Business Finance - Operations Management OPMT 620: Operations Management - Case Study McDonalds Assignment

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Demand

Forecasting

Sam Lampropoulos George Brown College

Chapter

Bombardier Business Aircraft

Every year, Bombardier Business Aircraft (BBA) produces a 10-year rolling demand forecast for its business jets. Factors such as world GDP growth, stock market returns, positive interest rate spread, and oil prices are all closely monitored inputs to the forecasting process.

Learning Objectives

Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches.

Describe at least three judgmental forecasting methods.

Describe the components of a time series model, and explain averaging techniques and solve typical problems.

Describe trend forecasting and solve typical problems.

Describe seasonality forecasting and solve typical problems using both the centered moving average and annual average methods.

Describe associative models (regression) and solve typical problems.

Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems.

Identify the major factors to consider when choosing a forecasting technique.

What is forecasting?

Features common to all forecasts

Elements of a good forecast

Steps in the forecasting process

Approaches to forecasting

Judgmental methods

Time series models

Associative models

Accuracy and control of forecasts

Choosing a forecasting technique

Excel Templates

Chapter Outline

What is Forecasting?

I see that you will get a 100 in OM this semester.

A demand forecast is an estimate of demand expected over a future time period

Forecasting Answers…

How big a facility do I need to manufacture a new videophone?

How much money do I need to run operations of my accounting office?

How many pairs of white shoes should I order for the summer season in my store?

How many operators should I schedule next month for my call centre?

How much lettuce should I buy for next week in my restaurant?

3 Uses for Forecasts

Design the System

Long term (annual)

(Types of products & services to offer, capacities, equipment, location)

Use of the System

Medium term (monthly)

(Inventory, workforce levels, planning production)

Schedule the System

Short term (daily, weekly)

(Production, purchasing, staff scheduling)

Features Common to All Forecasts

Assumes causal system past ==> future

Forecasts rarely perfect because of randomness

Forecasts more accurate for groups vs. individuals

Forecast accuracy decreases as time horizon increases

Page #61.

A manager cannot simply delegate forecasting to models or computers and then forget about it, because unplanned or special occurrences can wreak havoc with forecasts. For instance, weather-related events, sales promotions, and changes in features or prices of the company’s own and competing goods or services can have a major impact on demand. Consequently, a manager must be alert to such occurrences and be ready to override forecasts.

Elements of a Good Forecast

1. The forecast should be timely. The forecasting horizon must cover the time necessary to implement possible changes so that its results can be used.

2. The degree of accuracy of the forecast should be stated.

3. The forecasting method/software chosen should be reliable; it should work consistently.

4. The forecast should be expressed in meaningful units. Financial planners need to know demand in dollars, whereas demand and production planners need to know demand in units.

5. The forecast should be in writing so all concerned are using the same information, In addition, a written forecast will permit an objective basis for evaluating the forecast once actual results are in.

6. The forecasting technique should be simple to understand and use.

7. The forecast should be cost-effective. The benefits should outweigh the costs.

Accurate and in writing

Reliable

Meaningful

Cost-effective

Simple to understand & use

Useful time horizon

Steps in the Forecasting Process

1. Determine purpose of forecast

2. Establish a time horizon

3. Gather and analyze relevant historical data

5. Prepare the forecast

6. Monitor the forecast

4. Select a forecasting technique

Approaches to Forecasting

Judgmental

Non-quantitative analysis of subjective inputs

Considers “soft” information such as human factors, experience, gut instinct

Quantitative: analyze “hard” data

Time series models

Extends historical patterns of numerical data

Associative models

Create equations with explanatory variables to predict the future

There are two general approaches to forecasting: judgmental and quantitative. Judgmental methods consist mainly of subjective inputs, which may defy precise numerical description (but may still depend on historical data). Quantitative methods involve either the use of a time series model to extend the historical pattern of data into the future, or the development of associative models that attempt to utilize causal (explanatory) variables to make a forecast.

Judgmental Methods

Executive opinions

Pool opinions of high-level executives

Long term strategic or new product development

Sales force opinions

Based on direct customer contact

Judgmental Methods

Consumer surveys

Questionnaires or focus groups

Historical analogies

Use demand for a similar product

Expert opinions

Delphi method: iterative questionnaires circulated until consensus is reached

Technological forecasting

What is a Time Series?

Time series is a time ordered sequence of observations taken at regular intervals of time.

