Forecasting Demand

ISQA 511Dr. Mellie Pullman

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Forecasting (Basics)Independent vs. Dependent Demand

Qualitative Forecasting Methods

Simple & Weighted Moving Average Forecasts

Exponential Smoothing Forecast

Causal Forecast (Regression)

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Independent vs. Dependent Demand

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Independent Demand:Finished Goods

B(4) C(2)

D(2) E(1) D(3) F(2)

Dependent Demand:Raw Materials, Component parts,Sub-assemblies, etc.

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Types of ForecastsQualitative– Judgmental

methods

Quantitative– Time Series

Analysis

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Quantitative Method:Time Series Analysis

Uses historical data

Many types of models available

Pick a model based on:

1. Fits previous data best

2. Time horizon to forecast

3. Data availability

4. Accuracy required

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Components of Demand

Average demand for a period of time

Trend

Seasonal element

Cyclical elements

Random variation

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Patterns of DemandQ

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Time(a) Horizontal (Random): Data cluster about a horizontal line.

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Time(b) Trend: Data consistently increase or decrease. 7

Patterns of DemandQ

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| | | | | |1 2 3 4 5 years

(d) Cyclical: Data reveal gradual increases and decreases over extended periods.

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| | | | | | | | | | | |J F M A M J J A S O N

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Year 1

Year 2

(c) Seasonal: Data consistently show peaks and valleys.

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Finding Components of Demand

1 2 3 4

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Seasonal variation

Linear

Trend

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Simple Moving Average

n

D+...+D +D +D =F 1n-t2-t1-tt

1t

Dt = actual demand from period t

Ft+1 = forecast of demand for period t+1 (next period that has not occurred yet)

Forecast for the next period t+1 = average from the last n periods of actual demand.

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Simple Moving AverageWeek Demand

1 6502 6783 7204 7855 8596 9207 8508 7589 89210 92011 78912 844

n

D+...+D +D +D =F 1n-t2-t1-tt

1t

Let’s develop 3-week and 6-week moving average forecasts for demand.

Assume you only have 3 weeks and 6 weeks of actual demand data for the respective forecasts

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Week Demand 3-Week 6-Week1 6502 6783 7204 785 682.675 859 727.676 920 788.007 850 854.67 768.678 758 876.33 802.009 892 842.67 815.33

10 920 833.33 844.0011 789 856.67 866.5012 844 867.00 854.83

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In-Class Exercise

Week Demand1 8202 7753 6804 6555 6206 6007 575

Develop 3-week and 5-week moving average forecasts for demand for week 8

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Weighted Moving Average

1-n-t1-n-t2-t2-t1-t1-ttt1t Dw+...+Dw+D w+D w=F

w = 1ii=1

n

Determine the 3-period weighted moving average forecast for period 4.

Weights: t .5t-1 .3t-2 .2

Week Demand1 6502 6783 7204

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Solution

Week Demand Forecast1 6502 6783 7204 693.4

F= .5(720)+.3(678)+.2(650)4

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In-Class Exercise

Determine the 3-period weighted moving average forecast for period 5.

Weights: t .7t-1 .2t-2 .1

Week Demand1 8202 7753 6804 655

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Exponential Smoothing( is the smoothing parameter)

Premise — we should determine how much weight to put on recent information versus older information.

0 < < 1High such as .7 puts weight on recent demandLow such as .2 puts weight on many previous periods

Ft+1 = Dt + (1-)Ft

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Exponential Smoothing Example

Week Demand1 8202 7753 6804 6555 7506 8027 7988 6899 775

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Determine exponential smoothing forecasts for periods 2-10 using =.10 and =.60.

