Problem 1: Observations of the demand for a certain part stocked at a parts supply depot during the calendar year 1999 were Month January February March April May June Demand 89 57 144 221 177 280 Month July August September October November December Demand 223 286 212 275 188 312

a. Determine the one-step-ahead forecasts for the demand for January 2000 using 3-, 6-, and 12-month moving averages. b. Using a four-month moving average, determine the one-step-ahead forecasts for July through December 1999. c. Compute MAD, MSE, MAPE for the forecasts obtained in b. Solution: a. MA (3) forecast: 258.33 MA (6) forecast: 249.33 MA (12) forecast: 205.33 b. Month July August September October November December Forecast 205.50 225.25 241.50 250.25 249.00 240.25 Demand 223 286 212 275 188 312 Error -17.50 -60.75 29.50 -24.75 61.00 -71.75

c. MAD = 44.21 MSE = 2391.45 MAPE = 17.91%

EMIS 8348 Homework 1 – Part 1

Solutions

Problem 2: Observed weekly sales of ball peen hammers at the town hardware store over an eightweek period have been 14, 9, 30, 22, 34, 12, 19, 23. a. Suppose that three-week moving averages are used to forecast sales. Determine the one-step-ahead forecasts for weeks 4 through 8. b. Suppose that exponential smoothing is used with a smoothing constant of α = 0.15. Find the exponential smoothing forecasts for weeks 4 through 8. c. Based on the MAD, which method did better? Solution: a. Week 4 5 6 7 8 b. and c. You may start ES forecast from week 1 or start ES forecast from week 4 using MA(3) forecast for the first period. The following are the results for each of the cases. Starting ES forecast from week 1: Week 1 2 3 4 5 6 7 8 Demand 14 9 30 22 34 12 19 23 ES(.15) 14 14 13.25 15.76 16.70 19.29 18.20 18.32 MA(3) |Error|ES |Error|MA

...$83,000, respectively
a) What sales would you predict for 2013, using a simple four-year moving average?
F2013 =
= $65,500
$65,000 is the forecast for 2013
b) What sales would you predict for 2013, using a weighted moving average with
weights of0.50 for the immediate preceding year and 0.3, 0.15, and 0.05 for the
three years before that?
F2013 = 0.50A2012 + 0.3A2011 + 0.15A2010 + 0.05A2009
=0.50(83000) + 0.30(67000) + 0.15(64000) + 0.05(48000)
= 41,500 + 20,100 + 9,600 + 2,400
= $73,600
$73,600 is the forecast for 2013
Q2. Using exponentialsmoothing with a weight of 0.6 on actual values:
a) If sales are $45,000 and $50,000 for 2010 and 2011, what would you forecast for 2012?
(The first forecast is equal to the actual value of the preceding year.)
Actual values are
2010: $45,000
2011: $50,000
α = 0.6
F2012 = 0.60A2011 + 0.40A2010
= 0.60(50000) + 0.40(45000)
=48000
Forecast for 2012 is $48,000
b) Given this forecast and actual 2012 sales of $53,000, what would you then forecast for2009?
Actual value of 2012 = $53,000
F2009 =
Q3. In question 4-1, taking actual 2009 sales of $48,000 as the forecast for 2010, what sales
would you forecast for 2011, 2012, and 2013, using...

...F1 and F2. The actual and the two sets of forecast are as follows
|Period |Demand |F1 |F2 |
|1 |68 |66 |66 |
|2 |75 |68 |68 |
|3 |70 |72 |70 |
|4 |74 |71 |72 |
|5 |69 |72 |74 |
|6 |72 |70 |76 |
|7 |80 |71 |78 |
| | | | |
:
a. Calculate the MAD, for each set of forecast. Given your results, which technique appears to be more accurate? Explain [6 marks]
b. Calculate the MSE, for each set of forecast. Given your results, which technique appears to be more accurate? [6 marks]
c. Calculate the MAPE, for each set of forecast. Given your results, which technique appears to be more accurate? [6 marks]
d. Explain which method is preferable to you [ 2 marks]
Solution Q 2 [20 marks]
.
Question # 3 [10 Marks]
A weather satellite has an expected life of 10 years from the time it is place into earth’s orbit. Determine its probability of failure after each of the following lengths of service....

...exports, forecast the expected number of units to be exported next year.
|Year |Exports |Year |Exports |
|1 |33 |4 |26 |
|2 |32 |5 |27 |
|3 |29 |6 |24 |
b) A small hospital is planning for future needs in its maternity wing. The data below show the number of births in each of the past eight years.
|Year |Births |Year |Births |
|1 |565 |5 |615 |
|2 |590 |6 |611 |
|3 |583 |7 |610 |
|4 |597 |8 |623 |
Use simple linear regression to forecast the annual number of births for each of the next three years. Determine the coefficient of determination for the data and interpret its meaning.
Moving Averages
IPC’s Plant estimates weekly demand for its many materials...