The following six patterns could be identified in a time series:

Level: (average) horizontal pattern

Trend: steady upward or downward movement

Seasonality: regular variations related to time of year or day

Cycles: wavelike variations lasting more than one year

Irregular variations: caused by unusual circumstances, not reflective of typical behaviour

Random variations: residual variations after all other behaviours are accounted for (called noise)

Patterns of a Time Series

Year

Seasonal peaks (winters)

Trend component

Actual demand line

Demand for snowboards

Random variation

Time Series Models

Naive methods

Averaging methods

Moving average

Weighted moving average

Exponential smoothing

Trend models

Linear and non-linear trend

Trend adjusted exponential smoothing

Techniques for seasonality

Techniques for cycles

Naive Methods

Next period = last period

Simple to use and understand

Very low cost

Low accuracy

F = forecast A = actual

Page #66

A simple but widely used approach to forecasting is the naïve method. The naïve method can be used with a stable series (level or average with random variations), with seasonal variations, or with trend. With a stable series, the last data point becomes the naïve forecast for the next period. Thus, if the demand for a product last week was 20 cases, the forecast for this week is 20 cases.

With seasonal variations, the naïve forecast for this “season” is equal to the value of the series last “season.” For example, the forecast for demand for turkeys this Christmas is equal to demand for turkeys last Christmas.

For data with trend, the naïve forecast is equal to the last value of the series plus or minus the difference between the last two values of the series.

Naive Method - Example

Uh, give me a minute....

We sold 250 wheels last

week.... Now, next week we should sell....

Page #66

Answer is 250

Naive Method with Trend: Example

2 years ago we sold 50 memberships. Last year we sold 75 memberships. This year we expect to sell …

100

Page #66

Averaging Methods

F = forecast A = actual  = smoothing constant

Moving Average

Average of last few actual data values, updated each period:

Easy to calculate and understand

Smooths bumps, lags behind changes

Choose number of periods to include:

Fewer data points = more sensitive to changes

More data points = smoother, less responsive

Moving Average - Example

Compute a three-period moving average forecast for period 6, given the demand below:

Example 3-1

Example 3-1 Page # 67.

Graph of Moving Average

| | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12

Quantity

30 –

28 –

26 –

24 –

22 –

20 –

18 –

16 –

14 –

12 –

10 –

Actual Sales

Moving Average Forecast

Figure 3-3 Page #68 displays the smoothing aspect of a moving average forecast. This graphic displays both the smoothing aspect as well as the responsiveness lag of this technique.

Weighted Moving Average - Example

Compute a 4-period weighted moving average forecast for period 6 using a weight of 0.4 for the most recent period, 0.3 for the next, 0.2 for the next, and 0.1 for the next.

The choice of weights may involve the use of trial and error to find a suitable weighting scheme.

Weights must add up to 100%.

Example 3-2

Example 3-2 Page #68-#69

Weighted Moving Average Example

1 9

2 12

3 14

4 16

5 19

6 23

7 26

Period Demand Forecast

Apply weights of .5 for most recent period, then .3, then .2

[(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6

[(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1

[(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4

[(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4

Note: now the weights remain in the same place in the model. As the demand data becomes “older” it is pushed back in the formula and less weight is applied as this data becomes less relevant in the model.

Moving Average and Weighted Moving Average

30 –

25 –

20 –

15 –

10 –

5 –

Quantity

| | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12

Actual sales

Moving average

Weighted moving average

Depending on the weights used the weighted moving average model can be more responsive than the moving average model.

Exponential Smoothing

Sophisticated weighted moving average

New forecast is based on the previous forecast plus a percentage of the difference between that forecast and the previous actual value

Subjectively choose smoothing constant 

 ranges from 0 to 1 (commonly .05 to .5)

Widely used

Easy to use

Easy to alter weighting

Exponential Smoothing Formula

New Forecast = previous forecast plus a percentage of the forecast error

Actual - Forecast is the error term

 is the % of the error applied to the previous forecast to generate a new forecast

Ft = Ft-1 + (At-1 - Ft-1)

F = forecast A = actual

Formula 3-2a

Page #69-#70 Formula 3-2a

Exponential Smoothing: Example

Forecasted demand = 142 video games

Actual demand = 153

Smoothing constant  = .20

New forecast = 142 + .2 (153 - 142)

= 142 + .2 (11)

= 142 + 2.2 ≈ 144.2 games

Exponential Smoothing: Alternate Formula

Forecast = previous forecast plus a percentage of the forecast error

 is the weight on actual demand

(1 -) is the weight on previous forecast

Ft = (1 - )Ft-1 + (At-1)

F = forecast A = actual

Formula 3-2b

Page # 69 Formula 3-2b

Exponential Smoothing: Example

Forecasted demand = 142 video games

Actual demand = 153

Smoothing constant  = .20

New forecast = .2 (153) + (1 - .2)(142)

= 30.6 + 113.6

= 144.2 ≈ 144 games

Example using 3-2b formula

Exponential Smoothing: Example

Prepare a forecast using smoothing constant  = 0.40.