Let F1=D1

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Week Demand 0.1 0.61 8202 775 820.00 820.003 680 815.50 793.004 655 801.95 725.205 750 787.26 683.086 802 783.53 723.237 798 785.38 770.498 689 786.64 787.009 775 776.88 728.20

10 776.69 756.28

Forecast

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In-Class Exercise (Solution)

Week Demand 0.51 8202 7753 6804 655

Forecast

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Forecasting with Causal Relationships

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Potential Relationships

Temperature and Sales

Interest rate and number of loans

Average daily temperature or rainfall with acre-feet of water used

Others?

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Simple Linear Regression Model

b represents?

a represents?

Yt = a + bx

0 1 2 3 4 5 x (weeks)

Y

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Regression Equation Example

Week Sales1 1502 1573 1624 1665 177

Develop a regression equation to predict sales

based on these five points.24

Forecast Accuracy

Forecasts Consist of 2 Numbers

1. The projection of actual demand (D), called the forecast (F) which projects historical patterns or relationships

2. The error (E) which defines deviation between the forecast and the actual demand

Measures of Forecast Error

Et = Dt - Ft

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Example- Error Calculation

Month Sales Forecast

1 220 n/a

2 250 255

3 210 205

4 300 320

5 325 315

Determine the Error for the four forecast periods

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Forecast ErrorsStudy the formula for a moment. Now, what does each calculation tell you?

– MFA: mean forecast error

– MAD: mean absolute deviation

n

FD =MFE

n

1=ttt

n

F-D =MAD

n

1=ttt

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Best Error Measurement(What it the problem with the MAD calculation as an error measurement for long histories?)

Day Demand Forecast Error----------- ----------- ------------ ----------1 200 200.0 0.02 134 200.0 -66.03 157 180.2 -23.24 165 173.2 -8.25 177 170.8 6.26 125 172.6 -47.67 146 158.3 -12.38 150 154.6 -4.69 182 153.2 28.810 197 161.9 35.111 136 172.4 -36.412 163 161.5 1.513 157 161.9 -4.914 169 160.5 8.5

--------- --------- ---------TOTALS 2258.0 2381.3 -123.3

365 days Averaged ?

Solution?

Smoothed MAD

Phi () is a smoothing parameter, which is set in advance.

It is important that we fix (set) phi BEFORE we try to find the best forecasting method. Why?

11 tttt MADFDMAD

Phi

Phi controls the period of time over which we are evaluating forecast accuracy--the smaller the value of phi, the larger the number of historical periods that are considered in the measurement of the "average" forecast error.

What effect would changing phi have while you are trying to compare the accuracy of two different forecasting methods?

Suggested Values for Phi

Forecasting Interval

Good Values of Phi

Daily .02 (149 days)

.03 (99 days)

.04 (74 days)

.05 (59 days)

.10 (29 days)

Weekly .05 (59 weeks)

.10 (29 weeks)

.15 (19 weeks)

.20 (14 weeks)

Monthly .10 (29 months)

.15 (19 months)

.20 (14 months)

.25 (11 months)

.30 (9 months)

Phi 0.3

Month Demand Forecast Error MAD

- - - - -

1 200 200.0 0.0 0.0

2 134 200.0 -66.0 19.8

3 157 180.2 -23.2 20.8

4 165 173.2 -8.2 17.0

5 177 170.8 6.2 13.8

6 125 172.6 -47.6 24.0

7 146 158.3 -12.3 20.5

8 150 154.6 -4.6 15.7

9 182 153.2 28.8 19.6

10 197 161.9 35.1 24.3

11 136 172.4 -36.4 27.9

12 163 161.5 1.5 20.0

13 157 161.9 -4.9 15.5

14 169 160.5 8.5 13.4

--------- --------- --------- ---------

TOTALS 2258.0 2381.3 -123.3 252.3

Quarter Year 1 Year 2 Year 3 Year 4

1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200 Average 250 300 450 550

Seasonal Index/Factor

We estimate 2600 for Year 5 but need to know how manyto make each quarter.