...(production output or sales). In the scenario in the book exercise 9.1 they want you to forecast what the 20X5 figures would be. It does give you some background information, such as the Human services expenses over the past four years.
20X1 [$5,250,000]
20X2 [$5,500,000]
20X3 [$6,000,000]
20X4 [$6,750,000]
Weighted moving averages and moving averages, just use the data for the past three fiscal years. This would look like this
Moving Averages-
20X2 [$5,500,000]
20X3 [$6,000,000]
20X4 [$6,750,000]
20X5 [$6,083,000]
With just the three we already knew the total of $18,250,000. If you divide the total by three you get, $6,083,000.
Weight averages-
20X2 $5,500,000 1=$5,500,000
20X3 $6,000,000 2=12,000,000
20X4 $6,750,000 3=$20,250,000
20X5 $6,300,000 6=$37,750,000
For 20X5 I divided by 6 (which represents the values 1+2+3=6), which equals $6,291,667 or $6,300,000 as a weighted average. From the information gathered a prediction for the forecast can be made.
Exponentialsmoothing:
The alpha method of 0.95 would work here. The formula would look like this: NF=LF + a (LD- LF)
Last Forecast (LF) = $6,300,000
Last Data (LD) = $6,750,000
a = 0.9
NF = LF + (LD LF)
NF = 6,300,000 + 0.95(6,750,000 - 6,300,000)
NF=6,300,000 + 0.95*450,000
NF=6,300,000 +427,500
NF= 6,727,500
Exercise 9.3
Here you are being asked to find the...

...shown below. Develop a 3-week moving average.
|Week |Auto Sales |
|1 |8 |
|2 |10 |
|3 |9 |
|4 |11 |
|5 |10 |
|6 |13 |
|7 |- |
Problem 2:
Carmen’s decides to forecast auto sales by weighting the three weeks as follows:
|Weights Applied |Period |
|3 |Last week |
|2 |Twoweeks ago |
|1 |Three weeks ago |
|6 |Total |
Problem 3:
A firm uses simple exponentialsmoothing with [pic] to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8.
Problem 4:
Exponentialsmoothing is used to forecast automobile battery sales. Two value of [pic] are examined, [pic] and [pic] Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below:
|Month |Actual |Forecast |
| |Battery Sales| |
|January |20 |22 |
|February |21 | ...

...the ecosystem.
b. unless the species require different abiotic factors.
c. because of the competitive exclusion principle.
d. unless the species require different biotic factors.
_____ 5. What would likely happen if the population of the bird species shown in the ecosystem in Figure 4–1 were to suddenly decrease?
a. The fish population would decrease.
b. The fish population would increase.
c. The fish population would remain the same.
d. Fish would leave the ecosystem.
_____ 6. A wolf pack hunts, kills, and feeds on a moose. In this interaction, the wolves are
a. hosts. c. mutualists.
b. prey. d. predators.
_____ 7. A symbiotic relationship in which one organism is harmed and another benefits is
a. mutualism. c. commensalism.
b. parasitism. d. predation.
_____ 8. What is one difference between primary and secondary succession?
a. Primary succession is rapid and secondary succession is slow.
b. Secondary succession begins on soil and primary succession begins on newly exposed surfaces.
c. Primary succession modifies the environment and secondary succession does not.
d. Secondary succession begins with lichens and primary succession begins with trees.
_____ 9. A tropical rain forest may not return to its original climax community after which of the following disturbances?
a. burning of a forest fire c. volcanic eruption
b. clearing and farming d. flooding after a hurricane
_____ 10. Which two...

...ExponentialSmoothing Forecasting Method with Naïve start
Formula: Ft = α (At-1) + (1 – α) (Ft – 1) where:
Ft Forecast for time t
Ft – 1 Past forecast; 1 time ahead or earlier than time t
At-1 Past Actual data; 1 time ahead or earlier than time t
α (read as alpha) as a smoothing constant takes the value between 0 and 1;
or has value of either 0.1 to 0.9.
With value more than 0 .5 (categorized as high), it gives more weight to
recent data;
with value less than 0.5 (categorized as low), it gives more weight to past
data.
With value equal to 0.5, forecast is giving emphasis on the past 3 periods;
With value equal to 0.1, there is little weight on recent data and more on
Past, about 19 periods in the past.
Naïve start is used in absence of forecast data. It is the actual prior...

...Hershey’s, Marketing One Generation Ahead
Joe
MKT350 – Consumer Behavior
Siena Heights University
December 2, 2012
Abstract
Hershey’s Chocolate is one of the most recognizable brands in the U.S. Hershey built this recognition by building brand loyalty. They began to build this loyalty in the early 1990’s by targeting their marketing to adults. The reasons for this are many, but two are that adults eat about 55% of all candy consumed and that mothers shape their children’s early taste in candy. Hershey revised their marketing strategy in several ways. Hershey also has an amusement park in the hometown of the Company, Hershey, Pennsylvania.
Hershey’s, Marketing One Generation Ahead
According to Hubpages (n.d.), Hershey and its rival Mars “…have been fighting for years to obtain market share.” Hershey left their marketing strategy that targeted children and young
adults and chose a marketing strategy that targets adults. The reasons include the fact that adults eat more than 55% of the candy sold and that mothers determine their children’s early taste in candy (Peter & Olson, 2012, p. 383). They have done this by changing the packaging sizes of some of their candy and by introducing other candy that is more popular with adults. This packaging and introduction of new items can change the affectation and cognition of consumers and relate to an increase in awareness which translates to an...