What is the starting point? An initial forecast value must be determined.

a) average of several periods of actual data

b) subjective estimate (for this example, use 60)

c) first actual value (naïve approach)

The slide identifies three different methods a), b), c) to determine an initial forecast value for period #1.

Exponential Smoothing: Your Turn!

What are the exponential smoothing forecasts for periods 2-5 using  =0.7?

Use naïve approach for 1st week

F2= 820 + 7 (820 - 820) =820

F3= 820 + .7 (775 - 820) = 788.5

Exponential Smoothing: Your Turn!

Selecting a Smoothing Constant 

The larger the smoothing constant (alpha) the more responsive the forecast!

Page #70 The smoothing constant of .4 in the example results in a more responsive forecast than a smoothing constant of .1.

Choosing 

When demand is fairly stable, use a lower value for 

Smooths out random fluctuations

When demand increasing or decreasing, use a higher value for 

More responsive to real changes

Try to find balance

Trial and error

Can change over time

True or False?

A moving average forecast tends to be more responsive to changes in the data series when more data points are included in the average.

False

As compared to a simple moving average, the weighted moving average is more reflective of the recent changes.

True

A smoothing constant of .1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of .3 will.

False

Excel: Exponential Smoothing

Solved Problem 1: Excel Template

Note: this template is not included in the text.

Techniques for Trend

Involves the development of an equation that describes the trend (presuming a trend is present in the data)

Look at historical data to discover if a trend exists

Nonlinear Trends

Figure 3-5

Figure 3-5 Page #71

Linear Trend Equation

Fit a trend line to a series of historical data

Use regression to find the equation of the line (called the Least Squares Line)

Page # 71 formulas (3-3), (3-4), (3-5)

Linear Trend

Deviation

Time

Demand

Actual observation

Points on the line

A linear trend line develops a “line of best fit” amongst the actual observation “data points”.

Linear Trend: Example

Excel - Linear Trend

Insert Chart

Scatter

Highlight data range

Right Click on a data point

Add Trendline Type: Linear Options: Display equation on chart

Or Insert Functions:

=SLOPE(Range of y's,Range of x's)

=INTERCEPT(Range of y's,Range of x's)

Excel - Linear Trend

Page #72

Trend-Adjusted Exponential Smoothing

Select values (usually through trial and error) for:

a = Smoothing constant for average

b = Smoothing constant for trend

Estimate starting smoothed average and smoothed trend

Use most recent data

Trend-adjusted exponential smoothing; variation of exponential smoothing used when a time series exhibits trend.

A variation of simple exponential smoothing can be used when a time series exhibits trend. It is called trend-adjusted exponential smoothing or double exponential smoothing. If a series exhibits trend, and exponential smoothing is used on it, the forecasts will all lag behind the trend: if the data are increasing, each forecast will be too low; if the data are decreasing, each forecast will be too high.

Trend-Adjusted Exponential Smoothing

TAFt+1 = St + Tt

Where:

St = smoothed series at the end of period t

Tt = smoothed trend at the end of period t

St = TAFt +α(At  TAFt)

Tt = Tt-1 + ( St  St-1 Tt-1)

Page #74 formulas (3-6) , (3-7)

where α and β are smoothing constants, and At = actual value in period t. In order to use this method, one must select values of α and β (usually through trial and error) and make an estimate of starting smoothed series and smoothed trend. We will use the first few data points to estimate the smoothed series and smoothed trend.

Trend-Adjusted Forecast: Example

Table 3-1

Table 3-1 Page #74

Techniques for Seasonality

Seasonal Variations: regularly repeating wavelike movements in series values that can be tied to recurring events, weather, or a calendar.

Examples of seasonality are retail trade, ice cream production, and residential natural gas sales

Most seasonal variations repeat annually.

also applied to shorter lengths of repeating patterns.

e.g. rush hour traffic occurs twice a day

Theatres and restaurants demand higher on Fridays or weekend

Banks may experience daily and weekly repeating “seasonal” variations (heavier traffic at lunch, just before closing, on Friday)

Techniques for Seasonality

Additive or Multiplicative Model

Quantity added to average or trend

Or proportion x average or trend

Time

Demand

Additive Model

Demand = Trend + Seasonality

Multiplicative Model

Demand = Trend x Seasonality

Figure 3-6

Figure 3-6 Page #77

There are two different models of seasonality: additive and multiplicative. In the additive model, seasonality is expressed as a quantity (e.g., 20 units), which is added to or subtracted from the series average (or trend). In the multiplicative model, seasonality is expressed as a proportion of the average (or trend) amount (e.g., 1.10), which is then multiplied by the average (or trend) of the series.

