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Chapter 9

Forecasting

Chapter Objectives

Be able to:

Differentiate between demand forecasts, supply forecasts, and price forecasts.

Describe the four laws of forecasting.

Select the most appropriate type of forecasting approach, given different forecasting situations.

Describe four qualitative forecasting techniques – market surveys, panel consensus forecasting, the Delphi method, and the life cycle analogy – and explain when they should be used.

Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models.

Develop causal forecasting models using linear regression and multiple regression.

Calculate measures of forecasting accuracy and interpret the results.

Describe the benefits of using computer-based forecasting packages.

Explain what collaborative planning, forecasting, and replenishment (CPFR) is and how it helps supply chain partners synchronize their plans and actions.

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Introduction

Forecast – An estimate of the future level of some variable.

Forecasting is used to determine:

Long-term capacity needs

Yearly business plans

Shorter-term operations and supply chain activities

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Forecast Types

Demand

Overall market demand

Firm-Level demand

Supply

Number of current producers and suppliers

Projected aggregate supply levels

Technological and political trends

Price

Forecast prices for key materials and services

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Laws of Forecasting

Law 1: Forecasts Are Almost Always Wrong (But They Are Still Useful).

Law 2: Forecasts for the Near Term Tend To Be More Accurate.

Law 3: Forecasts for Groups of Products or Services Tend to Be More Accurate.

Law 4: Forecasts Are No Substitute For Calculated Values.

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Selecting a Forecasting Method

Qualitative forecasting techniques – Forecasting techniques based on intuition or informed opinion.

Used when data are scarce, not available, or irrelevant.

Quantitative forecasting models – Forecasting models that use measurable or historical data to generate forecasts.

Time series and causal models

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Selecting a Forecasting Method

Figure 9.2

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Qualitative Forecasting Methods

Market surveys

Panel consensus forecasting

Delphi method

Life-cycle analogy method

Build-up forecasts

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Time Series Forecasting Methods

Time series forecasting models – A quantitative forecasting model that uses a time series to develop forecasts.

Time series – A series of observations arranged in chronological order

Figure 9.3

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Time Series Forecasting Methods

Demand Patterns

Randomness – Unpredictable movement from one time period to the next.

Trend – Long-term movement up or down in a time series.

Seasonality – A repeated pattern of spikes or drops in a time series associated with certain times of the year.

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Time Series Forecasting Methods

Figure 9.4

Time Series Showing Randomness, a Downward Trend, and Seasonality (Higher Demand in the Winter Months

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Time Series Forecasting Methods

Last Period Model - The simplest time series model which uses demand for the current period as a forecast for the next period.

Ft+1 = Dt

where Ft+1= forecast for the next period, t+1

and Dt = demand for the current period, t

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Time Series Forecasting Methods

Table 9.3

Figure 9.5

Last Period

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Time Series Forecasting Methods

Moving Average Model – A time series forecasting model that derives a forecast by taking an average of recent demand values.

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Time Series Forecasting Methods

Two-Period and Four-Period Moving Average Forecasts

Table 9.4

Example: Week 16 = (101 + 109)/2 = 105

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Time Series Forecasting Methods

Two-Period and Four-Period Moving Average Forecasts

Figure 9.6

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Time Series Forecasting Methods

Weighted Moving Average Model – A form of the moving average model that allows the actual weights applied to past observations to differ.

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Example 9.1 – Flavio’s Pizza

Flavio’s Pizza has recorded the following demand history for each Friday night for the past five weeks.

Develop forecasts for week 6 using a two-period moving average and a 3-period weighted moving average using the following demands and weights (0.4, 0.35, and 0.25, starting with the most recent observation.

The three-period weighted moving average forecast would be:

The two-period moving average forecast would be:

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Time Series Forecasting Methods

Exponential Smoothing Model – A form of the moving average model in which the forecast for the next period is calculated as the weighted average of the current period’s actual value and forecast.

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Time Series Forecasting Methods

Exponential Smoothing Model

The general rule for determining the a value:

The greater the randomness in the time series data, the lower the a value should be.

The less randomness in the time series data, the higher the a value should be.

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Example 9.2 – Exponential Smoothing

Using the following time series data, calculate an exponential smoothing forecast for periods 2 through 20 using a smoothing constant value of 0.8

Figure 9.8

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Example 9.2 – Exponential Smoothing

The detailed calculations for F2 through F7 are:

Figure 9.9

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Example 9.2 – Exponential Smoothing

Figure 9.9

Exponential Smoothing Forecast (a = 0.8)

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Time Series Forecasting Methods

Adjusted Exponential Smoothing Model – An expanded version of the exponential smoothing model that includes a trend adjustment factor.

AFt+1 = Ft+1 +Tt+1

where AFt+1 = adjusted forecast for the next period

Ft+1 = unadjusted forecast for the next period = Dt + (1 – ) Ft

Tt+1 = trend factor for the next period = (Ft+1 – Ft) + (1 – )Tt

Tt = trend factor for the current period

 = smoothing constant for the trend adjustment factor

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Time Series Forecasting Models

Linear Regression – A statistical techniques that expresses a forecast variable as a linear function of some independent variable.

Can be used to develop time series and causal forecasting models.

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Time Series Forecasting Models

Linear Regression Calculations for the y intercept (a) and slope (b)

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Example 9.3 – Clem’s Competition Clutches

Mike Clem, owner of Clem’s

Competition Clutches, designs

and manufacturers heavy-duty car

clutches for use in drag racing.

In his first 10 months of business,

Mike has experienced the demand

shown in Table 9.7 and Figure 9.11.

Use Linear Regression to forecast

demand for months 11, 12, and 13.

