Department of Decision Sciences
San Francisco State University
FINAL EXAM QUESTIONS
The sample problems below are organized by topic. Where possible, answers are given.
Disclaimers:
• These questions are questions that have appeared on previous years’ (final) examinations.
They are for practice only. There is no guarantee that the questions on your finals will be
the same, or that different professors will give the same types of questions.
• Not all 412/786 sections cover the same material. The questions may contain material
that is unfamiliar to you, or not contain material you covered. If you have concerns about
the topics for your final, talk to your professor.
• Short answer and multiple choice questions are not included in this handout.
• Some questions may have been slightly modified to make them more general.
Decision Analysis
1. Sheree is deciding on how to invest her $1000 tax refund. She reads that Merck is partnering
with a small biotech firm to produce a cancer drug which may or may not receive FDA approval
in the next six months. If the FDA approves it, the biotech firm’s stock will double in value, but
if it rejects it, the firm goes bankrupt and its stock becomes worthless. Merck is a huge
pharmaceutical, so approval will result in a 20% appreciation in stock, and rejection in a 10%
decrease. She is also considering hedging her bets and investing half her money in Merck and
half in the Biotech firm. She could also put her money in a safe mutual fund, with a small (but
guaranteed) 3% increase in value in the next six months.
a) Fill in the decision table, labeling all decisions, outcomes and payoffs. Express payoffs
in terms of expected portfolio value at the end of six months. Hint: the table has the
correct dimensions.
Outcomes
___________
Decisions
_____________
___________
___________
___________
_______
b) Given the payoff table what is Sheree’s best decision using the Laplace, Maximax, and
Maximin decision criteria? Please show the decision, not just the payoff amount for full
credit. (Merck, Biotech, Mutual Funds)
c) Sheree thinks that the chance of the FDA approving the drug is 40%. Compute the
expected values for each decision, and circle her best decision, assuming she is rational
and risk neutral. (all Biotech 800, Merck 1020, 50/50 910, Mutual Funds 1030)
d) Construct the opportunity table below and show what investment Sheree would make
under the Minimax Regret Decision Criteria (no points just for guessing!) (50/50)
DS 412/BUS 786 Final Review Sheet
Decision Analysis
Page 1
Department of Decision Sciences
San Francisco State University
2. Yonni is considering expanding his Yuppie Yoga franchise by building a new studio in
Russian hill that will cost 6 million dollars to build and operate (over the relevant timeframe of
the model). Customer demand is uncertain, however. There is a 0.6 probability it will be high,
yielding him 10 million in revenues, but if it is low he only will earn 5 million in revenues from a
half-full club. If demand is low, he does have the option of trying to raise it through a marketing
campaign. If successful, this raises his club's revenue's to 8 million dollars. However, the
campaign will cost 2 million and only has a 50% chance of success and if unsuccessful, club
revenues remain at 5 million. Also, Yonni can choose not to build (and his profit would be 0).
a) Draw a decision tree to show Yonni's decision process, wherein he attempts to maximize
his profits. Show all final payoffs and intermediate expected values. (Reminder: profit
= revenues- costs. All costs that are relevant to the problem are mentioned explicitly!)
b) Assuming Yonni is a risk-neutral, rational decision maker, what is his course of action
over the timeframe of the model? (build studio, don’t advertise)
c) What is the expected value of this decision tree? ($2 million)
3. Bratt's Bed and Breakfast, in a small historic New England town, must decide how to
subdivide (remodel) the large old home that will become their inn. There are three alternatives:
Option A would modernize all baths and combine rooms, leaving the inn with four suites, each
suitable for two to four adults each. Option B would modernize only the second floor; the results
would be six suites, four for two to four adults, two for two adults only. Option C (the status quo
option) leaves all walls intact. In this case, there are eight rooms available, but only two are
suitable for four adults, and four rooms will not have private baths. Below are the details of profit
and demand patterns that will accompany each option.
