fall, 2012 emba 512 demand forecasting boise state university 1 demand forecasting
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Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Objectives• Understand the role of forecasting• Understand the issues• Understand basic tools and techniques
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Forecasting• Developing predictions or estimates of
future values– Demand volume– Price levels– Lead times– Resource availability– ...
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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The Role of Forecasting
• Necessary Input to all Planning Decisions– Operations: Inventory, Production Planning &
Scheduling– Finance: Plant Investment & Budgeting– Marketing: Sales-Force Allocation, Pricing
Promotions– Human Resources: Workforce Planning
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Demand Forecasting
For manufactured items and conventional goods, forecasts are used to determine
• Replenishment levels and safety stocks• Set production plans• Determine procurement schedules• Capacity planning, financial planning, &
workforce planning
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Demand Forecasting
For services, demand forecasts are used for• Capacity planning, workforce scheduling,
procurement & budgeting.• Because services cannot be stored,
demand forecasting for services is often concerned with forecasting the peak demand, rather than the average demand and its range.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Characteristics of Forecasts
• Forecast are always wrong. A good forecast is more than a single value.
• Forecast accuracy decreases with the forecast horizon.
• Aggregate forecasts are more accurate than disaggregated forecasts.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Independent vs. Dependent Demand
• Independent– Exogenously controlled– Subject to random or unpredictable changes– What we forecast
• Dependent or Derived– Calculated or derived from other sources– Do not forecast
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Forecasting MethodsQualitative or Judgmental
– Ask people who ought to know• Historical Projection or Extrapolation
– Time Series Models• Moving Averages• Exponential Smoothing
– Regression based methods
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Basic Approach to Demand Forecasting
• Identify the Objective of the Forecast• Integrate Forecasting with Planning• Identify the Factors that Influence the
Demand Forecast• Identify the Appropriate Forecasting Model• Monitor the Forecast (Measure Errors)
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series Methods
• Appropriate when future demand is expected to follow past demand patterns.
• Future demand is assumed to be influenced by the current demand, as well as historical growth and seasonal patterns.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series Models
With time series models observed demand can be broken down into two components: systematic and random.
Observed Demand = Systematic Component + Random Component
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series Methods
The systematic component is the expected demand value. It is comprised of the underlying average demand, the trend in demand, and the seasonal fluctuations (seasonality) in demand.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Idea Behind Time Series Models
Distinguish between random fluctuations and true changes in
underlying demand patterns.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series Components of Demand
Time
Demand
Random component
Monthly chart of the DJIA's changes from month to month along with a 3 period simple moving average.
Fall, 2012 16EMBA 512 Demand ForecastingBoise State University
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series Methods
• The random component cannot be predicted. However, its size and variability can be estimated to provide a measure of forecast error. The objective of forecasting is to filter the random component and model (estimate) the systematic component.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Moving Averages• Simple, widely used• Reduce random noise• One Extreme
– Prediction next period = Demand this period• Another Extreme
– Prediction next period = Long run average• Intermediate View
– Prediction next period = Average of last n periods
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Moving Average Models
Period Demand1 122 153 114 95 106 87 148 12
3-period moving averageforecast for Period 8:
= (14 + 8 + 10) / 3= 10.67
n
DF
n
iit
t
11
1
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Weighted Moving Averages
Forecast for Period 8= [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.2)= 11.4
What are the advantages?What do the weights add up to?Could we use different weights?Compare with a simple 3-period moving average.
n
iit
n
iitit
tW
DWF
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111
1
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Table of Forecasts and Demand Values . . .
PeriodActual
Demand
Two-PeriodMovingAverageForecast
Three-Period Weighted MovingAverage Forecast Weights =
0.5, 0.3, 0.2
1 12
2 15
3 11 13.5
4 9 13 12.4
5 10 10 10.8
6 8 9.5 9.9
7 14 9 8.8
8 12 11 11.4
9 13 11.8
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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. . . and Resulting Graph
Note how the forecasts smooth out variations
0
5
10
15
20
1 2 3 4 5 6 7 8 9
Period
Volu
me Demand
2-Period Avg
3-Period Wt. Avg.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Simple Exponential Smoothing
• Sophisticated weighted averaging model• Needs only three numbers:
Ft = Forecast for the current period tDt = Actual demand for the current period t
a = Weight between 0 and 1
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Exponential Smoothing
• Moving Averages – Equal weight to older observations
• Exponential Smoothing– More weight to more recent observations
• Forecast for next period is a weighted average of – Observation for this period– Forecast for this period
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Simple Exponential Smoothing
Formula
Ft+1 = Ft + a (Dt – Ft) = a × Dt + (1 – a)
× Ft
• Where did the current forecast come from?• What happens as a gets closer to 0 or 1?• Where does the very first forecast come from?
