FORECASTING Operations Management Dr Ron Lembke Predicting the

FORECASTING Operations Management Dr. Ron Lembke

Predicting the Future We know the forecast will be wrong. Try to make the best forecast we can, ▫ Given the time we want to invest ▫ Given the available data • The “Rules” of Forecasting: 1. The forecast will always be wrong 2. The farther out you are, the worse your forecast is likely to be. 3. Aggregate forecasts are more likely to accurate than individual item ones

Independent vs Dependent • Independent Demand ▫ Things demanded by end users • Dependent Demand ▫ Demand known, once demand for end items is known

Time Horizons Different decisions require projections about different time periods: • Short-range: who works when, what to make each day (weeks to months) • Medium-range: when to hire, lay off (months to years) • Long-range: where to build plants, enter new markets, products (years to decades)

Forecast Impact Finance & Accounting: budget planning Human Resources: hiring, training, laying off employees Capacity: not enough, customers go away angry, too much, costs are too high Supply-Chain Management: bringing in new vendors takes time, and rushing it can lead to quality problems later

Qualitative Methods • Sales force composite / Grass Roots • Market Research / Consumer market surveys & interviews • Jury of Executive Opinion / Panel Consensus • Delphi Method • Historical Analogy - DVDs like VCRs • Naïve approach

Quantitative Methods Time Series Methods 1. Simple Moving Average 2. Weighted Moving Average 3. Exponential Smoothing 4. Exponential smoothing with trend 5. Linear regression Causal Methods Linear Regression

Evaluating Forecasts How far off is the forecast? Forecasts Demands What do we do with this information?

Measuring the Errors Period A-F Method 1 A-F Method 2 1 100 10 2 -100 10 3 100 10 4 -100 10 5 100 10 6 -100 10 7 100 10 8 -100 10 9 100 10 10 -100 10 RSFE 0 100 • Method 1 forecasts are low, high, etc. • Method 2 forecasts always too low. • Bias ▫ Sum of all errors ▫ Running Sum of Forecast Errors, RSFE

Evaluating Forecasts Mean Absolute Deviation Mean Squared Error Mean Absolute Percent Error

MAD of examples Period |A-F| Method 1 |A-F| Method 2 1 100 10 2 100 10 3 100 10 4 100 10 5 100 10 6 100 10 7 100 10 8 100 10 9 100 10 10 10 MAD 100 10 • MAD shows that method 1 is off by a larger amount • Method 2 was biased • However, overall, Method 2 seems preferable

Forecast Errors

Tracking Signal • To monitor, compute tracking signal • If >4 or <-4 something is wrong • Top should sum to 0 over time. If not, forecast is biased.

Monitoring Forecast Accuracy Forecast Error • Monitor forecast error each period, to see if it becomes too great 4 Upper Limit 0 -4 Forecast Period Lower Limit

Time Series Forecasting Assume patterns in data will continue, including: Trend (T) Seasonality (S) Cycles (C) Random Variations

Moving Average Compute forecast using n most recent periods Jan Feb Mar Apr May Jun Jul 3 month Moving Avg: June forecast: FJun = (AMar + AApr + AMay)/3 If no seasonality, freedom to choose n If seasonality is N periods, must use N, 2 N, 3 N etc. number of periods

Moving Average Advantages: ▫ ▫ ▫ Ignores data that is “too” old Requires less data than simple average More responsive than simple average Disadvantages: ▫ ▫ ▫ Still lacks behind trend like simple average, (though not as badly) The larger n is, more smoothing, but the more it will lag The smaller n is, the more over-reaction

Simple and Moving Averages

Stability vs. Responsiveness • Responsive ▫ Real-time accuracy ▫ Market conditions • Stable ▫ Forecasts being used throughout the company ▫ Long-term decisions based on forecasts ▫ Don’t whipsaw those folks

Old Data Comparison of simple, moving averages clearly shows that getting rid of old data makes forecast respond to trends faster Moving average still lags the trend, but it suggests to us we give newer data more weight, older data less weight.

