3. The Autoridad Metropolitana de Autobuses (AMA) uses 275,000 gallons of diesel per year. It may satisfy its fuel requirement either by one annual contract or separate monthly contracts for the year. The cost for the annual contract is $2.25 per gallon. The cost for the monthly contract will average $1.90 if diesel fuel production is increased, but the average cost will be $1.65 if diesel fuel production is not increased. The manager estimates a 0.2 probability of no increase in diesel fuel production.
It is also possible to get a professional forecast on diesel fuel production at a cost of $12,000. The manager believes that the following conditional probabilities are realistic appraisals of the forecast’s accuracy.
P(forecast indicating no increase | actual no increase) = 0.70
P(forecast indicating no increase | actual increase) = 0.1
Based on a tree diagram, what is the optimal decision strategy, the associated expected value, and expected value of the forecast? Explain what they mean.



Test 2: Decision Theory
Instructions:
? Máximo de seis páginas, incluyendo gráficas, tablas u otros features que
desee incluir.
? Formato PDF.
? Times New Roman, 12 pts., 1.5” entre líneas, 1” margen (alrededor), no
-characters.
? No escriba la situación y “No cover page.”
? Su nombre (únicamente) en el lado superior derecho, en la primera página,
a espacio sencillo.
? Cuando lo envíe, escribir en el Subject: “DMTTest2-2013”.
? Tendrá una deducción de 5% por cada una de las instrucciones previas que
omitan.
? Si hace la prueba en castellano y desea utilizar un término en inglés, utilice
itálica.
? Dos o más exámenes cuyas respuestas sean relativamente -similares
obtendrán una calificación de 0%.
? Debe enviar el mismo antes de las 9:00pm, del 2 de junio. (Habrá una
deducción del 10% del total que obtenga, por cada hora de retraso.)
Situations:
1. Ms. María Acosta, director of logistics for the Scenic Calendar Company,
wishes to evaluate two methods of time series forecasting. She has
collected quarterly calendar sales data from the years 2011 and 2012.
2011
Qtr.
1
2
3
4

2012
Actual
Sales
1200
800
200
1000

Qtr.
1
2
3
4

Actual
Sales
1300
800
250
1200

a.

b.

c.
d.

Use the moving averages technique to find forecasted sa les for the
third quarter of 2012 based on actual sales from the previous 3
quarters.
Use simple exponential smoothing to forecast each quarter’s sales in
2012, given that Ms. Acosta qualitatively forecasted 900 calendars
for quarter 4, 2011. Ms. Acosta has assigned an alpha factor of .1 for
time series sensitivity.
Repeat the simple exponential smoothing problem above (part b)
with Ms. Acosta employing an alpha factor of .2.
How well do the moving averages and simple exponential smoothing
techniques seem to work in Ms. Acosta’s situation? In what ways do
the techniques appear to fail?

2. The annual demand for Lipiprozac, a wonder drug, is normally distributed
with mean 40,000 and standard deviation 5,000. There is evidence that the
maximum and minimum annual demands are 52,000 and 21,000,
respectively. Assume that demand during each of the next 10 years is an
independent random draw from this distribution. The company producing
Lipiprozac needs to determine how large a manufacturing plant to build to
maximize its expected profit over the next 10 years. If the company build a
plant that can produce x units of the drug per year, it will cost $18 for each
of these units. The company will produce only the amount demanded each
year, and each unit of Lipiprozac produce will sell for 51.25. Each unit of
Lipiprozac produced incurs a variable production cost of $0.35. The cost per
year to operate a unit of capacity follows a triangular distribution with the
following parameters (in dollars): 0.28, 0.38, and 0.48. It has been found
that this last cost and the annual demand has a correlation of 0. 86.
a.
Using simulation, among the capacity levels of 20,000, 30,000,
40,000, 50,000, and 60,000 units per year, which level maximizes
expected profit?
b.
Using the capacity from you answer to part a, the company can be
95% certain the expected profit for the 10-year period will be
between what two values?
c.
Using the capacity from you answer to part a, the company cab be
90% certain the actual profit for the 10-year period will be between
what two values?

3. The Autoridad Metropolitana de Autobuses (A MA) uses 275,000 gallons of
diesel per year. It may satisfy its fuel requirement either by one annual
contract or separate monthly contracts for the year. The cost for the
annual contract is $2.25 per gallon. The cost for the monthly contract will
average $1.90 if diesel fuel production is increased, but the average cost
will be $1.65 if diesel fuel production is not increased. The manager
estimates a 0.2 probability of no increase in diesel fuel production.
It is also possible to get a professional forecast on diesel fuel production at
a cost of $12,000. The manager believes that the following conditional
probabilities are realistic appraisals of the forecast’s accuracy.
P(forecast indicating no increase | actual no increase) = 0.70
P(forecast indicating no increase | actual increase) = 0.1
Based on a tree diagram, what is the optimal decision strategy , the
associated expected value , and expected value of the forecast? Explain
what they mean.
4. The IPCOS Company sells and delivers office supplies to companies,
schools, and agencies within a 25-mile radius of its warehouse. The office
supply business is competitive, and the ability to deliver orders promptly is
a big factor in getting new customers and maintaining old ones. (Offices
typically order not when they run low on supplies, but when they
completely run out. As a result, they need their orders immediately.) The
manager of the company wants to be certain that enough drivers and
vehicles are available to deliver orders promptly and that they have
adequate inventory in stock. Therefore, the manager wants to be able to
forecast the demand for deliveries during the next month. From the
records of previous orders, management has accumulated the following
data for the past 10 months:
Month
Orders