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Exponential Smoothing Forecast with a = 0.3
F2 = 0.3×12 + 0.7×11 = 3.6 + 7.7 = 11.3
F3 = 0.3×15 + 0.7×11.3 = 12.41
PeriodActual
Demand
Exponential Smoothing Forecast
1 12 11.00 (given)
2 15 11.30
3 11 12.41
4 9 11.99
5 10 11.09
6 8 10.76
7 14 9.93
8 12 11.15
9 11.41
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Resulting Graph
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9
Period
De
ma
nd
Demand
Forecast
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time Series with
Time
Demand
random and trend components
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Linear TrendDow Jones Monthly Average
1500
1700
1900
2100
2300
2500
2700
2900
3100
3300
3500
Jan-88 Jul-88 Feb-89 Aug-89 Mar-90 Oct-90 Apr-91 Nov-91
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Exponential TrendIntel Quarterly Sales in Millions of Dollars
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
12/19/85 5/3/87 9/14/88 1/27/90 6/11/91 10/23/92 3/7/94 7/20/95
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Trends
What do you think will happen to a moving average or exponential smoothing model
when there is a trend in the data?
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Simple Exponential Smoothing Always Lags A Trend
Because the modelis based onhistorical demand,it always lagsthe obviousupward trend
PeriodActual
Demand
Exponential Smoothing Forecast
1 11 11.00
2 12 11.00
3 13 11.30
4 14 11.81
5 15 12.47
6 16 13.23
7 17 14.06
8 18 14.94
9 15.86
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Simple Linear Regression• Time Series
– Find best fit of proposed model to past data– Project that fit forward
• Assumes a linear relationship: y = a + b(x)
y
x
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Definitions
Y = a + b(X)
Y = predicted variable (i.e., demand)
X = predictor variable
“X” is the time period for linear trend models.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Example:Regression Used to Estimate
A Linear Trend Line
Period (X)Demand
(Y)
1 110
2 190
3 320
4 410
5 490
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Resulting Regression Model:Forecast = 10 + 98×Period
0
100
200
300
400
500
600
1 2 3 4 5
Period
De
ma
nd
Demand
Regression
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Time series with
Demand
random, trend and seasonal components
June June June June
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Trend & SeasonalityCoca Cola Quarterly Sales in Millions of Dollars
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
$5,000
$5,500
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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SeasonalityToys "R" Us Quarterly Revenues in Millions of Dollars
$500
$1,000
$1,500
$2,000
$2,500
$3,000
$3,500
$4,000
$4,500
Q1-92 Q2-92 Q3-92 Q4-92 Q1-93 Q2-93 Q3-93 Q4-93 Q1-94 Q2-94 Q3-94 Q4-94 Q1-95 Q2-95 Q3-95 Q4-95
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Modeling Trend & Seasonal Components
Quarter Period Demand
Winter 07 1 80Spring 2 240Summer 3 300Fall 4 440Winter 08 5 400Spring 6 720Summer 7 700Fall 8 880
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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What Do You Notice?
Forecasted Demand = –18.57 + 108.57 x Period
PeriodActual
DemandRegression
ForecastForecast
ErrorWinter 07 1 80 90 -10
Spring 2 240 198.6 41.4Summer 3 300 307.1 -7.1
Fall 4 440 415.7 24.3Winter 08 5 400 524.3 -124.3
Spring 6 720 632.9 87.2Summer 7 700 741.4 -41.4
Fall 8 880 850 30
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Regression picks up trend, butnot the seasonality effect
0
200
400
600
800
1000
1 2 3 4 5 6 7 8
Demand
Forecast
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Calculating Seasonal Index: Winter Quarter
(Actual / Forecast) for Winter Quarters:
Winter ‘07: (80 / 90) = 0.89Winter ‘08: (400 / 524.3) = 0.76
Average of these two = 0.83
Interpret!
