PS8
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School
University of Washington *
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Course
450
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
3
Uploaded by 1227Soccer
Problem Set 8
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Simulation and Optquest QMETH 450
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Professor Hillier Individual Submission due Tuesday, May 30, 11:59pm Team Submission due Wednesday, May 31, 11:59pm Instructions 1.
Do each problem in a separate spreadsheet file. Title each file with the question number (e.g., Q1, Q2a, Q2b). It is fine (even encouraged) to discuss and/or get help from classmates. Any help provided should be via discussion only and should not
include sending or copying of files or portions of files. 2.
Please use the following Cell Preference: Set Cell Value to Distribution Mean
. 3.
Please use the following Run Preferences: 1000
Trials
, Use Same Sequence of Random Numbers
with an Initial Seed Value
of 999, and the Latin Hypercube
sampling method. 4.
Type answers to questions directly in the spreadsheet and paste in any Crystal Ball results needed to support your answer. (Choose Copy
under the Edit
menu of the forecast window.) 5.
Submit your individual solution to Canvas no later than the date and time shown above. 6.
Meet with your study team. Create a single submission for the team. At this stage (after everyone on the team has submitted their individual submissions), sharing of files is permitted. 7.
One member of your team should submit the team assignment to Canvas no later than the due date and time shown above. 1.
Saving for Retirement You are ten years away from retirement. You have accumulated a $400,000 nest egg that you would like to invest for your golden years. Furthermore, you are confident that you can invest $20,000 more each year until retirement. You are curious what kind of nest egg you can expect to have accumulated at retirement ten years from now.
You plan to split your investments evenly among four investments: a Money Market Fund, an Income Fund, a Growth & Income Fund, and an Aggressive Growth Fund. You expect each of these funds to perform in each of the upcoming ten years according to the distributions in the Portfolio Allocation example considered in class (Session 17, Pages 1-2, without correlation).
Assume the initial nest egg ($400,000) and the first year’s investment ($20,000) are made right now (start of year 1) and are split evenly among the four funds (i.e., $105,000 in each fund). The returns of each fund are allowed to accumulate (i.e., are re-invested) in the same fund, and no redistribution will be done before retirement. Furthermore, nine additional investments of $20,000 will be made and split evenly among the four funds ($5000 each) at the start of year 2, year 3, ..., year 10.
You feel like you can retire comfortably if you accumulate $1 million by ten years from now (end of year 10 / start of year 11). Use a 1000-trial Crystal Ball simulation to estimate the mean size of the total nest egg ten years from now. What is the probability that the total nest egg will be greater than $1 million? Paste in any Crystal Ball output used in your analysis (use Copy from the Edit menu of the forecast window).
Hint: You will need 10 assumption cells for each fund to capture the independent returns over each of the 10 years. Then track the balances in each fund over the 10 years.
2.
New Business School Building A prestigious university in the Pacific Northwest is planning to build a new building on campus for the business school. To accomplish this, the activities listed in the following table must be completed. For most of these activities there is a set of predecessor activities that must be completed before the activity begins. For example, the foundation cannot be laid until the building is designed and the site prepared. Activity Predecessors A Obtain Funding —
B Design Building A C Prepare Site A D Lay Foundation B, C E Erect Walls and Roof D F Finish Exterior E G Finish Interior E H Landscape Grounds F, G The time required to obtain funding depends largely on whether they land a large gift for the naming rights of the building. The university estimates a 50% chance of securing the naming rights gift. If so, the funding should be obtained in anywhere between 8 and 10 months. If not, the funding will require anywhere between 14 and 16 months to secure. The architect can complete the initial design in 4 months. However, the design requires the approval of the council, and if it is not approved, a redesign will be done. Each redesign will be completed in one month, but the number of redesigns required before council approval is uncertain. It is estimated that each design (whether the initial design or any redesign) put before the council stands a 60% chance of being approved. The general contractor has provided three estimates for each of the construction tasks
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an optimistic scenario (minimum time required if the weather is good and all goes well), a most likely scenario, and a pessimistic scenario (maximum time required, e.g., if there are weather or other problems). These estimates are provided in the table below. Finally, the landscaper has guaranteed that his work can be completed in 5 months. Activity Optimistic Most Likely Pessimistic C Prepare Site 5 8 12 D Lay Foundation 4 5 6 E Erect Walls and Roof 6 8 10 F Finish Exterior 6 9 12 G Finish Interior 5 9 12 a.
Estimate the expected time (mean) for project completion using a 1000-trial Crystal Ball simulation, as well as the probability that the project will be completed in 48 months or less. Paste in any Crystal Ball output used in your analysis (use Copy
from the Edit
menu of the forecast window). b.
Now suppose it is critical that the building be completed within 48 months. There are a number of ways that the project can be shortened. For a cost of $50,000, the dean can make additional visits to potential donors for the naming rights gift. This would increase the probability to 75% that they would secure the gift. Each of the construction activities can also be shortened (“crashed”) by hiring additional labor. The maximum amount each construction activity can be crashed (in percentage terms) along with the cost to crash is shown in the table below. If an activity is crashed, it is assumed that the optimistic, most-likely, and pessimistic estimates would all be reduced by the same percentage. Finally, for $20,000 the university can use a different landscaper that has guaranteed to complete the job within 3 months.
Activity Maximum Possible Reduction Cost of Reduction (per % reduced) C Prepare Site 20% $2500 D Lay Foundation 0% —
E Erect Walls and Roof 20% $3000 F Finish Exterior 25% $2400 G Finish Interior 15% $2000 The university has a maximum budget of $140,000 for shortening the project. Use OptQuest to determine which methods should be used to shorten the project so as to maximize the probability that it will be completed within 48 months. Copy the optimal values of the decision variables into the spreadsheet (Edit>Copy Best Solution to Spreadsheet in the Performance Chart) and paste in the performance chart itself (Edit>Copy Chart) showing the new probability of completing the building within 48 months.
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