04 - Forecasts based on Time Series Data (Ch03) - Q&A PDF

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Book Name: Operations Management - Stevenson - 11th Edition
Chapter 3 (Forecasting)
Materials Type: Practice...

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Forecasts based on Time Series Data REVISION SHEET DR. ALY ELSHEKH

Forecasts based on Time Series Data 2021 1. Essay Questions a) Explain the different patterns of the forecasts based on time series data and illustrate your answer using diagrams. Trend  long-term upward or downward in data Seasonality  short-term regular variations related to the calendar or time of day. Cycle  Wavelike variations of more than one year’s duration Irregular variations  Caused by unusual circumstances, not reflective of typical behavior. Random variations  Residual variations after all other behaviors are accounted for.

…………………………………………………………………………………………………………. b) Discuss the characteristics of the naïve forecasts.

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Simple to use

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Virtually no cost

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Quick and easy to prepare

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No data analysis

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Easily understandable

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Cannot provide high accuracy

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Can be a standard for accuracy

Forecasts based on Time Series Data 2021

…………………………………………………………………………………………………………. c) Describe three averaging techniques Moving average Definition  Technique that averages a number of recent actual values, updated as new values become available. n

Mathematical Form 

MA n =

A t−i ∑ i=1 n

Weighted average Definition  More recent values in a series are given more weight in computing a forecast. Mathematical Form  Ft = (At-1 * Wt-1 ) + (At-2 * Wt-2 ) + (At-3 * Wt-3) Exponential smoothing Definition  A weighted averaging method based on previous forecast plus a percentage of the forecast error. Mathematical Form  Ft = Ft-1 + a (At-1 - Ft-1)

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Forecasts based on Time Series Data 2021

2. True / False Questions Question

T/F

Explanation

1. Forecasting techniques that are based on time series data assume that future values of the series will duplicate past values.

F

Time-series forecast assume that future patterns in the series will mimic past patterns in the series.

2. The naive forecast can serve as a quick and easy standard of comparison against which to judge the cost and accuracy of other techniques.

T

Often the naïve forecast performs reasonably well when compared to more complex techniques.

3. In order to update a moving average forecast, the values of each data point in the average must be known.

T

The moving average cannot be updated until the most recent value is known.

4. Exponential smoothing adds a percentage (called alpha) of last period's forecast to estimate next period's demand.

F

Exponential smoothing adds a percentage to the last period's forecast error.

5. Exponential smoothing is a form of weighted averaging.

T

The most recent period is given the most weight, but prior periods also factor in.

6. An advantage of a weighted moving average is that recent actual results can be given more importance than what occurred a while ago.

T

7. Exponential smoothing adds a percentage (called alpha) of last period's forecast to estimate next period's demand.

F

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Exponential smoothing adds a percentage to the last period's forecast error.

Forecasts based on Time Series Data 2021

3. Problems Problem 1: An electrical contractor’s records during the last five weeks indicate the number of job requests:

Predict the number of requests for week 6 using each of these methods: a) Naive b) A four-period moving average c) Exponential smoothing with α = .30; use 20 for week 2 forecast Solution: a) 22 22 + 18 + 21 + 22 =20. 75 4 b)

c) F3 = 20 + .30(22 – 20) = 20.6 F4 = 20.6 + .30(18 – 20.6) = 19.82 F5 = 19.82 + .30(21 – 19.82) = 20.17 F6 = 20.17 + .30(22 – 20.17) = 20.72 ………………………………………………………………………………………………

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Forecasts based on Time Series Data 2021 Problem 2: Simple exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be four units less than actual demand. The next forecast is 66.6, implying a smoothing constant, alpha, equal to: Given: Ft-1 = 66 Ft = 66.6 At-1 = 70 Solution: Ft = Ft-1 + α (At-1 - Ft-1) 66.6 = 66 + α x 4 α = 0.6 / 4 = 0.15 ……………………………………………………………………………………………… Problem 3: Given an actual demand of (59), a previous forecast of (64), and an alpha of (0.3). what would the forecast for the next period be using simple exponential smoothing? Given: Ft-1 = 64 At-1 = 59 α = 0.3 Solution: Ft = Ft-1 + α (At-1 - Ft-1) Ft = 64 + 0.3 x -5 = 62.5 ………………………………………………………………………………………………

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Forecasts based on Time Series Data 2021 Problem 4: Given an actual demand of 105, a forecasted value of 97, and an alpha of .4, the simple exponential smoothing forecast for the next period would be: Given: Ft-1 = 97 At-1 = 105 α = 0.4 Solution: Ft = Ft-1 + α (At-1 - Ft-1) Ft = 97 + 0.4 x 8 = 100.2 ……………………………………………………………………………………………… Problem 5: A manager is using exponential smoothing to predict merchandise returns at a suburban branch of a department store chain. Given a previous forecast of 140 items, an actual number of returns of 148 items, and a smoothing constant equal to .15, what is the forecast for the next period? Given: Ft-1 = 140 At-1 = 148 α = 0.15 Solution: Ft = Ft-1 + α (At-1 - Ft-1) Ft = 140 + 0.15 x 8 = 141.2 ……………………………………………………………………………………………… Problem 6: A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing constant of .1 is used. a) Prepare a forecast for September. b) Assuming actual September usage of 92 percent, prepare a forecast for October usage.

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Forecasts based on Time Series Data 2021 Solution: a) FSeptember = 88 + .1(89.6 – 88) = 88.16 b) FOctober

= 88.16 + .1(92 – 88.16) = 88.54

……………………………………………………………………………………………… Problem 7: Given the following historical data, what is the simple three-period moving average forecast for period 6?

Solution: = (67 + 72 + 65) / 3 = 68 ………………………………………………………………………………………………

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Forecasts based on Time Series Data 2021 Problem 8: Develop a forecast for the next period, given the data below, using a 3-period moving average.

Solution: = (17 + 19 + 18) / 3 = 18 …………………………………………………………………………………………… Problem 9: The owner of Darkest Tans Unlimited in a local mall is forecasting this month's (October's) demand for the one new tanning booth based on the following historical data:

Solution: = 0.4 x 160 + 0.3 x 120 + 0.2 x 150 + 0.1 x 110 = 141 …………………………………………………………………………………………… Problem 10: Given the data below, develop a forecast for period 6 using a four-period weighted moving average and weights of .4, .3, .2 and .1

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Forecasts based on Time Series Data 2021

Solution: = 0.4 x 17 + 0.3 x 19 + 0.2 x 18 + 0.1 x 20 = 18.1 …………………………………………………………………………………………… Problem 11: Given the following historical data and weights of .5, .3, and .2, what is the threeperiod moving average forecast for period 5?

Solution: = 0.5 x 144 + 0.3 x 148 + 0.2 x 142 = 144.8 ………………………………………………………………………………………………

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