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Seasonally Adjusted Forecast Model
For Winter Quarter
[ –18.57 + 108.57×Period ] × 0.83
Or more generally:
[ –18.57 + 108.57 × Period ] × Seasonal Index
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Seasonally Adjusted Forecasts
Forecasted Demand = –18.57 + 108.57 x Period
PeriodActual
DemandRegression
ForecastDemand/Forecast
Seasonal Index
Seasonally Adjusted Forecast
Forecast Error
Winter 07 1 80 90 0.89 0.83 74.33 5.67
Spring 2 240 198.6 1.21 1.17 232.97 7.03
Summer 3 300 307.1 0.98 0.96 294.98 5.02
Fall 4 440 415.7 1.06 1.05 435.19 4.81
Winter 08 5 400 524.3 0.76 0.83 433.02 -33.02
Spring 6 720 632.9 1.14 1.17 742.42 -22.42
Summer 7 700 741.4 0.94 0.96 712.13 -12.13
Fall 8 880 850 1.04 1.05 889.84 -9.84
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Would You Expect the Forecast Model to Perform This Well With Future Data?
0
200
400
600
800
1000
1 2 3 4 5 6 7 8
Demand
forecast
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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The Perfect (Imaginary) Forecast
Actual vs. Forecast
0
200
400
600
800
1000
1200
1400
0 200 400 600 800 1000 1200 1400
Actual Demand
Fore
cast
Dem
and
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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A More Realistic Forecast
Actual vs. Forecast
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Actual Demand
Fo
reca
st D
eman
d
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Forecast Error• Building a Forecast
– Fit to historical data– Project future data
• Forecast Error– How well does model fit historical data– Do we need to tune or refine the model– Can we offer confidence intervals about our
predictions
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Forecast Error
• The forecast error measures the difference between the actual demand and the forecast of demand. The forecast is based on the systematic component and the random component is estimated based on the forecast error.
• Forecast Error = Actual – Forecast
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Measures of Forecast Accuracy
• Forecast Errort (Et)= Demandt-Forecastt
• Mean Squared Error (MSE) • Mean Absolute Deviation (MAD)• Bias • Tracking Signal • Relative Forecast Errors
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Mean Squared Error (MSE)
n
tt
n EnMSE
1
21
The MSE estimates the variance of the forecast error.
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Mean Absolute Deviation (MAD)
n
ttn E
nMAD
1
1
The MAD can be used to estimate the standard deviation of the random component, assuming the random component is normally distributed:
σ = 1.25MAD
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Bias
• To determine whether a forecasting method consistently over-or- underestimates demand, calculate the sum of the forecast errors:
n
ttn EBias
1
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Tracking Signal
The tracking signal (TS) is the ratio of the bias to the MAD. Tracking signals outside the range + 6 indicates that the forecast is biased and either under predicting (negative) or over predicting (positive) demand.
t
tt MAD
BiasTS
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Forecast Accuracy & Demand Variability (Normally Distributed Demand)
Coefficient of Variation
Probability Demand is Within
25% of the Forecast
0.10 98.76%
0.25 68.27%
0.50 38.29%
0.75 26.11%
1.00 19.74%
1.50 13.24%
2.00 9.95%
3.00 6.64%
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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• Forecasting is a necessary evil, try to reduce the need for it.
• Complexity costs money, does it provide better forecasts?
• Aggregation provides accuracy, but precludes local information
• Forecast the right thing
Issues
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Taco Bell• Labor is 30% of revenue• Make to order environment• Significant “seasonality”
– 52% of days sales during lunch – 25% of days sales during busiest hour
• Balance staff with demand
Feed the dog
Fall, 2012 EMBA 512 Demand ForecastingBoise State University
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Value Meals• Drove demand
• Forecasting system in each store– forecasts arrivals within 15 minute intervals
• Simulation system – “predicts” congestion and lost sales
• Optimization system– Finds the minimum cost allocation of workers