solution
What are some of the questions that can be answered with PERT and CPM? (4)
b. Describe, in your own words, the meaning of slack and discuss how it can be determined. (4)
QUESTION 2 [42]
Haygood Brothers Construction Company
George and Harry Haygood are building contractors who specialize in the construction of private home dwellings, storage warehouses, and small businesses (less than 20,000 sq. ft. of floor space). Both George and Harry entered a carpenter union’s apprenticeship program in the early 1990s and, upon completion of the apprenticeship, became skilled craftsmen in 1996. Before going into business for themselves, they worked for several local building contractors in the Detroit area.
Typically, the Haygood Brothers submit competitive bids for the construction of proposed dwellings. Whenever their bids are accepted, various aspects of the construction (electrical wiring, plumbing, brick laying, painting, and so forth) are subcontracted. George and Harry, however, perform all carpentry work. In addition, they plan and schedule all construction operations, frequently arrange interim financing, and supervise all construction activities.
The philosophy under which the Haygood Brothers have always operated can be simply stated: “Time is money.†Delays in construction increase the costs of interim financing and postpone the initiation of their building projects. Consequently, they deal with all bottlenecks promptly and avoid all delays whenever possible. To minimize the time consumed in a construction project, the Haygood Brothers use PERT.
First, all construction activities and events are itemized and properly arranged (in parallel and sequential combinations) in a network. Then time estimates for each activity are made, the expected time for completing each activity is determined, and the critical (longest) path is calculated. Finally, earliest times, latest times, and slack values are computed. Having made these calculations, George and Harry can place their resources in the critical areas to minimize the time of completing the project.
The following are the activities that constitute an upcoming project (home dwelling) of the Haygood Brothers:
1. Arrange financing (A)
2. Let subcontracts (B)
3. Set and pour foundations (C)
4. Plumbing (D)
5. Framing (E)
6. Roofing (F)
7. Electrical wiring (G).
8. Installation of windows and doors (H)
9. Ductwork and insulation (including heating and cooling units) (I)
10. Sheetrock, paneling, and paper hanging (J)
11. Bricking (K)
12. Installation of cabinets (L)
13. Inside trim (including fixtures) (M)
14. Outside trim (N)
15. Painting (O)
16. Flooring (P)
The immediate predecessors and the optimistic (a), most likely (m), and pessimistic (b) time estimates, are shown in Table 1.
TABLE 1. Haygood Brothers Construction Co.
DAYS
ACTIVITY Immediate
Predecessor a m b
A – 4 5 6
B A 2 5 8
C B 5 7 9
D B 4 5 6
E C 2 4 6
F E 3 5 9
G E 4 5 6
H E 3 4 7
I E 5 7 9
J D, I 10 11 12
K F, G, H, J 7 8 9
L F, G, H, J 4 6 8
M L 5 7 9
N K 4 5 10
O M 5 6 7
P N, O 2 3 4
a. What is the time length of the critical path? What is the significance of the critical path?
b. Compute the amount of time that the completion of each activity can be delayed without affecting the overall project.
c. The project was begun August 1. What is the probability that the project can be completed by September 30? (Note: Scheduled completion time = 60 days.)
SECTION B
QUESTION 1 [10]
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest project and recorded them using different colors of sand on a pristine slab of white marble. She used red for late start and late finish times and green for early start and early finish times. Activity durations and their identifiers were written with black sand. She finished her task and had an opportunity to admire her work only briefly before a colleague came by and swept most of it away. Sadly, this was before Carrie could record the numbers on a more permanent medium, so now she turns to you to help. Fill in all of the missing information from the table.
Activity Predecessor Duration Early Start Early Finish Late Start Late Finish
A – 10
B – 7 11
C A 7
D A 15 14
E B 11 19
F B 10
G D,E 24
H F 24
J C 28
K G,H,J 36
QUESTION 2 [30]
Mdluli Machinery specializes in developing weed harvesting equipment that is used to clear small lakes of weeds. George Mdluli, president of Mdluli Machinery, is convinced that harvesting weeds is far better than using chemicals to kill weeds. Chemicals cause pollution, and the weeds seem to grow faster after chemicals have been used. George is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities that are necessary to build one of these experimental weed-harvesting machines are listed in the following table. Construct a network for these activities. (8)
After consulting with Butch Radner, George Mdluli was able to determine the activity times for constructing the weed-harvesting machine to be used on narrow rivers. George would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical path should also be determined. The activity times are shown in the following table: (22)
b. Describe, in your own words, the meaning of slack and discuss how it can be determined. (4)
QUESTION 2 [42]
Haygood Brothers Construction Company
George and Harry Haygood are building contractors who specialize in the construction of private home dwellings, storage warehouses, and small businesses (less than 20,000 sq. ft. of floor space). Both George and Harry entered a carpenter union’s apprenticeship program in the early 1990s and, upon completion of the apprenticeship, became skilled craftsmen in 1996. Before going into business for themselves, they worked for several local building contractors in the Detroit area.