Using Seasonal Relatives

Seasonal Relative (or index)

Equals proportion of average or trend for a season in the multiplicative model

Seasonal relative of 1.2 = 20% above average

Deseasonalize

Remove seasonal component to more clearly see other components

Divide by seasonal relative

Reseasonalize

Adjust the forecast for seasonal component

Multiply by seasonal relative

Seasonal relatives are used first to deseasonalize the data, and later to incorporate seasonality in the forecast of deseasonalized data (i.e., to reseasonalize the data).

Times Series Decomposition

1. Compute the seasonal relatives.

2. De-seasonalize the demand data.

3. Fit a model to de-seasonalized demand data, e.g., moving average or trend.

4. Forecast using this model and the de-seasonalized demand data.

5. Re-seasonalize the deseasonalized forecasts.

Techniques for Seasonality - Example

Predict quarterly demand for a certain loveseat

The series has both trend and seasonality

Quarterly relatives:Q1= 1.20, Q2 = 1.10, Q3 = 0.75, Q4 =0.95.

Trend equation yt=124+7.5t (t = quarter 15)

Predict demand for quarter 2 (where t 15 = quarter 2)

Example 3-7

Example 3-7 Page #79

Techniques for Cycles

Cycles are wavelike movements, similar to seasonal variations, but of longer duration—say, two to six years between peaks.

Examples of cyclical variations can be found in the economies of countries where they experience times of growth (inflation) followed by recession (slowing down or “shrinking” economy).

Associative Forecasting

Associative models rely on identification of related variables that can be used to predict values of the variable of interest.

For example, the number of new housing starts in Canada is related to mortgage rates. As mortgage rates fluctuate so too does the demand for new homes.

Lending rates

Demand for homes

Associative Forecasting

If I want to predict ridership originating from a new train station, what data might I look at?

Find (predictor) variables that are associated with ridership at other stations

Associated = correlated = as one moves the other moves

Create a model that shows the relationship between the predictor variables and the predicted variable (e.g., ridership)

Technique is regression analysis

Simple linear regression with one variable

Multiple regression (can be non-linear)

Test the model to see which variables most useful in predicting ridership

Use the model to predict ridership, given values of the predictor variables

Associative Models

Predictor variables (x): used to predict values of the variable of interest (y)

(also called independent variables)

Linear regression: process of finding a straight line that best fits a set of points on a graph

(use the Least Squares Equation)

Multiple regression: models with more than one predictor variable

(computations complex, created with computer)

Simple Linear Regression

Would a linear model be reasonable?

Computed relationship

Like Figure 3-8 Page # 84

Note the equations and method is the same as linear trend

Excel: Simple Linear Regression

Table 3-2 Example 3-11

Table 3-2 Page #86. Image of Excel template for Example 3-11

Correlation coefficient (r): measure of the strength of relationship between two variables

Ranges from -1 to +1

-1 = two variables move together in same direction

+1 = two variables move together in opposite direction

=CORREL(Range of y values, Range of x values)

r2 measures proportion of variation in the values of y that is “explained” by the predictor variables in the regression model

Ranges from 0 to 1

higher values = more useful predictors

=RSQ(Range of y values, Range of x values)

Correlation and Excel

Accuracy and Control of Forecasts

Accuracy and control of the forecasting process are vital aspects of forecasting.

Forecasting accuracy is the degree of correctness of the forecasts generated by the forecasting process.

Accurate forecasts are necessary for the success of daily activities of every organization.

Inaccurate forecasts can result in too few or too many resources, too little or too much output, or the wrong output!

Accuracy and Control of Forecasts

Error = Actual value - Forecast value

+ve = forecast too low, -ve = too high

Three measures of forecasts are used:

Mean absolute deviation (MAD)

Mean squared error (MSE)

Mean absolute percent error (MAPE)

Control charts

plot errors to see if within pre-set control limits

Tracking signal

Ratio of cumulative error and MAD

Error, MAD, MSE and MAPE

Page #90 Formulas (3-13), (3-14), (3-15)

MAD, MSE and MAPE; Characteristics

MAD

Easy to compute

Weights errors linearly

MSE

Squares error

More weight to large errors

MAPE

Puts errors in perspective

Above 70% satisfactory

MAD, MSE and MAPE: Example

Compute MAD, MSE, and MAPE for the following data.