Jan.
110

Feb.
120

Mar.
90

Apr.
97

May
150

Jun.
90

Jul.
95

Aug.
110

Sep.
90

Oct.
90

a. Compute the monthly demand forecast for October using a 3-month
moving average.

b. Compute the monthly demand forecast for October using a 4-month
moving average.
c. Compute the monthly demand forecast for October using a 3-month
weighted moving average. Use weights of 0.50, 0.30, and 0.20, with the
heavier weights on the more recent months.
d. Which method would you use to forecast demand fo r October based on
MAD?
e. What would be October’s estimate using a simple regression model?
5. ‘DeAqui’, a puertorrican small food processing business, is investigating an
investment in a “mofongo” machine, to serve the European market, but
they were uncertain about the extent of the investment needed. Initial
research led them to identify three potential courses of action:
?
A large investment, which would involve purchasing a full -scale
machine system, including robotics, thus allowing them to serve a
large amount of restaurants in Puerto Rico . This machine would give
them greater capability, because it can also be used to make
piononos and other similar products.
?
A medium investment, which would give them the same general
capability as alternative A, but the equipment would operate at a
much lower speed, and wouldn’t make piononos, etc. This would
prevent them from serving certain restaurants needs.
?
A small investment, which would limit them to produce fewer [only]
mofongos.
DeAqui also identified three potential trends that they believed the market
demand for the product produced by the machine could take.
?
Rapidly increasing demand due to the capability of the machine
?
Moderately increasing demand
?
Slight increase in demand as more restaurants added their own
mofongo and products processes capability

Large investment
Medium investment
Small investment

Large demand
$5 million
$3.5 million
$2 million

Moderate demand
$3.5 million
$5.5 million
$1.5 million

Small demand
-$2 million
-$15 million
$1 million

Based on the maximin criterion, maximax criterion, and minimax regret
criterion, what should be the company’s decisions?
6. Mr. Juan Cruz, distribution center manager for Burey Kitchenware, must
determine when to resupply his stock of “guayos”. The DC experiences a daily
demand of 400 guayos. The average length of the performance cycle for guayos
is 14 days. Mr. Cruz requires that 500 guayos be retained as safety stock to deal
with demand uncertainty.
a. Use simple reorder point logic to determine the order quantity for guayos.
b. Based on your answer to part (a), find Mr. Cruz’s average inventory level of guayos.
7. Mr. Cruz recently realizes that there are significant costs associated with ordering and maintaining inventory at his dis tribution center. Mr. Cruz has learned that the EOQ is the replenishment logic that minimizes these costs , and in an effort to find the EOQ for measuring cups, he has gathered relevant data. Mr. Cruz expects to sell 44,000 measuring cups this year. Burey acquires the measuring cups for 75 cents each from Yoyo Industries, which charges $8 for processing each order. In addition, Mr. Cruz estimates his company’s inventory carrying cost to be 12 percent annually.
a. Find Mr. Cruz’s EOQ for measuring cups. Assume that Mr. Cruz accepts ownership of products upon arrival at his DC.
b. Now assume Mr. Cruz must arrange for inbound transportation of the measuring cups since Burey accepts ownership of products at the supplier’s shipping point. Quantities of fewer than 4,000 measuring
cups cost 5 cents per unit to ship. Quantities of 4,000 and above cost
4 cents per unit to ship. Determine the difference in total costs
associated with an EOQ of 4,000 units and the EOQ level found in part (a) when transportation costs must be considered.
c. Given the information above and the low cost EOQ alternative
determined in part (b), use period-order-quantity logic to determine the number of orders Burey would place each year for measuring cups and the time interval between orders.
7. Mr. David Juanes manages the warehouse inventory for Atleticos, a distributor of sports watches. From his experience, Mr. J uanes knows that the PR-5 jogging watch has an average daily demand of 100 units and a performan ce cycle of 8 days. Mr. Juanes requires no buffer stock at this time.
a. Assume Mr. Juanes perpetually reviews inventory levels. Find the reorder point for the PR-5 jogging watch.
b. Find the average inventory level of the PR -5 watch.
c. How might the reorde r point change if Mr. Juanes reviews inventory once each week? Find the reorder point under these conditions.
d.Find the average inventory level of the PR -5 watch under this periodicreview.