     $400
                    B            A            4    3      $300     $600
                    C            A            1    1      $300     $300
                    D         B and C         3    2      $500     $550
                    E            D            2    1      $500     $900




Competitive Advantage from Operations          3                                        Professor Juran
   9. If you crash this project to reduce the total time by four days, what is the total time
      of the project and total cost?
          a. Total time is 10 days, total cost is $2500
          b. Total time is 9 days, total cost is $2300
          c. Total time is 8 days, total cost is $2750
          d. Total time is 8 days, total cost is $1850
          e. Total time is 9 days, total cost is $2350
Normally we would have to use some sophisticated analysis to figure out a problem like
this, but in this special instance it is fairly obvious what would have to happen for the
project to be accelerated by four days. There are only four activities that can be “crashed”,
and each of them only has one day of potential time reduction.
                                        Activity       Cost
                                           A       $      400
                                           B       $      600
                                           C       $      300
                                           D       $      550
                                           E       $      900
                                        Total      $    2,750
Just for illustration, here’s how to set this up in HOM. First, we run the project with no
crashing, and figure out that the “uncrashed” duration is 12.




Competitive Advantage from Operations              4                            Professor Juran
Note: You need to go back and forth between your data sheet and the “parameters”
window. The minimum duration and cost/time data can’t be entered unless you “enable
cost crashing”. However, you don’t know the Desired Project Completion Time until
you’ve run the model once without any crashing.




The results of the “basic” CPM run:
        Critical Path Method Calculations Results.

        Activity                                      Early           Early        Late           Late
         Name                                         Start           Finish       Start         Finish        Slack
        ========                                     ========         ========    ========       ========     ========
        A                                                    0                3           0              3            0
        B                                                    3                7           3              7            0
        C                                                    3                4           6              7            3
        D                                                    7               10           7             10            0
        E                                                   10               12          10             12            0

        Expected Completion Time       :                      12

        Critical Path:
        A                                            B                D           E



Now, we enable crashing, set the desired completion time to 12 – 4 = 8, and run again:
 Activity                          Crashed       Cost of      Present      Early      Early       Late        Late
  Name                              by           Crashing     Duration     Start      Finish      Start      Finish        Slack
 ========                          ====          ====         =====       ======      ======     ======      =====        =====
 A                                           1         200            2          0           2          0             2            0
 B                                           1         300            3          2           5          2             5            0
 C                                           0            0           1          2           3          4             5            2
 D                                           1           50           2          5           7          5             7            0
 E                                           1         400            1          7           8          7             8            0

 Expected Completion Time     :              8
 Total Crashing Cost    :                  950

 Critical Path:
 A                                 B             D            E




Competitive Advantage from Operations                             5                                           Professor Juran
Below are the data for a Time-Cost CPM Scheduling model analysis. The time is in days
and the costs include both direct and indirect costs.
                            Immediate     Normal Crash Normal Crash
                  Activity Predecessor     Time       Time Cost    Cost
                    A          None          3          2  $200    $400
                    B           A            4          3  $300    $600
                    C           A            1          1  $200    $200
                    D        B and C         3          2  $500    $550
                     E          D            2          1  $500    $900

   10. What are the total time of this project and total normal cost?
           a. Total time is 13 days, total cost is $1200
           b. Total time is 12 days, total cost is $1700
           c. Total time is 11 days, total cost is $1600
           d. Total time is 10 days, total cost is $1750
           e. Total time is 9 days, total cost is $1700
                                        B
                                        4
              A                                 3          D       4        E          5
       1                    2                              3
              3                                                             20
                                        C
                                        1


A simple project listing of five activities and their respective time estimates are presented
below:
                       Activity Immediate Predecessor Time in Days
                          A                  None                  1
                           B                  A                    2
                           C                  A                    1
                          D                B and C                 3
                           E                  D                    2

   11. Using the Single Time Estimate CPM procedure, which activities make up the
       critical path?
           a. A, C, D, E
           b. A, B, D, E
           c. A, C, B, D, E
           d. A, D, E
           e. None of the above




Competitive Advantage from Operations          6                                 Professor Juran
   12. You ask your subordinates how long it will take to complete the job they are
       working on. The subordinates say, “If everything goes right it will take 6 hours,
       most likely it will take 8 hours, and if everything goes wrong it will take until the
       end of tomorrow or another 16 hours.” Since this job is a part of a larger project
       you must estimate the expected time it will take to complete the job. Using the
       three activity time estimation procedure for CPM, what is the expected time for this
       job?
          a. 8 hours
          b. 9 hours
          c. 10 hours
          d. 11 hours
          e. 12 hours


   13. You are working on a project that has 12 activities and want to perform a CPM
       analysis on the project. You determine the critical path consists of only five
       activities. You then compute the variances for the five critical path activities and
       these variances are 3, 4, 2, 1, and 6 days. If the desired completion date for the
       project is 50 days and the expected completion date for the project is 40 days, what
       is the probability that the project will be completed by the desired completion date?
          a. 0.99379
          b. 0.99180
          c. 0.99772
          d. 0.91924
          e. 0.67364




Competitive Advantage from Operations        7                                Professor Juran