Weighted Moving Average FJun = (AMar + AApr + AMay)/3 = (3 AMar + 3 AApr + 3 AMay)/9 Why not consider: FJun = (2 AMar + 3 AApr + 4 AMay)/9 FJun = 2/9 AMar + 3/9 AApr + 4/9 AMay Ft = w 1 At-3 + w 2 At-2 + w 3 At-1 Complicated: • Have to decide number of periods, and weights for each • Weights have to add up to 1. 0 • Most recent probably most relevant, gets most weight • Carry around n periods of data to make new forecast

Weighted Moving Average Wts = 0. 5, 0. 3, 0. 2

Setting Parameters • Weighted Moving Average ▫ Number of Periods ▫ Individual weights • Trial and Error ▫ Evaluate performance of forecast based on some metric

Exponential Smoothing F 10 = F 9 + 0. 2 (A 9 - F 9) F 10 = 0. 8 F 9 + 0. 2 (A 9 - F 9) At-1 Actual demand in period t-1 Forecast for period t-1 Smoothing constant >0, <1 Forecast is old forecast plus a portion of the error of the last forecast. Formulas are equivalent, give same answer

Exponential Smoothing • Smoothing Constant between 0. 1 -0. 3 • Easier to compute than moving average • Most widely used forecasting method, because of its easy use • F 1 = 1, 050, = 0. 05, A 1 = 1, 000 • F 2 = F 1 + (A 1 - F 1) • = 1, 050 + 0. 05(1, 000 – 1, 050) • = 1, 050 + 0. 05(-50) = 1, 047. 5 units • BTW, we have to make a starting forecast to get started. Often, use actual A 1

Exponential Smoothing Alpha = 0. 3

Exponential Smoothing Alpha = 0. 5

Exponential Smoothing We take: And substitute in to get: and if we continue doing this, we get: Older demands get exponentially less weight

Choosing • Low : if demand is stable, we don’t want to get thrown into a wild-goose chase, over-reacting to “trends” that are really just short-term variation • High : If demand really is changing rapidly, we want to react as quickly as possible

Averaging Methods • • Simple Average Moving Average Weighted Moving Average Exponentially Weighted Moving Average (Exponential Smoothing) • They ALL take an average of the past ▫ With a trend, all do badly ▫ Average must be in-between 30 20 10

Trend-Adjusted Ex. Smoothing

Trend-Adjusted Ex. Smoothing Trend-Adjusted Forecast for period 2 was Suppose actual demand is 115, A 2=115

Trend-Adjusted Ex. Smoothing Suppose actual demand is 120, A 3=120

TAF 6=S 5+T 5 A 5 S 5 F 6

Selecting and β • You could: ▫ Try an initial value for each parameter. ▫ Try lots of combinations and see what looks best. ▫ But how do we decide “what looks best? ” • Let’s measure the amount of forecast error. • Then, try lots of combinations of parameters in a methodical way. ▫ Let = 0 to 1, increasing by 0. 1 For each value, try = 0 to 1, increasing by 0. 1

Techniques for Trend • Determine how demand increases as a function of time t = periods since beginning of data b = Slope of the line a = Value of yt at t = 0

Computing Values

Linear Regression • Four methods 1. Type in formulas for trend, intercept 2. Tools | Data Analysis | Regression 3. Graph, and R click on data, add a trendline, and display the equation. 4. Use intercept(Y, X), slope(Y, X) and RSQ(Y, X) commands • Fits a trend and intercept to the data. • R 2 measures the percentage of change in y that can be explained by changes in x. • Gives all data equal weight. • Exp. smoothing with a trend gives more weight to recent, less to old.

Causal Forecasting • Linear regression seeks a linear relationship between the input variable and the output quantity. • For example, furniture sales correlates to housing sales • Not easy, multiple sources of error: ▫ Understand quantify relationship ▫ Someone else has to forecast the x values for you

Video sales of Shrek 2? • Shrek did $500 m at the box office, and sold almost 50 million DVDs & videos • Shrek 2 did $920 m at the box office

Video sales of Shrek 2? • Assume 1 -1 ratio: • • ▫ 920/500 = 1. 84 ▫ 1. 84 * 50 million = 92 million videos? ▫ Fortunately, not that dumb. January 3, 2005: 37 million sold! March analyst call: 40 m by end Q 1 March SEC filing: 33. 7 million sold. Oops. May 10 Announcement: ▫ In 2 nd public Q, missed earnings targets by 25%. ▫ May 9, word started leaking ▫ Stock dropped 16. 7%

