School of Engineering
Assessment 2: Case studies
You need to choose one of the simulation case studies
Case study 1
For investment advisors, a major consideration in planning for a client in retirement is the
determination of a withdrawal amount that will provide the client to with the funds necessary to
maintain his or her desired standard of living throughout the client’s remaining lifetime. If a client
withdraws too much or if investment returns fall below expectations, there is a danger of either
running out of funds or reducing the desired standard
of living. A sustainable retirement withdrawal is the inflation-adjusted monetary amount a client can
withdraw periodically from his or her retirement funds for an assumed planning horizon. This amount
cannot be determined with complete certainty because of the random nature of investment returns.
Usually, the sustainable retirement withdrawal is determined by limiting the probability of running out
of funds to some specified level, such as 5%. The sustainable retirement withdrawal amount is typically
expressed as a percentage of the initial value of the assets in the retirement portfolio but is actually the
inflation-adjusted monetary amount that the client would like each year for living expenses.
Assume an investment advisor, Roy Dodson, is assisting a widowed client in determining a sustainable
retirement withdrawal. The client is a 59 year-old woman who turns 60 in two months. She has
$1,000,000 in a tax-deferred retirement account that will be the primary source of her retirement
income. Roy has designed a portfolio for his client with returns he expects to be normally distributed
with a mean of 8% and standard deviation of 2%. Withdrawals will be made at the beginning of each
year on the client’s birthday.
Roy assumes that the inflation rate will be 3%, based on long-term historic data. So if her withdrawal at
the beginning of the first year is $40,000, her inflation-adjusted withdrawal at the beginning of the
second year will be $41,200, and third year’s withdrawal will be
$42,436, and so on.
For his initial analysis, Roy wants to assume his client will live until age 90. In consultation with his
client, he also wants to limit the chance that she will run out of money before her death to a maximum
1. What is the maximum amount Roy should advise his client to withdraw on her 60th birthday? If
she lives until age 90, how much should the client expect to leave to her heirs?
2. Roy is now concerned about basing his analysis on the assumption that his client will live to age
90. After all, she is healthy and might live to be 110, or she could be in a car accident and die at
age 62. To account for this uncertainty in the client’s age at death, Roy would like to model the
client’s remaining life expectancy as a random variable between 0 and 50 years that follows a
lognormal distribution with a mean of
20 and standard deviation of 10 (rounded to the nearest integer). Under this assumption, what is the
maximum amount Roy should advise his client to withdraw on her 60th birthday, and how much
should the client expect to leave to her heirs? Hint: Modify your spreadsheet to accommodate ages up
to 110, and use a VLOOKUP( ) function to return the client’s ending balance in her randomly
determined year of death.).
Case study 2
Calls to the 24-hour customer support line for Richman Financial Services occur randomly following a
Poisson distribution with the following average rates during different hours of the day:
|Midnight – 1
|2||Noon – 1 p.m.||35|
|1 a.m.- 2 a.m.||2||1 p.m.- 2 p.m.||20|
|2 a.m.- 3 a.m.||2||2 p.m.- 3 p.m.||20|
|3 a.m.- 4 a.m.||4||3 p.m.- 4 p.m.||20|
|4 a.m.- 5 a.m.||4||4 p.m.- 5 p.m.||18|
|5 a.m.- 6 a.m.||8||5 p.m.- 6 p.m.||18|
|6 a.m.- 7 a.m.||12||6 p.m.- 7 p.m.||15|
|7 a.m.- 8 a.m.||18||7 p.m.- 8 p.m.||10|
|8 a.m.- 9 a.m.||25||8 p.m.- 9 p.m.||6|
|9 a.m.- 10 a.m.||30||9 p.m.- 10 p.m.||5|
|10 a.m.- 11
|25||10 p.m.- 11
|11 a.m.- Noon||20||11 p.m.-
Richman’s customer service representatives spend approximately seven minutes on each call and are
assigned to work eight-hour shifts that begin at the top of each hour. Richman wants to ensure that, on
average, they can provide a 98% service level.
1. Determine the customer service schedule that allows Richman to achieve their service level
objective using the fewest number of employees.
2. According to your solution, how many customer service representatives should Richman
employ and how should they be scheduled?
Case study 3
Amy White is the director of marketing for the Imagination Toy Corporation (ITC). She just received a
phone call from her boss indicating that the company’s board of directors gave final approval for the
production and marketing of the Mighty Morphin’ Monkeys—a new product line of action play toys for
ITC. Amy worked hard in developing the concept for this product line and is thrilled that her ideas will
become reality. But this news also means that she must get busy developing the marketing and sales
force training materials needed to launch this new product line successfully. Amy’s boss wants to know
how soon she can have the sales staff trained and equipped to handle the new line.
The development of marketing materials and training of the sales staff for the new product line
constitute a project. Amy identifies 10 specific project tasks that need to be accomplished before she
can roll out the marketing program for this product line. First, Amy needs to collect information about
the details of the decisions made by the board of directors. She can start this task (task A) immediately,
and she estimates that it will take 5 days to determine exactly which items and accessories will be
included in the first offering of the product line. After she completes this task, she will request
prototypes of all items from the engineering department (task B), which she expects will take 10
working days. While waiting for the prototypes, she can begin laying out the marketing program (task
C). She expects this activity to take 8 days. After the prototypes (task B) are available, Amy estimates
that it will take 7 days to prepare instructions (task D) on the operation and use of the items in the
product line and 9 days to design its packaging (task E). When the marketing program (task C) is
finished, it must be approved (task F) by the president of the company. Amy expects this approval to
take 3 days.
Amy plans to hold a 2-day training course (task G) for the sales force after the operating instructions
(task D) and the packaging design (task E) are completed. When the operating instructions (task D) are
finished and the marketing plan is approved (task F), Amy will develop an information guide (task H)
that the sales force can distribute to retailers. Amy expects to take 8 days to complete the information
guide. Also, as part of the marketing plan, Amy wants to hire a number of actors to portray Mighty
Morphin’ Monkeys (task I) at various promotional events around the country. Hiring and training these
actors is expected to take 8 days and can be done only after the marketing plan is approved (task F).
Finally, after the marketing plan (task F) has been approved and the packaging for the product has
designed (task E), special pointof- sale display racks must be manufactured (task J). Amy expects this
activity to take 12 working days.
1. Create a Gantt chart.
2. Develop an AON network for this problem.
3. Create a spreadsheet to calculate and summarize the earliest and latest start and finish
times, the slack for each activity, and the critical activities.
4. Identify the critical path.
5. If Amy starts working immediately, how long will it take her to complete this project?
6. Suppose that the engineering department can create the prototypes in only eight days if the
engineers work overtime on this activity. Would this help reduce the length of time required
to complete this project?
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