Typically, the Haygood Brothers submit competitive bids for the construction of proposed dwellings. Whenever their bids are accepted, various aspects of the construction (electrical wiring, plumbing, brick laying, painting, and so forth) are subcontracted. George and Harry, however, perform all carpentry work. In addition, they plan and schedule all construction operations, frequently arrange interim financing, and supervise all construction activities.
The philosophy under which the Haygood Brothers have always operated can be simply stated: “Time is money.†Delays in construction increase the costs of interim financing and postpone the initiation of their building projects. Consequently, they deal with all bottlenecks promptly and avoid all delays whenever possible. To minimize the time consumed in a construction project, the Haygood Brothers use PERT.
First, all construction activities and events are itemized and properly arranged (in parallel and sequential combinations) in a network. Then time estimates for each activity are made, the expected time for completing each activity is determined, and the critical (longest) path is calculated. Finally, earliest times, latest times, and slack values are computed. Having made these calculations, George and Harry can place their resources in the critical areas to minimize the time of completing the project.
The following are the activities that constitute an upcoming project (home dwelling) of the Haygood Brothers:
1. Arrange financing (A)
2. Let subcontracts (B)
3. Set and pour foundations (C)
4. Plumbing (D)
5. Framing (E)
6. Roofing (F)
7. Electrical wiring (G).
8. Installation of windows and doors (H)
9. Ductwork and insulation (including heating and cooling units) (I)
10. Sheetrock, paneling, and paper hanging (J)
11. Bricking (K)
12. Installation of cabinets (L)
13. Inside trim (including fixtures) (M)
14. Outside trim (N)
15. Painting (O)
16. Flooring (P)
The immediate predecessors and the optimistic (a), most likely (m), and pessimistic (b) time estimates, are shown in Table 1.
TABLE 1. Haygood Brothers Construction Co.
DAYS
ACTIVITY Immediate
Predecessor a m b
A – 4 5 6
B A 2 5 8
C B 5 7 9
D B 4 5 6
E C 2 4 6
F E 3 5 9
G E 4 5 6
H E 3 4 7
I E 5 7 9
J D, I 10 11 12
K F, G, H, J 7 8 9
L F, G, H, J 4 6 8
M L 5 7 9
N K 4 5 10
O M 5 6 7
P N, O 2 3 4
a. What is the time length of the critical path? What is the significance of the critical path?
b. Compute the amount of time that the completion of each activity can be delayed without affecting the overall project.
c. The project was begun August 1. What is the probability that the project can be completed by September 30? (Note: Scheduled completion time = 60 days.)
SECTION B
QUESTION 1 [10]
Project Sand Mandala
Carrie meticulously calculated the early and late start and finish times for her latest project and recorded them using different colors of sand on a pristine slab of white marble. She used red for late start and late finish times and green for early start and early finish times. Activity durations and their identifiers were written with black sand. She finished her task and had an opportunity to admire her work only briefly before a colleague came by and swept most of it away. Sadly, this was before Carrie could record the numbers on a more permanent medium, so now she turns to you to help. Fill in all of the missing information from the table.
Activity Predecessor Duration Early Start Early Finish Late Start Late Finish
A – 10
B – 7 11
C A 7
D A 15 14
E B 11 19
F B 10
G D,E 24
H F 24
J C 28
K G,H,J 36
QUESTION 2 [30]
Mdluli Machinery specializes in developing weed harvesting equipment that is used to clear small lakes of weeds. George Mdluli, president of Mdluli Machinery, is convinced that harvesting weeds is far better than using chemicals to kill weeds. Chemicals cause pollution, and the weeds seem to grow faster after chemicals have been used. George is contemplating the construction of a machine that would harvest weeds on narrow rivers and waterways. The activities that are necessary to build one of these experimental weed-harvesting machines are listed in the following table. Construct a network for these activities. (8)
After consulting with Butch Radner, George Mdluli was able to determine the activity times for constructing the weed-harvesting machine to be used on narrow rivers. George would like to determine ES, EF, LS, LF, and slack for each activity. The total project completion time and the critical path should also be determined. The activity times are shown in the following table: (22)
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