Annual profit under various demand patterns
Capacity p
Average p
0.5 $25,000 0.5
(Modernize all) $90,000
nd
0.4 $70,000 0.6
(Modernize 2 ) $80,000
(Status Quo)
$60,000
0.3 $55,000
0.7
a) Construct a decision tree.
b) Which option has the highest expected value? (Option B, $74,000)
4. The Slumber Mist Company is considering marketing a new water bed. If the new bed is
successful, it will mean a $4 million profit (present value) over the life of the product. If
unsuccessful, a $2 million loss on investment will be incurred. Slumber Mist is considering
whether to hire a market research company, Market Competition Inc. (MCI), to perform an
analysis. The results of 40 previous studies by MCI are given below:
Forecast success
Forecast failure
Actual outcome
Success
Failure
18
3
4
15
MCI charges $100,000 for its survey. Draw a decision tree for this problem. Describe the
optimal strategy in words. (use MCI; if success predicted, market; if failure predicted, don’t)
DS 412/BUS 786 Final Review Sheet
Decision Analysis
Page 2
Department of Decision Sciences
San Francisco State University
5. Steve has a choice of one of three ways of going to school. The time it takes for him to travel
not only depends on which way he travels, but also on the weather that day. Steve is a man of fixed
habits who likes always to take the same way to work each day, regardless of the weather that day.
The following is a Decision Table giving the minutes to school under each weather condition.
Sunny
25
Route 280
Highway 101 30
35
19th Avenue
a)
b)
c)
d)
Windy
55
35
40
Rainy
60
45
40
If Steve is a Pessimist, which way should he choose? (19th Ave)
Give another name for the Pessimist's Criterion.
Which way should Steve choose if he is an Optimist? (280)
If Steve believes that any type of weather is equally likely, which way should he go, using
expected travel time as the criterion? (101)
6. The XYZ Book Publishing Company receives manuscripts (drafts of books) from authors which
it then considers for publication. A book that sells well should bring a profit of $80,000 whereas a
poor-selling book will lose $100,000. (These figures don’t include reviewing fees.) Until recently,
XYZ had sent every manuscript to a reviewer, who charged $3000 to read the manuscript and either
“recommended” or “did not recommend” it for publication (a positive recommendation indicates that
the reviewer believes the book would sell well if it were published). Until recently, the XYZ
Company received so few manuscripts that it automatically published them all, irrespective of
whether they were “recommended” by the reviewer or not. The following table summarizes what
happened in the past:
Actual sales of the book
High sales Low sales
3
1
Reviewer “recommended”
6
10
Reviewer “did not recommend”
(For example, there were 6 manuscripts which sold well even though they were not recommended by
the reviewers.) XYZ has been losing money recently, and has started to ask itself questions like
these: Do we need a reviewer? If we have a reviewer, shouldn't our decision to publish be based on
what the reviewer says?
a) Draw a single decision tree that will determine a better operating policy, and answer the
above questions.
b) Summarize in words the best strategy as indicated by the tree, and state the expected profit
that would be obtained with this strategy. (use reviewer, if recommends, publish; if not,
don’t)
c) If the optimal strategy was adopted for the next fifty manuscripts, what would XYZ's total
profit be, approximately? ($650,000)
DS 412/BUS 786 Final Review Sheet
Decision Analysis
Page 3
Department of Decision Sciences
San Francisco State University
7. A greengrocer sells fresh mixed fruit which he buys from the farm for $1.50 per lb in 100 lb lots.
He tries to sell it the same day at a price of $2.00 per lb. (If he has any fruit left unsold at the end of
the day he sells it at $0.50 per lb. to a local market; he can sell any amount of fruit at this lower
price.) The daily demand for fresh fruit is as follows:
Demand (lbs) Probability
100
0.4
200
0.4
300
0.2
Note that this table shows the demand for fresh fruit. There is an unlimited demand for old fruit.
a) Give the decision table for this problem.
b) What should the greengrocer do to maximize his expected profit? Record your calculations
in the above table. (purchase 100 lbs)
c) What should the greengrocer do if he is a pessimist/uses maximin? (purchase 100 lbs)
8. Selfless Cell Company (SCC) is trying to determine the best course of action to take with
customers whose bills are overdue. The choices are disconnecting service, waiting, sending letters,
and calling the customers. Waiting does not have an associated cost. Sending letters and
disconnecting service each cost $1, while calling customers costs $3. The average size of an
outstanding bill is $50. In all cases, SCC is willing to wait at most 2 months before disconnecting
service. Disconnecting service is the simplest option; however, there is no possibility of collecting on
the debt in this case. SCC can choose to wait for a month to see if the customer pays the bill without
prompting. There is a 50% of this happening. If payment is still not forthcoming after this month,
SCC must decide what to do next. The customer may have service discontinued, may receive a
reminder letter, or may receive a call. Customers receiving the letter will pay with probability 40%.
75% pay if they are called pay. SCC may also decide to send the customer a nice reminder letter.
70% of customers receiving the nice letter will pay. Those that do not pay may receive a phone call,
a nasty letter, or be disconnected. 80% of those receiving the call pay, while 60% of the nasty-letterrecipients do.