Example 3-13

Example 3-13 Page #90

Forecast Errors and Bias!

Bias = the sum of the forecast errors

+ve bias = frequent underestimation

-ve bias = frequent overestimation

Possible sources of error include:

Model may be inadequate (things have changed)

Incorrect use of forecasting technique

Irregular variations

Controlling the Forecasting Process

It is necessary to monitor forecast errors to ensure that the forecasting process is performing adequately and remains accurate enough.

If not, corrective action should be taken.

Monitoring forecast errors is usually accomplished by either a control chart or a tracking signal.

Control Chart

Tracking Signal

Accurate Forecast!

Controlling the Forecasting Process

Control chart

A visual tool for monitoring forecast errors

Used to detect non-randomness in errors

Set limits that are multiples of the √MSE

Forecasting errors are “in control” when only random errors, no errors from identifiable causes

“In control” if

All errors are within control limits

No patterns (e.g. trends or cycles) are present

Errors outside limit = need corrective action

Control Chart

Figure 3-11

Conceptual representation of a control chart.

Figure 3-11 Page #91

Controlling Forecasts: Control Limits

Standard deviation of error

Control Limits

0 ± 2 (or 3) s

95% of all errors should be within 2s

97.7% of all errors should be within 3s

Note: the denominator is typically n-1 (as using sample data to estimate the standard deviation). The text uses n to simplify. This is accurate enough if have a large n. See note at bottom of page # 91

Control Chart Example

Errors should be within ± 2(6.46).

Lower limit = -12.92 Upper limit = 12.92

Example 3-15

Example 3-15 Page # 92

Control Chart Example

All the errors are within the control limits?

What is happening to our forecast accuracy?

Is there an identifiable pattern to our forecast errors?

Upper Control Limit

Lower Control Limit

Mean

Month

Example 3-15 Page # 92 continued… Month

All of the errors are within the established control limits. However, there is a trend to our forecast errors and our forecast is starting to display Bias (excessively negative errors.)

Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart.

Month

Sales

Forecast

220

n/a

250

255

210

205

300

320

325

315

Pharmacy Forecast Control: Your Turn!

Month

Sales

Forecast

Abs Error

220

n/a

250

255

210

205

300

320

325

315

Sq. Error

400

100

550

Pharmacy Forecast Control: Your Turn!

All the errors are within the control limits

Errors should be within ± 2(11.7).

Lower limit = -23.4 Upper limit = 23.4

Upper Control Limit

Lower Control Limit

Mean

Tracking Signal

Tracking Signal: used to control the forecasting process

Sum of forecast errors divided by MAD

Can be plotted on a control chart

Investigate if TS > 4

Tracking signal

(Actual

forecast)

MAD



True or False?

When error values fall outside the limits of a control chart, this signals a need for corrective action.

Ans: True

When all errors plotted on a control chart are either all positive, or all negative, this shows that the forecasting technique is performing adequately.

Ans: False

A random pattern of errors within the limits of a control chart signals a need for corrective action.

Ans: False

Choosing a Forecasting Technique

No single technique works in every situation

Two most important factors

Cost

Accuracy

Other factors in selecting a forecasting technique:

Availability of historical data

Forecasting horizon

Pattern of Data

Choosing a Forecast Technique

Table 3-3

Forecasting Method	Amount of Historical Data	Data Pattern	Forecasting Horizon	Preparation Time	Complexity
Simple exponential smoothing	5 to 10 observations	Data should be stationary	Short	Short	Little sophistication
Trend-adjusted exponential smoothing	10 to 15 observations	Trend	Short to medium	Short	Moderate sophistication
Regression trend models	10 to 20 observations	Trend	Short, medium, long	Short	Moderate sophistication
Seasonal	Enough observations to see two peaks and troughs	Seasonal patterns	Medium	Short to moderate	Moderate sophistication
Causal regression models	10 observations per independent variable	Can handle complex patterns	Medium or long	Long	Considerable sophistication

Table 3-3 Page #93 Table 3-3 provides a guide for selecting an appropriate forecasting method.

Choosing a Forecast Technique

Table 3-4

<t</t[removed]

Factor	Short Term	Medium Term	Long Term
Frequency	Daily, weekly	Monthly, quarterly	Annual
2. Level of aggregation	Item	Product family	Total output
3. Type of model	Smoothing, trend, regression	Trend and seasonal regression	Managerial judgement, trend, regression