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Seasonal Factor Method

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Quarter Year 1 Year 2 Year 3 Year 4

1 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200 Average 250 300 450 550

Seasonal Index = Actual Demand

Average Demand

Seasonal Index/Factor

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Quarter Year 1 Year 2 Year 3 Year 4

1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39

Quarter Average Seasonal Index Forecast

1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 1302 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 650(1.30) = 8453 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 650(2.00) = 13004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 650(0.50) = 325

Seasonal Influences

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In- Class Problem: Forecast Year 3(Overall forecast = 1500)

Qtr

Year 1 Year 2Average

IndexDemand Index Demand Index

1 100 192

2 400 408

3 300 384

4 200 216

Avg

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Decomposition of Season & Trend

Decompose the data into components– Find seasonal component– Deseasonalize demand– Find Trend component

Forecast future values of each component– Project Trend component into future– Multiply trend component by seasonal

component

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Example of Deseasonalized Data

Period x Quarter Actual Demand SF for X ASF DeseasonlizeAve SF Demand/ASF

1 I 600 0.47 0.74 809.912 II 1550 1.20 1.13 1376.693 III 1500 1.17 1.01 1479.914 IV 1500 1.17 1.12 1339.635 I 2400 0.87 0.74 3243.246 II 3100 1.13 1.13 2753.387 III 2600 0.95 1.01 2565.178 IV 2900 1.05 1.12 2589.969 I 3800 0.88 0.74 5135.1410 II 4500 1.05 1.13 3996.8411 III 4000 0.93 1.01 3946.4112 IV 4900 1.14 1.12 4376.13

Slope 338.4754Intercept 600.944

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Project Future and Re-seasonalize

Period Forecast SF Seasonalize13 4999.9 0.74 3699.9314 5338.31 1.13 6032.2915 5676.72 1.01 5733.4916 6015.13 1.12 6736.95

Slope 338.41Intercept 600.57

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Trend Adjusted Trend Adjusted Exponential SmoothingExponential Smoothing

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Trend-Adjusted Exponential Smoothing

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Actual room requests

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Trend-Adjusted Exponential Smoothing

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Trend-Adjusted Exponential Smoothing

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Guest Arrivals

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

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Trend-Adjusted Exponential Smoothing

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A1 = T1 =

Guest Arrivals

A0 = 28 g D1 = 27 g T0 = 3 g

= 0.20 = 0.20

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

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Trend-Adjusted Exponential Smoothing

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A1 = 0.2(27) + 0.80(28 + 3)= 30.2T1 = 0.2(30.2 - 28) + 0.80(3)= 2.8

Guest Arrivals

A0 = 28 g D1 = 27 g T0 = 3 g

= 0.20 = 0.20

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

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Trend-Adjusted Exponential Smoothing

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A1 = 30.2T1 = 2.8

Guest Arrivals

A0 = 28 guests T0 = 3 guests

= 0.20 = 0.20

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

Forecast2 = 30.2 + 2.8 = 33

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Trend-Adjusted Exponential Smoothing

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Guest Arrivals

A1 = 30.2 D2 = 44 T1 = 2.8

= 0.20 = 0.20

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

A2 = 0.2(44) + 0.80(30.2 + 2.8)= 35.2T2 = 0.2(35.2 - 30.2) + 0.80(2.8)= 3.2

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Trend-Adjusted Exponential Smoothing

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Guest Arrivals

A1 = 30.2 D2 = 44 T1 = 2.8

= 0.20 = 0.20

At = Dt + (1 - )(At-1 + Tt-1)Tt = (At - At-1) + (1 - )Tt-1

A2 = 35.2T2 = 3.2

Forecast = 35.2 + 3.2 = 38.4

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Trend-Adjusted Exponential Smoothing

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Trend-adjusted forecast

Actual guest arrivals

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In Class Exercise

Amar = 300,000 cases; Tmar = +8,000 cases

Dapr = 330,000 cases; = 0.20 =.10

What are the forecasts for May and July?

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