Finally, SCC may choose to call overdue customers. 90% of those receiving a call will immediately
pay. If they do not, SCC can try calling them again (with a success probability of 5%), or can
disconnect their service. Construct a decision tree to help SCC decide the best course of action.
What are the best decisions to be made at each step if SCC wishes to maximize profits?
(send a nice letter, then call)
9. Randy Hearst sells copies of a daily newspaper for $0.75 each at a street corner. Every
morning, Randy buys newspapers from the local distributor for $0.50. If he runs out of
newspapers during the day, he cannot order any more that day. On the other hand, if he has any
papers unsold at the end of the day, he can return them to the distributor for a refund of $0.15.
From past experience, Randy has estimated that the daily demand for newspapers will be either
18, 19, or 20, with probabilities of 0.3, 0.4, and 0.3.
a) Set up the decision table.
b) How many newspapers should Randy buy every morning to maximize expected profit?
(19)
DS 412/BUS 786 Final Review Sheet
Decision Analysis
Page 4
Department of Decision Sciences
San Francisco State University
10. The CEO of a biotech company must decide whether to spend $2 million to continue with a
particular research project or to stop the development. The success of the project (as measured by
obtaining a patent) is not assured. At this point the CEO judges only a 70% chance of getting the
patent. If the patent is awarded, the company can either license the patent for an estimated profit
of $25 million or invest an additional $12 million to create a production and marketing system to
sell the product directly. If the CEO chooses the latter, he/she faces uncertainty of demand and
associated profits from sales as follows:
Demand level Probability Profit from Sales
High
0.25
$55 million
Medium
0.55
$33 million
Low
0.2
$15 million
a) Draw the decision tree.
b) Using the EMV rule, what is the optimal strategy? What is the EMV for this strategy?
(invest, then license if successful)
11. A high school student is trying to decide what to do after high school. She could get a job, where
she expects to make an average of $25,000 per year over the next 10 years. She assumes she will
have no problems finding a job. She can attend an Ivy League school, which will cost $30,000/year
for 4 years if she gets a degree in the liberal arts or business. If she decides to major in engineering,
she concludes (perhaps incorrectly) that her studies will be much more stressful, and that she should
assign an extra $10,000/year in costs. There is a 50% chance that she will get into an Ivy League
school. If she does not, she can either get a job immediately, or go to a local state school. If she gets
an Ivy League degree, she anticipates an average salary of $60,000/year if she does not get an
engineering degree, or $80,000/year if she does. There is an 80% chance she will get such a job after
she graduates. If not, she can find the type of job she would have gotten had she not gone to college.
If she attends a state school, her costs will be $10,000/year for liberal arts/business and $15,000/year
for engineering. She assumes there is a 95% chance she will be accepted at a state school, and a 75%
chance she will be able to find a position after graduating. She anticipates average salaries of
$50,000/year and $65,000/year, depending on her major. Assume there are no time value of money
concerns. Draw the decision tree and make recommendations on which decisions are the most
appropriate. (go to a state school, major in engineering)
12. Once a week, Nan's Newsstand purchases copies of Money Magazine from the publisher at a cost
of $2.00/copy. Nan then sells the magazines for $4.00/copy. Copies not sold by the end of the week
are discarded. Based on past sales, Nan estimates demand for Money Magazine as follows.
Copies Demanded/Week
Probability
60
10%
80
50%
100
40%
Nan must decide how many copies of Money Magazine to buy each week. There are no shortage or
penalty costs.
a) Draw Nan's decision tree below. Show the relevant decisions, outcomes & profits. Label
clearly.
b) Evaluate the tree. What decision maximizes Nan's expected weekly profit? (purchase 80)
c) Calculate the expected value of perfect information (EVPI). ($20)
DS 412/BUS 786 Final Review Sheet
Decision Analysis
Page 5
Department of Decision Sciences
San Francisco State University
Forecasting
1. City Cycles has just started selling the new XYZ-10 mountain bike, and below are the
monthly sales. Amit wants to forecast by exponential smoothing (setting February's forecast
equal to January's sales) with alpha = 0.1 Barbara wants to use a 3-period moving average.
Sales Amit Barbara Amit error Barbara Error
400 -----January
380
400
February
410
March
375
April
May
a) Is there a strong linear trend in sales over time?
b) Fill in the table with what Amit and Barbara each forecast for May and the earlier
months, as relevant.
c) Assume that May's figure turns out to be 405. Append the table with error columns then
calculate MAD for both Amit's and Barbara's method. (16.11 and 19.17)
d) Based on these calculations, which method seems more accurate?
