Student’s Name
Institution Affiliati
House Construction: MS Project
Task 1, 2, 3

Activity ID Activity Name Predecessor Earliest (a) Likely (m) Latest (b) Mean Time (E ) Variance (D)
1 Site clearance 0 4 7 10 7 1
2 Ground breaking and excavation 1 1 3 5 3 0.444444
3 Foundation 2 7 10 14 10.16666667 1.361111
4 Framing 3 5 9 13 9 1.777778
5 Boundary wall and gates 1 3 5 7 5 0.444444
6 Installation of windows and doors 7 2 5 7 4.833333333 0.694444
7 Roofing 4 5 8 14 8.5 2.25
8 Siding 6 10 14 21 14.5 3.361111
9 Rough electrical 7 3 4 5 4 0.111111
10 Rough plumbing 7 3 5 7 5 0.444444
11 Rough HVAC 9 2 4 7 4.166666667 0.694444
12 Insulation 11 4 6 8 6 0.444444
13 Underlayment 12 2 4 6 4 0.444444
14 Trim 13 2 3 5 3.166666667 0.25
15 Painting 14, 8 4 6 8 6 0.444444
16 Finish electrical 15 1 2 3 2 0.111111
17 Bathroom and kitchen counters and cabinets 15 1 2 3 2 0.111111
18 Finish plumbing 15, 10 1 2 3 2 0.111111
19 Carpet and flooring 18 1 2 3 2 0.111111
20 Finish HVAC 16 1 2 3 2 0.111111
21 Hookup to water main 17 1 3 4 2.833333333 0.25
22 Hookup to sewer line 18 1 2 3 2 0.111111
23 Completion certificate 22, 5, 21, 20 1 2 4 2.166666667 0.25
24 Hardscaping and Landscaping 7 7 10 15 10.33333333 1.777778
25 Final cleanup 22, 19 1 3 4 2.833333333 0.25
26 Moving In 25, 24, 23 1 3 5 3 0.444444

 
Task 4: AON Diagram is drawn using the attached MS Project
Task 5: Calculation of slacks

Activity ID Early Finish Duration Late Finish Slack
5 5/16/2018 5 7/6/2018 21
6 6/27/2018 6 6/27//2018 0
8 7/17/2018 14 7/19/2018 2
16 7/31/2018 2 7/21/2018 0
20 8/2/2018 2 8/5/2018 3
10 6/27/2018 5 7/29/2018 32
24 7/4/2018 10 8/5/2017 31
18 7/31/2018 2 7/31/2018 0
19 8/2/2018 2 8/5/2018 3
22 8/2/2018 2 8/5/2018 3
Total Slack 95 days

Task 6: Critical path
From the Network diagrams the critical path is as follows:
1-2-3-4-7-9-11-12-13-14-15-17-21-23-25-26
Task 7: Calculation of mean and variance of the project

Activity ID Activity Name Mean (E ) Variance (D)
1 Site clearance 7 1
2 Groundbreaking and excavation 3 0.444444
3 Foundation 10 1.361111
4 Framing 9 1.777778
7 Roofing 8.5 2.25
9 Rough electrical 4 0.111111
11 Rough HVAC 4.17 0.694444
12 Insulation 6 0.444444
13 Underlayment 4 0.444444
14 Trim 3.17 0.25
15 Painting 6 0.444444
17 Bathroom and kitchen counters and cabinets 2 0.111111
21 Hookup to water main 2.83 0.25
23 Completion certificate 2.17 0.25
25 Final cleanup 2.83 0.25
26 Moving In 3 0.444444
Total 77.67 10.527

 
Task 8: Probability of completing the project using 10% less time.
Normal time for the project is 69.9 days
Variance 10.527
Standard deviation (s) = 3.2445
Probability of finishing with 10% less time (90%*467= 420 days)
P= {(x-77.67)/s} <= {(69.9-77.67)/3.2445}
P= Z= -2.3948 (standard deviation tables)
Z= 0.00842
Probability (1-0.00842= 0.99158)
Probability = 99.158%
Task 9: Crashing
Crashing refers to measures that are undertaken to reduce the time taken to complete each activity (Kelley, 1961). Some of the crash programs that can be undertaken in any project include working overtime, hiring additional help, using special saving materials, and using costly but specialized and fast equipment. In the cost-price-method (CPM) of time-cost trade-offs establishes the optimal activities to crash that will result in the greatest value for a project. A typical time-cost graph shows the normal and crash point. The normal point indicates the time (duration to complete a task) and the cost of each activity when it is performed in an ordinary manner. The crash point, on the other hand, indicate the time and cost for the maximum crashing of each activity (Błaszczyk & Nowak, 2009). Noteworthy, CPM assumes that crashing times and costs can be reliably predicted. In most projects, partial crashing of activities is the most preferred.
Time-Cost Graph for an Activity
Ways of Crashing Activities
The fundamental goal of any crashing program is usually to establish the least expensive ways of crashing activities to enable the completion of a task within the set deadline. One popular method of solving the crashing problem is the marginal cost analysis. In this method, the activities that lie in the critical path are first identified. By checking the marginal cost of each activity in the critical path, the project manager identifies those that have the least crashing cost per day (Lieberman & Hillier, 2000). He/she then selects to crash activities starting with those that are least expensive to the most costly ones in terms of marginal cost. All activities in the non-critical path are started earliest possible to avoid the need of crashing them. Another popular crashing method, which is mostly used for huge projects is linear programming (Karmarker & Halder, 2017). The objective of this method is usually to minimize the cost constraint. One tool that can be used in this method is the solver package in Microsoft Excel.
Procedures for Identifying the Cost of Reducing Project Time
Typically, project managers consider both direct and indirect costs when deciding the activities to crash. The critical activities show the lowest direct cost activities that can shorten time spent on a project. A comparison is then established of the benefits of reducing the cost of specific activities before the start of a project or when it is in progress. Noteworthy, projects have both indirect and direct costs (Kelley, 1961). Total costs are the sum of direct and indirect costs. Indirect costs continue throughout the life of a project; therefore, a reduction in a project’s duration leads to the reduction in this expense. Direct costs relate to the expenses of specific activities, and they usually increase when a project’s duration is reduced. Indirect costs are usually overheads such as supervision, administration, or consultation fees (Larson & Gray, 2011). Since they are not associated with any specific work, they usually vary with the time needed for these services. Direct costs usually represent materials, labor, and equipment that are assigned to specific activities. In this case, only extra investment in direct costs resources leads to a reduction in activity time.
 
 
 
Cost Duration Graph
 
References
Błaszczyk, T., & Nowak, M. (2009). The time‐cost trade‐off analysis in construction project using computer simulation and interactive procedure. Technological and Economic Development of Economy, 15(4), 523-539.
Karmarker, C. & Halder, P. (2017). Scheduling Project Crashing Time Using Linear Programming Approach: Case Study. International Journal of Research in Industrial Engineering, 6(4), 283-292.
Kelley, E. (1961). Critical-path planning and scheduling: Mathematical basis. Operations Research, 9(3), 296-320.
Larson, E., & Gray, C. (2011). Project management: The managerial process (5th Ed.). New York, NY: McGraw-Hill.
Lieberman, G., & Hillier, F. (2000). Introduction to operations research (7th Ed.). New York, NY: McGraw-Hill.