Karen Matthews of Century Engineering is excited that the Vice President of Development recently approved her project. The 25,000-seat basketball stadium will be the largest project her firm has undertaken in the last five years, and her future with the company will be very bright if she is able to bring the project in on-time and on-budget. In two days, she must brief the Board of Directors on her estimate of the total project length. She has collected the following information on the project over the last two weeks:

	The stadium is an indoor structure with a seating capacity of 25,000. The project begins with a 10-week activity, clearing the site. When the site is clear, work can begin simultaneously on the structure and the floor.
		Structure
		Work on the structure begins with excavation, followed by the pouring of concrete footings. After the footings are complete, work can begin on erecting exterior walls. When the exterior walls are complete, work can begin simultaneously on the exterior of the stadium, the interior of the stadium, and the roof.
			Exterior
			Exterior work includes covering the exterior walls with brick and landscaping. These two tasks can proceed simultaneously. After landscaping is complete, exterior sidewalks can be poured. After the brick is installed, exterior windows and doors can be installed.
			Interior
			After the exterior walls are complete, interior work can begin. Interior work starts with installation of plumbing, electrical, and seat supports, all of which can proceed simultaneously. After completion of plumbing and electrical, work can proceed on drywall/interior finish. After the seat supports are installed, final seating can be attached to the supports. After drywall/interior finish is complete, concession appliances/equipment can be installed.
			Roof
			After completion of the exterior walls, the steel support structure for the roof can be installed, followed by final roofing.
		Floor
		After the site is cleared, work on the floor can proceed. First, the concrete slab is poured, followed by the assembly and installation of a permanent wood floor. After the floor is installed, a final polish and finish is applied, and then the lines and other designs can be painted on the floor.
		After all structural work and floor work is completed, there will be a final checkout and inspection of the entire stadium. After this, the stadium will be ready for use.

After several meetings with the construction managers and crew, Karen has compiled the following specific data on the tasks (time estimates in weeks):

Activity	Optimistic Time (a)	Most Likely Time (m)	Pessimistic Time (b)
Clear Site	8	10	12
Excavation	1	4	7
Pour Concrete Footings	2	3	4
Exterior Walls	3.5	4.4	8.9
Brick	2	3	4
Landscaping	2.5	3.8	6.3
Sidewalks	1.5	2	2.5
Exterior windows/doors	1	2	3
Plumbing	3	3.25	8
Electrical	2.5	3	3.5
Seat Supports	3	4.5	15
Drywall/Interior Finish	3	5.25	12
Final Seating	3	4	5
Concessions	1	2	3
Steel Support Structure	4	5.75	15
Final Roofing	3	5	7
Concrete Slab	2	4	6
Permanent Wood Floor	5	6	7
Polish & Finish	1	3	5
Paint	1	2	3
Final Inspection	0.25	1	1.75

a.	Calculate expected durations and variances for all tasks.
b.	Draw the network using the expected task durations calculated in (a). Perform a forward pass and backward pass through the network, and show EST, EFT, LST, LFT, and slack for each task.
c.	Karen Matthews wants to present an estimated project duration to the Board of Directors that she is very confident she can meet. Since she is a risk averse person, she wants to present a conservative estimate of total project duration. Using the critical path, calculate a project duration for 95% confidence that the project will complete at or before that duration. (Note that there are two critical paths; justify your choice.)
d.	Verify your network calculations in (b) above with a linear programming model using Excel. Generate a table showing EST for each activity, a table showing LST for each activity, and a summary table showing EST, EFT, LST, LFT, slack, and critical path designation for each activity.
e.	Using the triangular distribution for each activity, simulate the network (use 1000 iterations) in Excel. Generate a table showing the average duration for each task and the percentage of the time each individual task is critical. Also generate a table showing the average completion time for the entire network, the variance for the entire network, and the minimum and maximum network completion times from your simulation. Finally, based upon the average network completion time and variance from the simulation, calculate a project duration for 95% confidence that the project will complete at or before that duration.
f.	Compare the critical path tasks in (b) and (c) above to the critical task analysis from the simulation in (e). Also compare the 95% confidence duration calculated in (c) to that calculated in (e). Explain and discuss any differences in results. Is the additional work necessary to perform the simulation analysis worth the trouble? Why or why not? If you were Karen Matthew, which technique would you prefer? Why?