2. Weekly sales of copy paper at Cubicle Suppliers are in the table below.
Week
1234567
Sales(cases) 19 24 29 34 21 20 25
a) Forecast week 8 using a three-period moving average. (22)
b) Forecast week 8 using the naïve forecast. (25)
c) Forecast week 8 using a weighted moving average using the weights: 0.5, 0.35, and 0.15
(where the largest weight is for most recent observation). (22.65)
3. Wine sales in the US are shown in the table below (in millions of gallons), where Year 1
represents 1993 and Year 8 represents 2000.
Year
Sales
1
449
2
458
3
464
4
500
5
520
6
526
7
551
8
565
a) What method should be used to forecast sales for 2001? (Trend projection or linear
regression)
b) Forecast wine sales for 2001. (583.57)
c) Using the same forecasting method, what forecasting error would have been made in
1999? (2.74)
DS 412/BUS 786 Final Review Sheet
Forecasting
Page 6
Department of Decision Sciences
San Francisco State University
4. Demand for cement over the last six months is given below. Forecast the demand for the next
month (month 7) using a 3-month moving average. (14)
1
2
3
4
5
6
Month
Demand 12.0 14.1 15.3 12.7 14.9 14.4
5. This is a spreadsheet table for Exponential Smoothing calculations, using a Level Model. Don’t
complete this table until you have first read this question completely and have answered parts
(a) through (e).
C
4
1
2
3
6
7
E
F
Demand
(tons)
Yt
12.0
14.1
15.3
Month
t
5
D
G
Level
Lt
a) Insert the two missing column headings, including the algebraic symbols that represent
them.
In answering parts (b) through (e), assume that the smoothing constant α is in cell B3. Write each
answer in the space below the question, not in the table.)
b) What should be typed into cell F5?
c) What should be typed into cell D6?
d) What formula should be typed into cell F6? (Note that this cell will be copied into the cells
below it in column F.)
e) What formula should be typed into cell G6? (Note that this cell will be copied into the cells
below it in column G.)
Now, complete spreadsheet rows 5, 6 and 7 (months 1, 2 and 3) in the above table as it would appear
on the screen, assuming that the smoothing constant is 0.2. That is, calculate the number that will
appear in each cell in the table. Do not write formulas into the cells in the table. Round each number
to 1 decimal place.
6. The manager of an industrial pump manufacturing facility must forecast future demand. She
has generated 2 series of forecasts already, and wishes to compare them to a 2-period moving
average forecast.
Time
1
2
3
4
5
6
Demand
492
470
485
493
498
492
Forecast 1
480
490
497
493
Forecast 2
Moving Average
478
488
492
493
a) Compute the 2-period moving average forecast.
b) Compute the ME and MAD for all three methods. (2, 4.25, 6.25; 2.5, 4.75, 8)
c) Which forecasting method would you recommend for these data? Why?
DS 412/BUS 786 Final Review Sheet
Forecasting
Page 7
Department of Decision Sciences
San Francisco State University
7. National Tiger Inc., sells rice cookers. Monthly sales for a 7-month period were as follows:
Feb Mar Apr May Jun Jul Aug
Month
15
20
18 22 20
Sales (in thousands) 19 18
Forecast September Sales volume using each of the following techniques (Note: round off all
values to two decimal places):
a) Naïve approach (for a stable series) (20)
b) A five-month moving average (19)
c) A weighted moving average using 0.6 for the most recent month, 0.3 and 0.1 for the next
most recent months. (20.4)
d) Exponential smoothing with a smoothing constant equal to 0.2, assuming a March
forecast of 19 (thousands). (19.26)
8. A cosmetic manufacturer’s marketing department has developed a linear trend equation that
can be used to predict annual sales of its popular Hand&Foot cream.
Ft = 80,000+15,000t
Where Ft = Annual sales (bottles)
t = 0 corresponding to year 1990
a) Are annual sales increasing or decreasing? By how much?
b) Predict annual sales for the year 2006 using the equation. (320,000)
9. A regression was run between the Annual Revenues (Y) of Celandine Corp. in millions of
dollars and the year (X). The following equation was obtained: Y = 16 + 2.4X, where X = 1 for
1987. An R-squared of 0.87 was obtained.
a) Interpret the values of the regression parameters a and b with specific reference to this
problem.
b) Is this a good regression model? Why?
