Problem set 3
Mgt-455
Complete problems 4.1, 4.3,
4.5, 4.27, 4.31., and 4.37 in the textbook.
Please ensure that the Excel file
includes the associated cell computations; this information is needed in order
to receive full credit for these problems.
Note:
PXmeans the problem may be solved with POM for Windows and/or Excel OM.
4.1
The following gives the number of pints of type B
blood used at Woodlawn Hospital in the past 6 weeks:
WEEK OF PINTS USED
Weeks of pints
used
August 31 360
September 7 389
September 14 410
September 21 381
September 28 368
October 5 374
a) Forecast the demand for the week of October 12 using a
3-week moving average.
b) Use a 3-week weighted moving average, with weights of .1, .3,
and .6, using .6 for the most recent week. Forecast demand for
the week of October 12.
c) Compute the forecast for the week of October 12 using
exponential
smoothing with a forecast for August 31 of 360 and a 5 .2. PX
4.2
year 1 2
3 4 5
6 7 8
9 10 11
demand 7 9
5 9 13
8 12 13
9 11 7
a) Plot the above data on a graph. Do you observe any trend,
cycles, or random variations?
b) Starting in year 4 and going to year 12, forecast demand using
a 3-year moving average. Plot your forecast on the same graph
as the original data.
c) Starting in year 4 and going to year 12, forecast demand using
a 3-year moving average with weights of .1, .3, and .6, using .6
for the most recent year. Plot this forecast on the same graph.
d) As you compare forecasts with the original data, which seems
to give the better results? PX
4.3
Refer to Problem 4.2.
Develop a forecast for years 2
through 12 using exponential smoothing with a 5 .4 and a forecast
for year 1 of 6. Plot your new forecast on a graph with the
actual data and the naive forecast. Based on a visual inspection,
which forecast is better? PX
4.5
The Carbondale Hospital is
considering the purchase
of a new ambulance. The decision will rest partly on the
anticipated
mileage to be driven next year. The miles driven during the
past 5 years are as follows
year mileage
1 3,000
2 4,000
3 3,400
4 3,800
5 3,700
a)
Forecast the mileage for next year (6th year) using a 2-year
moving
average.
b)
Find the MAD based on the 2-year moving average. (Hint:
You
will have only 3 years of matched data.)
c)
Use a weighted 2-year moving average with weights of .4
and
.6 to forecast next yearâs mileage. (The weight of .6 is
for
the most recent year.) What MAD results from using this
approach
to forecasting? (Hint: You will have only 3 years of
matched
data.)
d)
Compute the forecast for year 6 using exponential smoothing,
an
initial forecast for year 1 of 3,000 miles, and a 5 .5. PX
4.27
George
Kyparisis owns a company that manufactures
sailboats.
Actual demand for Georgeâs sailboats during each of
the
past four seasons was as follows:
year
season 1 2 3 4
winter 1400 1200 1000 900
spring 1500 1400 1600 1500
summer 1000 2100 2000 1900
fall 600 750 650 500
George
has forecasted that annual demand for his sailboats
in
year 5 will equal 5,600 sailboats. Based on this data and the
multiplicative
seasonal model, what will the demand level be for
Georgeâs
sailboats in the spring of year 5?
4.31
Caf.
Michiganâs manager, Gary Stark, suspects
that
demand for mocha latte coffees depends on the price being
charged.
Based on historical observations, Gary has gathered the
following
data, which show the numbers of these coffees sold over
six
different price values:
price number sold
$2.30 760
$3.50 510
$2.00 980
$4.20 250
$3.10 320
$4.05 480
Using
these data, how many mocha latte coffees would be forecast
to
be sold according to simple linear regression if the price
per
cup were $2.80? PX
4.37
Sales
of tablet computers at Ted Glickmanâs electronics
store
in Washington, D.C., over the past 10 weeks are shown
in
the table below:
weekdemand weekdemand
1 20 6 29
2 21 7 36
3 28 8 22
4 37 9 25
5 25 10 28
a)
Forecast demand for each week, including week 10, using
exponential
smoothing with a = .5 (initial forecast 5 20).
b)
Compute the MAD.
c)
Compute the tracking signal. PX
