Forecasting Demand ISQA 511 Dr. Mellie Pullman

Forecasting (Basics) Independent vs. Dependent Demand Qualitative Forecasting Methods Simple & Weighted Moving Average Forecasts Exponential Smoothing Forecast Causal Forecast (Regression) 2

Independent vs. Dependent Demand 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. 3

Types of Forecasts Qualitative Quantitative Judgmental methods Time Series Analysis 5

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 14

Components of Demand Average demand for a period of time Trend Seasonal element Cyclical elements Random variation 7

Patterns of Demand Quantity Time (a) Horizontal (Random): Data cluster about a horizontal line. Quantity Time (b) Trend: Data consistently increase or decrease.

Patterns of Demand Quantity Year 1 Year 2 | | | | | | | | | | | | | | | | | | | | | | | | J F M A M J J A S O N D Year 1 Year 2 (c) Seasonal: Data consistently show peaks and valleys. Quantity | | | | | | 1 2 3 4 5 years (d) Cyclical: Data reveal gradual increases and decreases over extended periods.

Finding Components of Demand 1 2 3 4 x Year Sales Seasonal variation Linear Trend 6

Simple Moving Average 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. 15

Simple Moving Average 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 15

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In-Class Exercise Develop 3-week and 5-week moving average forecasts for demand for week 8 18

Weighted Moving Average Determine the 3-period weighted moving average forecast for period 4. Weights: t .5 t-1 .3 t-2 .2 20

Solution 21

In-Class Exercise Determine the 3-period weighted moving average forecast for period 5. Weights: t .7 t-1 .2 t-2 .1 22

Exponential Smoothing (a is the smoothing parameter) Ft+1 = a Dt + (1-a)Ft Premise — we should determine how much weight to put on recent information versus older information. 0 < a < 1 High a such as .7 puts weight on recent demand Low a such as .2 puts weight on many previous periods 24

Exponential Smoothing Example Determine exponential smoothing forecasts for periods 2-10 using a=.10 and a=.60. Let F1=D1 25

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In-Class Exercise (Solution) 29

Forecasting with Causal Relationships

Potential Relationships Temperature and Sales Interest rate and number of loans Average daily temperature or rainfall with acre-feet of water used Others?

Simple Linear Regression Model Y Yt = a + bx 0 1 2 3 4 5 x (weeks) b represents? a represents? 35 35

Regression Equation Example Develop a regression equation to predict sales based on these five points. 37 37

Measures of Forecast Error 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

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 31 31

Forecast Errors Study the formula for a moment. Now, what does each calculation tell you? MFA: mean forecast error MAD: mean absolute deviation 30 30

Best Error Measurement (What it the problem with the MAD calculation as an error measurement for long histories?) 365 days Averaged ?

Solution? Smoothed MAD Phi (j) 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?

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 2 134 -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 -4.9 15.5 14 169 160.5 8.5 13.4 --------- TOTALS 2258.0 2381.3 -123.3 252.3

Seasonal Index/Factor ISQA Lecture 2 Notes 4/16/2017 Seasonal Index/Factor Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 We estimate 2600 for Year 5 but need to know how many to make each quarter. 60

Seasonal Factor Method ISQA Lecture 2 Notes 4/16/2017 Seasonal Factor Method

Seasonal Index/Factor ISQA Lecture 2 Notes 4/16/2017 Seasonal Index/Factor Quarter Year 1 Year 2 Year 3 Year 4 1 45 70 100 100 2 335 370 585 725 3 520 590 830 1160 4 100 170 285 215 Total 1000 1200 1800 2200 Average 250 300 450 550 Seasonal Index = Actual Demand Average Demand 61

Seasonal Influences Quarter Average Seasonal Index Forecast ISQA Lecture 2 Notes 4/16/2017 Seasonal Influences Quarter Year 1 Year 2 Year 3 Year 4 1 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.18 2 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.32 3 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.11 4 100/250 = 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) = 130 2 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 650(1.30) = 845 3 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 650(2.00) = 1300 4 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 650(0.50) = 325 69

In- Class Problem: Forecast Year 3 (Overall forecast = 1500) ISQA Lecture 2 Notes 4/16/2017 In- Class Problem: Forecast Year 3 (Overall forecast = 1500) Qtr Year 1 Year 2 Average Index Demand Index 1 100 192 2 400 408 3 300 384 4 200 216 Avg

Decomposition of Season & Trend ISQA Lecture 2 Notes 4/16/2017 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

Example of Deseasonalized Data ISQA Lecture 2 Notes 4/16/2017 Example of Deseasonalized Data

Project Future and Re-seasonalize ISQA Lecture 2 Notes 4/16/2017 Project Future and Re-seasonalize

Trend Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 The next series of slides presents Example12.5. The series builds in steps to the conclusion of the Example showing the development of key equations along the way. Trend Adjusted Exponential Smoothing 51

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week This is the actual data as presented in Figure 12.6. Actual room requests 51

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Guest Arrivals At = Dt + (1 - )(At-1 + Tt-1) Tt = (At - At-1) + (1 - )Tt-1 52

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week 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 Using the trend-adjusted exponential smoothing we can calculate a forecast. 53

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week A1 = 0.2(27) + 0.80(28 + 3)= 30.2 T1 = 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 Using the trend-adjusted exponential smoothing we can calculate a forecast. 53

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week A1 = 30.2 T1 = 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 54

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week 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)= 35.2 T2 = 0.2(35.2 - 30.2) + 0.80(2.8)= 3.2 55

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week 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 = 35.2 T2 = 3.2 Forecast = 35.2 + 3.2 = 38.4 56

Trend-Adjusted Exponential Smoothing ISQA Lecture 2 Notes 4/16/2017 Trend-Adjusted Exponential Smoothing | | | | | | | | | | | | | | | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 80 — 70 — 60 — 50 — 40 — 30 — Guest arrivals Week Trend-adjusted forecast This presents the entire Figure 12.6 with the forecast in place. Actual guest arrivals 57

In Class Exercise Amar = 300,000 cases; Tmar = +8,000 cases Dapr = 330,000 cases; a= 0.20 b=.10 What are the forecasts for May and July?