c) Forecast revenues for 2001 using the above model. (52)
10. Quarterly data on the number of tourists visiting a ski resort exhibits a pattern of seasonality
with trend, as shown below:
Qr. 1 Qr. 2 Qr. 3 Qr. 4
Year 1 6888 3276 1722 4914
Year 2 7176 3772 1794 5658
Using the decomposition principle, compute the mean seasonal factors. Then forecast the number
of tourists in year 3. (1.60, 0.80, 0.40, 1.20; 7040, 3520, 1760, 5280)
DS 412/BUS 786 Final Review Sheet
Forecasting
Page 8
Department of Decision Sciences
San Francisco State University
Inventory Management
1. Andronico’s in the financial center is open 300 days a year. They sell Organic Hummus; and
sales are approximately normally distributed with an average of 100 tubs/day and a standard
deviation of 25 tubs/day. The wholesale cost is $1.80/tub, and they calculate their annual holding
costs by using 20% of the wholesale cost. Orders cost $50 to place, regardless of number of tubs
ordered and take 4 days to arrive
a) What is the economic order quantity (EOQ) for Organic Hummus? (2887)
b) What are total annual cycle-stock holding costs for Organic Hummus? ($519.66)
c) What are the total annual fixed order costs for Organic Hummus? ($519.57)
d) Now Andronico’s has decided to save money and manufacture their own Hummus inhouse, with a production rate of 600 tubs/day, their setup cost would only be $7.50/run,
and their annual holding cost would be $0.20/tub, but all other parameters remain
unchanged. What is the Economic Production Quantity? (1643)
2. A gourmet coffee shop in downtown SF is open 200 days a year and sells an average of 75
pounds of Kona Coffee beans a day. (Demand can be assumed to be distributed normally with a
standard deviation of 15 pounds/day.) After ordering (fixed cost = $16 per order), beans are
always shipped from Hawaii within exactly 4 days. Per-pound annual holding costs for the beans
are $3.
a) What is the economic order quantity (EOQ) for Kona coffee beans? (400)
b) What are the total annual holding costs of cycle stock for Kona coffee beans? ($600)
c) What are the total annual fixed ordering costs for Kona coffee beans? ($600)
d) Assume that management has specified that no more than a 1% risk during stock out is
acceptable. What should our reorder point (ROP) be? (369.79)
e) What is the safety stock need to attain a 1% risk of stock-out during lead time? (69.79)
f) What is the annual holding cost of maintaining the level of safety stock needed to support
a 1% risk?
g) If management specified that a 2% risk of stock-out during lead time would be
acceptable, would our safety stock holding costs decrease or increase?
3. Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16.
Carrying costs are $1 per pound per week because space is very scarce. It costs the firm $8 to
prepare an order. Assume Groundz is open 52 weeks per year, and closed on Mondays.
a) How many pounds should Groundz order at a time? (8)
b) What is the total annual cost of managing this item? ($416 or $3744)
c) The lead time for orders to arrive is 1.5 (work) weeks. If the standard deviation of
weekly demand is 1.2 pounds, and Groundz wishes to achieve at least a 98% customer
satisfaction level, what is the reorder point? (9.03)
d) Groundz has been contacted by a new supplier who is offering to sell the same tea for
$12 per pound. In return, Groundz can place orders only once a month. Inventory and
ordering costs would remain the same. Is it more cost-effective for Groundz to switch
suppliers? Should Groundz switch? (new total cost $3042.67, switch)
DS 412/BUS 786 Final Review Sheet
Inventory Management
Page 9
Department of Decision Sciences
San Francisco State University
4. A firm that makes electronic circuits has been ordering a certain raw material 250 ounces at a
time. The firm estimates that carrying cost is 30% per year, and that ordering cost is about $20
per order. The current price of the ingredient is $200 per ounce. The assumptions of the basic
EOQ model are thought to apply. For what value of annual demand is their action optimal?
(93,750 ounces)
5. The following diagram shows how the quantity in stock of a certain item has changed over
the whole of 2005. The times of deliveries are marked by “D”. The times when orders were
placed for more stock are indicated by “O”. Te last delivery occurred on 12/31/05. The company
uses the Q,R system in which a fixed quantity Q is ordered whenver the quantity in stock reaches
the reorder level R. However, the company is not necessarily using the best values for Q and R.
It costs $5 to place an order for more stock, and $6 to hold one unit in stock for a whole year.
O
12/31/04
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
D
O
O
O
DO
OD O
DO DO D O
D
O
D
12/31/05
D
What is the value of Q the company is currently using? (12)
What is the value of R that the company is currently using? (8)
What was the annual demand D in 2005? (127)
How many order cycles were there in 2005? (11)
What was the demand during the lead time in each of these order...
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