Question

A developer that specializes in compact urban amusement parks has formulated the following list of activities necessary to release a contract for the preparation of a new site. Times are given in weeks.

                                                                                                                               Estimated                                                                                 Immediate            Activity Time

Activity           Description                                                     Predecessors         (weeks)            

A                     Preliminary architectural design                               _                      14

B                     Community impact hearings                                      A                     2

C                     Line up potential financiers                                       A                     12

D                     Permit application                                                      A                       5  

E                      Negotiate com’ity impact details                             B                      6

F                      Final Design                                                                  B                      8

G                     Loan approval                                                             C, F                   3

H                     Permit hearings                                                          D                       2

I                       Permit granting                                                          H                       8

J                      Negotiate contract                                                      G, I                    6

K                     Release contract                                                         E, J                      3

Which activities are on the critical path

Answer 1

Based on the given data, we prepare a project network diagram as shown below:

The above network diagram in the form of formulas is shown below for better understanding and reference:

The above project diagram is prepared as per the legend shown in the top-left corner.

EST = Early start time

LST = Late start time

EFT = Early finish time

LFT = Late finish time

SLK = Slack = LST - EST or Slack = LFT - EFT

The EST of an activity = EFT of previous activity

EFT of an activity = EST + Duration

Similarly, LFT & LST are calculated during the backward pass.

There are multiple paths in the diagram:

A-B-E-K

A-B-F-G-J-K

A-C-G-J-K

A-D-H-I-J-K

Out of the above paths, path A-C-G-J-K and A-D-H-I-J-K are the longest paths and have 0 slack for all activities on the path. Hence, these paths are the critical paths.

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