1. The manager of a small health clinic would like to use exponential smoothing to forecast demand for emergency services in the facility. However, she is not sure whether to use a high or low value of α. To make her decision, she would like to compare the forecast accuracy of a high and low α on historical data. She has decided to use an α = 0.7 for the high value and α = 0.1 for the low value.
For both alpha values, enter exponential smoothing forecasts for weeks 2-6, and calculate the MAD for each alpha value.
(Round your answers to 1 decimal place, the tolerance is +/- 0.5)
Initatilize the computations using the naïve method
Week / Demand(in patients serviced)
1 / 430
2 / 289
3 / 367
4 / 470
5 / 468
6 / 365
Exponential Smoothing Forecasts
Week / Demand / α = 0.10 / α = 0.70
1 / 430
2 / 289 / /
3 / 367 / /
4 / 470 / /
5 / 468 / /
6 / 365 / /
MAD: / /
It would be better to use α =
2. A manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. At the end of December, the company wishes to forecast sales for January. The estimate of trend through November has been 200 additional boards sold per month. Average sales have been around 1000 units per month. The demand for December was 1100 units. The company uses α = 0.20 and β = 0.10. Make a forecast including trend for the month of January.
(Round your answers to 0 decimal places, the tolerance is +/-2.)
The level of the series is units.
The trend is units.
The forecast including trend is units.
3. Rosa's Italian restaurant wants to develop forecasts of daily demand for the next week. The restaurant is closed on Mondays and experiences a seasonal pattern for the other six days of the week. Mario, the manager, has collected information on the number of customers served each day for the past two weeks. If Mario expects total demand for next week to be around 350, what is the forecast for each day of next week?
Day / Number of customersWeek 1 / Week 2
Tuesday / 52 / 48
Wednesday / 36 / 32
Thursday / 35 / 30
Friday / 89 / 97
Saturday / 98 / 99
Sunday / 65 / 69
Day / Forecast
Tuesday /
Wednesday /
Thursday /
Friday /
Saturday /
Sunday /
Round your answers to 1 decimal place, the tolerance is +/-0.5
4. The number of students enrolled at Spring Valley Elementary has been steadily increasing over the past five years. The school board would like to forecast enrollment for years 6 and 7 in order to better plan capacity. Use a linear trend line to forecast enrollment for years 6 and 7.
1 / 220
2 / 245
3 / 256
4 / 289
5 / 310
Year 6 forecast:
Year 7 forecast:
(Round your answers to 1 decimal place, the tolerance is +/-0.5)
5. A company uses exponential smoothing with trend to forecast monthly sales of its product, which show a trend pattern.
At the end of week 5, the company wants to forecast sales for week 6. The trend through week 4 has been twenty additional cases sold per week.
Average sales have been eighty-five cases per week. The demand for week 5 was ninety cases. The company uses α = 0.20 and β = 0.10. Make a forecast including trend for week 6.
The smoothing of the level of the series is .
The smoothing of the trend is .
The forecast including the trend is .
(Round your answers to 1 decimal place, the tolerance is +/- 0.3)
6. A company has used three different methods to forecast sales for the past five months. Use MAD and MSE to evaluate the performance of the three methods.
(a) Which forecasting method performed best?
Period / Actual / Method A / Method B / Method C1 / 10 / 10 / 9 / 8
2 / 8 / 11 / 10 / 11
3 / 12 / 12 / 8 / 10
4 / 11 / 13 / 12 / 11
5 / 12 / 14 / 11 / 12
MAD / MSE
Method A / /
Method B / /
Method C / /
(b) Which of these is actually the naïve method?
(Round your answers to 1 decimal place, no tolerance)
7. The following data were collected on the study of the relationship between a company’s retail sales and advertising dollars:
Retail Sales ($) / Advertising ($)31,133 / 17,858
34,557 / 18,683
38,524 / 20,700
43,207 / 23,747
47,274 / 25,515
49,652 / 27,443
53,227 / 31,810
56,070 / 35,033
58,755 / 37,205
60,073 / 38,598
a. Obtain a linear regression line for the data. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Retail Sales = + (advertising)
b. Compute a correlation coefficient and determine the strength of the linear relationship. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Correlation coefficient is . It indicates linear relationship. (Use not rounded amounts to answer this question.)
c. Using the linear regression equation, develop a forecast of retail sales for advertising dollars of $43,298. (Round your answer to 2 decimal places, the tolerance is +/-0.01. Do not round intermediate results used to achieve this answer.)
Forecast = $
8. A manufacturer of thermostats uses a kanban system to control the flow of materials. The packaging center processes 10 thermostats an hour and receives completed thermostats every 30 minutes. Containers hold 5 thermostats each.
(a) How many kanbans are needed for the packaging center?
(Round your answer to 1 decimal place, the tolerance is +/-0.1.)
(b) If management decides to keep two thermostats as safety stock, how many kanbans will be needed?
(Round your answer to 1 decimal place, the tolerance is +/-0.1.)
9. Carlos Gonzales is production manager at an assembly plant that manufactures cordless telephones. The company is planning to install a pull system. The process is being planned to have a usage rate of fifty pieces per hour. Each container is designed to hold ten pieces. It takes an average of thirty minutes to complete a cycle.
(a) How many containers will be needed? containers
(Round your answer to 1 decimal place, the tolerance is +/-0.1.)
b) How will the number of needed containers change as the system improves?
As cycle time decreases, number of containers needed .
10. Anna works on an assembly line where it takes her thirty minutes to produce twenty units of a product needed to fill a container. It takes her an additional five minutes to transport the container to Josh, who works at the next station. The company uses a safety stock of 20 percent. The current assembly line uses five kanbans between Anna’s and Josh’s stations. Compute the demand for the product.
units per minute
(Round your answer to 2 decimal places, the tolerance is +/-0.01.)
As cycle time decreases, number of containers needed .
11. Robert produces 300 units of a product per hour and 30 units are needed to fill a container. It takes fifteen minutes to receive the materials needed from the previous workstation. The company currently uses a safety stock of 10 percent. Determine how the number of kanbans and the inventory level will be affected if the time required for Robert to receive the material increases to thirty minutes.
units per minute
(Round your answer to 1 decimal place.)