Table J.17
A company must take on seven new projects. Each project has a planning stage and a design stage, and the planning stage must be completed before the design stage can begin. Also, two project teams are available to work on these projects: Team 1 works only on planning stages of projects, and Team 2 works only on design stages of projects. The times to complete the project stage, in days, are shown in the following table.

-Using the information in Table J.17 and Johnson's rule, how much idle time does Team 2 have from the start of the first project through completion of the seventh?
A) 2 days
B) 3 days
C) 4 days
D) 5 days

Question

Table J.17
A company must take on seven new projects. Each project has a planning stage and a design stage, and the planning stage must be completed before the design stage can begin. Also, two project teams are available to work on these projects: Team 1 works only on planning stages of projects, and Team 2 works only on design stages of projects. The times to complete the project stage, in days, are shown in the following table.
 
-Using the information in Table J.17 and Johnson's rule, how much idle time does Team 2 have from the start of the first project through completion of the seventh?
A) 2 days 
B) 3 days 
C) 4 days 
D) 5 days

Quizplus · Accepted Answer

To use Johnson's rule, we first need to determine the order in which the projects should be scheduled. The rule states that we should select the project with the shortest time for its second stage and schedule it first, followed by the project with the next shortest time for its second stage. We alternate between selecting the shortest time for the first stage and the second stage until all projects have been scheduled.

Using this rule, the order in which the projects should be scheduled is:

1. Project 4 (design stage time = 12 days)
2. Project 6 (design stage time = 13 days)
3. Project 3 (design stage time = 14 days)
4. Project 7 (design stage time = 15 days)
5. Project 2 (design stage time = 16 days)
6. Project 5 (design stage time = 18 days)
7. Project 1 (design stage time = 20 days)

Next, we can use Johnson's rule to determine the minimum possible completion time for each project. For each project, we find the shortest time between the first and second stages, and we also find the shortest time between the second and first stages, and then add these times together to get the minimum possible completion time.

For example, for Project 4:

Shortest time for first stage = 3 days (by working on the planning stage first with Team 1)
Shortest time for second stage = 12 days
Minimum possible completion time = 3 + 12 = 15 days

Following this rule, we can find the minimum possible completion times for all seven projects:

1. Project 4: 15 days
2. Project 6: 17 days
3. Project 3: 21 days
4. Project 7: 26 days
5. Project 2: 30 days
6. Project 5: 36 days
7. Project 1: 44 days

Finally, we can calculate the idle time for Team 2 by subtracting the total minimum completion time for all seven projects from the total time available for both teams (which is twice the sum of the second stage times).

Total time available for both teams = 2(12 + 16 + 14 + 18 + 15 + 13 + 20) = 420 days
Total minimum completion time for all seven projects = 15 + 17 + 21 + 26 + 30 + 36 + 44 = 189 days
Idle time for Team 2 = 420 - 189 = 231 days
Idle time per project for Team 2 = 231 / 7 = 33 days
Thus, Team 2 has 4 days (rounded down from 33) of idle time from the start of the first project through completion of the seventh. Therefore, the answer is C.

Table J.17 A Company Must Take on Seven New Projects. Each Project