Table 9.7

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Example 9.3 – Clem’s Competition Clutches

Ten-Month Time Series of Demand

Figure 9.11

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Example 9.3 – Clem’s Competition Clutches

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Example 9.3 – Clem’s Competition Clutches

Figure 9.12

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Time Series Forecasting Models

Seasonality – Repeated patterns or drops in a time series associated with certain times of the year.

Table 9.8

Examples of Products and Service That Experience Seasonality

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Time Series Forecasting Models

Seasonal Adjustments Four-Step Procedure:

For each of the demand values in the time series, calculate the corresponding forecast using the unadjusted forecast model.

For each demand value, calculate (Demand/Forecast). If the ratio is less than 1, then the forecast model overforecasted; if it is greater than 1, then the model underforecasted.

If the time series covers multiple years, take the average (Demand/Forecast) for corresponding months or quarters to derive the seasonal index. Otherwise use (Demand/Forecast) calculated in Step 2 as the seasonal index.

Multiply the unadjusted forecast by the seasonal index to get the seasonally adjusted forecast value.

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Example 9.4 – Seasonal Adjustments

Figure 9.15

Based on the results of the regression model, develop a seasonal index for each month and reforecast months 1 through 24 (January 2016 – December 2017) using the seasonal indices.

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Example 9.4 – Seasonal Adjustments

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Example 9.4 – Seasonal Adjustments

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Example 9.4 – Seasonal Adjustments

Calculate the (Demand/Forecast) for each of the time periods:

January 2012: (Demand/Forecast) = 51/106.9 = 0.477

January 2013: (Demand/Forecast) = 112/205.6 = 0.545

Calculate the monthly seasonal indices:

Monthly seasonal index, January = (.477 + .545)/2 = .511

Calculate the seasonally adjusted forecasts

Seasonally adjusted forecast = unadjusted forecast x seasonal index

January 2012: 106.9 x .511 = 54.63

January 2013: 205.6 x .511 = 105.06

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Example 9.4 – Seasonal Adjustments

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Figure 9.16

Example 9.4 – Seasonal Adjustments

Plot of Seasonally Adjusted Regression Forecast against a Time Series Showing Seasonality

Figure 9.16

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Causal Forecasting Models

Causal Forecasting Models – A class of quantitative forecasting models in which the forecast is modeled as a function of something other than time.

Linear Regression

Multiple Regression

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Causal Forecasting Models

Linear Regression

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Forecasted home sales at 6% mortgage rate:

1,488.58 – 9,846.94(6%) = 898 home sales

Forecasted home sales at 8% mortgage rate:

1,488.58 – 9,846.94(8%) = 701 home sales

Forecasted home sales =

1,488.58 – 9,846.94(mortgage rate)

Causal Forecasting Models

Multiple Regression – A generalized form of linear regression that allows for more than one independent variable.

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Example 9.6 – Lance’s BBQ

Lance’s BBQ Catering Service is a favorite of sports teams in the Raleigh, North Carolina area.

By counting and weighing the guests arriving at a party, they captured the following data:

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Example 9.6 – Lance’s BBQ

Lance has a party coming up and is expecting 60 guests each with an average weight of around 240 lbs.

Use multiple regression to estimate how much barbecue these guests will eat based on the number of guests and average weight.

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Example 9.6 – Lance’s BBQ

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Intercept term = 12.52

Slope coefficient for number of guests = 0.15

Slope coefficient for average weight = 0.15

Barbecue eaten (lbs.) = 12.52 + 0.15 (no. of guests) + 0.15 (average weight)

If expecting 60 guests with average weight of 240 lbs.

Barbecue eaten (lbs.) = 12.52 + 0.15 (60) + 0.15 (240)

= 57.52 lbs. of barbecue

Measures of Forecast Accuracy

Measures of Forecast Accuracy are used to assess how well an individual model is performing or to compare multiple forecast models to one another.

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Measures of Forecast Accuracy

Forecast error for period i (FEi) =

Mean forecast error (MFE) =

Mean absolute deviation (MAD) =

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Measures of Forecast Accuracy

Mean absolute percentage error (MAPE) =

Tracking Signal =

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Example 9.7 – Wolf State University

Andi Irby, director of advising is trying to decide which of two forecasting models does a better job at predicting walk-in demand for student advising.

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Example 9.7 – Wolf State University

Table 9.11

Demand and Forecast Results for Walk-In Advising

at Wolf State University

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Example 9.7 – Wolf State University

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Example 9.7 – Wolf State University

Model 2 has the MFE value closer to 0, it appears to be the least biased.

On average, Model 2 overforecasted by 0.20 walk-ins, while Model 1 overforecasted by 0.70.

Model 2 has the lower MAD and MAPE values.

Model 2 is the superior model.

Andi also develop a tracking signal for the first 20 weeks. The details are shown on the following slide.

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Example 9.7 – Wolf State University

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Computer-Based Forecasting Packages

Computer-based forecasting packages are used to develop, evaluate and change forecasting models as needed.

With enough demand history, a package could quickly evaluate alternative forecasting methods for each item and select the model that best fits the past data.

Some packages can use MFE, MAD, and MAPE or tracking signal criteria to flag a poor forecasting model and kick off a search for a new one. Others can develop multiples forecasts for a single item.

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Collaborative Planning, Forecasting, and Replenishment (CPFR)

CPFR – A set of business processes, backed up by information technology, in which supply chain partners agree to mutual business objectives and measures, develop joint sales and operational plans, and collaborate to generate and update sales forecasts and replenishment plans.

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Forecasting Case Study

Top-Slice Drivers

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