Forecasting – Defined
Predicting future events
One of the most important business functions as decisions are based on a forecast of the future
Goal: Generate good forecasts on the average over time and keep errors low
Forecasting is an ongoing process
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Principles of Forecasting
Many types of forecasting models differ in complexity and amount of data & way they generate forecasts.
Common features include:
Forecasts are rarely perfect
Forecasts are more accurate for grouped data than for individual items
Forecast are more accurate for shorter than longer time periods
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Types of Forecasting Methods
Decide what needs to be forecast
Level of detail, units of analysis & time horizon required
Evaluate and analyze appropriate data
Identify needed data & whether it’s available
Select and test the forecasting model
Cost, ease of use & accuracy
Generate the forecast
Monitor forecast accuracy over time
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Types of Forecasting Methods – cont’d
Classified into two groups:
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Types of Forecasting Models
Qualitative methods – judgmental methods
Forecasts generated subjectively by the forecaster
Educated guesses
Quantitative methods – based on mathematical modeling:
Forecasts generated through mathematical modeling
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Qualitative Methods
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Quantitative Methods
Time Series Models:
Assumes information needed to generate a forecast is contained in a time series of data
Assumes the future will follow same patterns as the past
Causal Models or Associative Models
Explores cause-and-effect relationships
Uses leading indicators to predict the future
Housing starts and appliance sales
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Time Series Models
Forecaster looks for data patterns as
Data = historic pattern + random variation
Historic pattern to be forecasted:
Level (long-term average) – data fluctuates around a constant mean
Trend – data exhibits an increasing or decreasing pattern
Seasonality – any pattern that regularly repeats itself and is of a constant length
Cycle – patterns created by economic fluctuations
Random Variation cannot be predicted
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Time Series Patterns
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Time Series Models
Naive:
The forecast is equal to the actual value observed during the last period – good for level patterns
Simple Mean:
The average of all available data – good for level patterns
Simple Moving Average:
The average value over a set time period
(e.g.: the last four weeks)
Each new forecast drops the oldest data point & adds a new observation
More responsive to a trend but still lags behind actual data – good for level patterns; trend + level = bad forecast
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Time Series Models cont'd
Weighted Moving Average:
Method in which “n” of the most recent observations are averaged and past observations may be weighted differently
All weights must add to 100% or 1.00
e.g. Ct .5, Ct-1 .3, Ct-2 .2 (weights add to 1.0)
Allows emphasizing one period over others; above indicates more weight on recent data (Ct=.5)
Differs from the simple moving average that weighs all periods equally – more responsive to trends
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Time Series Models cont'd
Exponential Smoothing:
Most frequently used time series method because of ease of use and minimal amount of data needed
Need just three pieces of data to start:
Last period’s forecast (Ft)
Last periods actual value (At)
Select value of smoothing coefficient, , between 0 and 1.0
If no last period forecast is available, average the last few periods or use naive method
Higher values (e.g. .7 or .8) place a lot of weight on current periods actual demand and influenced by random variation
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Time Series Problem
Determine forecast for periods 7 & 8
2-period moving average
4-period moving average
2-period weighted moving average with t-1 weighted 0.6 and t-2 weighted 0.4
Exponential smoothing with alpha=0.2 and the period 6 forecast being 375
| Period | Actual |
| 1 | 300 |
| 2 | 315 |
| 3 | 290 |
| 4 | 345 |
| 5 | 320 |
| 6 | 360 |
| 7 | 375 |
| 8 |
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Time Series Problem Solution
| Period | Actual | 2-Period | 4-Period | 2-Per.Wgted. | ExponentialSmoothing |
| 1 | 300 | ||||
| 2 | 315 | ||||
| 3 | 290 | ||||
| 4 | 345 | ||||
| 5 | 320 | ||||
| 6 | 360 | ||||
| 7 | 375 | 340.0 | 328.8 | 344.0 | 372.0 |
| 8 | 367.5 | 350.0 | 369.0 | 372.6 |
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Forecasting Trend
Basic forecasting models for trends compensate for the lagging that would otherwise occur
One model, trend-adjusted exponential smoothing uses a three step process
Step 1 – Smoothing the level of the series
Step 2 – Smoothing the trend
Step 3 – Forecast including the trend
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Forecasting trend problem: a company uses exponential smoothing with trend to forecast usage of its lawn care products. At the end of July the company wishes to forecast sales for August. July demand was 62. The trend through June has been 15 additional gallons of product sold per month. Average sales have been 57 gallons per month. The company uses alpha+0.2 and beta +0.10. Forecast for August.
Smooth the level of the series:
Smooth the trend:
Forecast including trend:
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Linear Trend Line
A time series technique that computes a forecast with trend by drawing a straight line through a set of data using this formula:
Y = a + bx
where
Y = forecast for period X
X = the number of time periods from X = 0
A = value of y at X = 0 (Y intercept)
B = slope of the line
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Forecasting Seasonality
Remember it is a regularly repeating pattern
Examples:
University enrollment varies between quarters or semesters; higher in the fall than in the summer
Seasonal Index:
Percentage amount by which data for each season are above or below the mean.
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Forecasting Seasonality Steps
Calculate the average demand per season
E.g.: average quarterly demand
Calculate a seasonal index for each season of each year:
Divide the actual demand of each season by the average demand per season for that year
Average the indexes by season
E.g.: take the average of all Spring indexes, then of all Summer indexes, …
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Forecasting Seasonality Steps – cont'd
Forecast demand for the next year & divide by the number of seasons
Use regular forecasting method & divide by four for average quarterly demand
Multiply next year’s average seasonal demand by each average seasonal index
Result is a forecast of demand for each season of next year
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Seasonality problem: a university must develop forecasts for the next year’s quarterly enrollments. It has collected quarterly enrollments for the past two years. It has also forecast total enrollment for next year to be 90,000 students. What is the forecast for each quarter of next year?
| Quarter | Year 1 | Seasonal Index | Year 2 | Seasonal Index | Avg. Index | Year3 |
| Fall | 24000 | 1.2 | 26000 | 1.238 | 1.22 | 27450 |
| Winter | 23000 | 22000 | ||||
| Spring | 19000 | 19000 | ||||
| Summer | 14000 | 17000 | ||||
| Total | 80000 | 84000 | 90000 | |||
| Average | 20000 | 21000 | 22500 |
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Causal Models
Often, leading indicators can help to predict changes in future demand e.g. housing starts
Causal models establish a cause-and-effect relationship between independent and dependent variables
A common tool of causal modeling is linear regression:
Additional related variables may require multiple regression modeling
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Measuring Forecast Accuracy
Forecasts are never perfect
Need to measure over time
Need to know how much we should rely on our chosen forecasting method
Measuring forecast error:
Note that over-forecasts = negative errors and under-forecasts = positive errors
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Measuring Forecasting Accuracy
Mean Absolute Deviation (MAD)
measures the total error in a forecast without regard to sign
Cumulative Forecast Error (CFE)
Measures any bias in the forecast
Mean Square Error (MSE)
Penalizes larger errors
Tracking Signal
Measures if your model is working; quality
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Accuracy & Tracking Signal Problem: A company is comparing the accuracy of two forecasting methods. Forecasts using both methods are shown below along with the actual values for January through May. The company also uses a tracking signal with ±4 limits to decide when a forecast should be reviewed. Which forecasting method is best?
| Month | Actual sales | Method A | Method B | ||||||
| F’cast | Error | Cum. Error | Tracking Signal | F’cast | Error | Cum. Error | Tracking Signal | ||
| Jan. | 30 | 28 | 2 | 2 | 2 | 28 | 2 | 2 | 1 |
| Feb. | 26 | 25 | 1 | 3 | 3 | 25 | 1 | 3 | 1.5 |
| March | 32 | 32 | 0 | 3 | 3 | 29 | 3 | 6 | 3 |
| April | 29 | 30 | -1 | 2 | 2 | 27 | 2 | 8 | 4 |
| May | 31 | 30 | 1 | 3 | 3 | 29 | 2 | 10 | 5 |
| MAD | 1 | 2 | |||||||
| MSE | 1.4 | 4.4 |
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Selecting the Right Forecasting Model
The amount & type of available data
Some methods require more data than others
Degree of accuracy required
Increasing accuracy means more data
Length of forecast horizon
Different models for 3 month vs. 10 years
Presence of data patterns
Lagging will occur when a forecasting model meant for a level pattern is applied with a trend
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Predictive Analytics and Forecasting
Uses statistics, modeling and data mining to analyze currentand historical facts to make predictions on the futureAbility to forecast events before they happen by sensing smallchanges over time
Forecasting Within OM: How It All Fits Together
Forecasts impact not only other business functions but all other operations decisions. Operations managers make many forecasts, such as the expected demand for a company’s products.
These forecasts are then used to determine:
Product designs that are expected to sell (Ch 2)
The quantity of product to produce (Chs 5 and 6)
The amount of needed supplies and materials (Ch 12)
Future space requirements (Ch 10)
Capacity and location needs (Ch 9)
The amount of labor needed (Ch 11)
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Forecasting within OM – cont'd
Forecasts drive strategic operations decisions, such as:
Choice of competitive priorities, changes in processes, and large technology purchases (Ch 3)
Forecast decisions serve as the basis for tactical planning; developing worker schedules (Ch 11)
Virtually all operations management decisions are based on a forecast of the future.
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