Lessons Learned • Flooded market with DVDs • Guaranteed Sales ▫ Promised the retailer they would sell them, or else the retailer could return them ▫ Didn’t know how many would come back • 5 years ago ▫ Typical movie 30% of sales in first week ▫ Animated movies even lower than that • 2004/5 50 -70% in first week ▫ Shrek 2: 12. 1 m in first 3 days ▫ American Idol ending, had to vote in first week

The Human Element • Colbert says you have more nerve endings in your gut than in your brain • Limited ability to include factors ▫ Can’t include everything • If it feels really wrong to your gut, maybe your gut is right

Seasonality Demand goes up and down on a regular, time-based pattern

Washoe Gaming Win, 1993 -96 What did they mean when they said it was down three quarters in a row? 1993 1994 1995 1996

Seasonality • Seasonality is regular up or down movements in the data • Can be hourly, daily, weekly, yearly • Naïve method ▫ N 1: Assume January sales will be same as December ▫ N 2: Assume this Friday’s ticket sales will be same as last

Seasonal Relatives • Seasonal relative for May is 1. 20, means May sales are typically 20% above the average • Factor for July is 0. 90, meaning July sales are typically 10% below the average

Seasonality & Assume No Trend Spring Summer Fall Winter Total Avg 2011 2012 200220210 350380365 300 320 150140145 Avg Relative 210/257. 5 = 0. 83 365/257. 5 = 1. 42 310/257. 5 = 1. 20 145/257. 5 = 0. 56 1, 000 1, 060 1, 030/4=257. 5 Relatives sum to 0. 83+1. 42+1. 20+0. 56 =4. 01

Seasonality & No Trend If we expected total demand for the next year to be 1, 100, the average per quarter would be 1, 100/4=275 Forecast Spring 275 * 0. 8 = 220 Summer 275 * 1. 4 = 385 Fall 275 * 1. 2 = 330 Winter 275 * 0. 6 = 165 Total 1, 100

Seasonality with a Trend • Demand goes up and down on a regular, time-based pattern • AND demand is on a long-term upward (or downward) trend

Trend & Seasonality • Deseasonalize to find the trend 1. Calculate seasonal relatives 2. Deseasonalize the demand 3. Find trend of deseasonalized line • Project trend into the future 4. Project trend line into future 5. Multiply trend line by seasonal relatives.

Washoe Gaming Win, 1993 -96 Looks like a downhill slide -Silver Legacy opened 95 Q 3 -Otherwise, upward trend 1993 1994 1995 1996 Source: Comstock Bank, Survey of Nevada Business & Economics

Washoe Win 1989 -1996 Definitely a general upward trend, slowed 93 -94

1989 -2007

1998 -2007 Cache Creek 9/11 Thunder CC Valley Expands

1997 -2012 Statewide 1997 -2012 1 400 000 1 200 000 Washoe Clark Statewide 1 000 000 800 000 600 000 400 000 200 000 0 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Quarterly Win 2003 -2012 350 000 300 000 Axis Title 250 000 200 000 150 000 100 000 Deseas R 2 = 0, 793 Raw data R 2 = 0, 6502 50 000 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Quarterly Win 2003 -2012 2013 Forecast using 2003 -12 SR 350 000 300 000 Axis Title 250 000 200 000 150 000 100 000 50 000 Data for LR Seasonal Relatives calculated using 2003 -12 data 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Predict 2013 250 000 200 000 150 000 Washoe Win Deseasonalized 100 000 Linear Seasonal Forecast 50 000 - 2009 2010 2011 2012 2013

2003 1. Compute Seasonal Relatives 350, 0 2004 300, 0 2005 250, 0 2006 200, 0 2007 150, 0 2008 2009 100, 0 2010 50, 0 2011 0, 0 Q 1 Q 2 Q 3 Q 4 2003 240. 1 259. 3 279. 8 246. 1 2004 231. 6 259. 8 297. 4 259. 6 2005 245. 8 269. 2 294. 8 257. 0 2006 245. 8 269. 7 294. 8 257. 2 2007 244. 6 273. 5 284. 7 246. 4 2008 227. 9 237. 0 259. 0 206. 2 2009 190. 1 211. 9 217. 2 186. 0 Q 2 2010 187. 0 198. 3 209. 6 175. 6 Q 3 2011 174. 1 192. 1 203. 9 175. 5 Q 4 Avg 2012 Avg 175. 4 216. 3 183. 3 235. 4 201. 8 254. 3 166. 8 217. 6 Avg Q 1 Q 2 Q 3 Q 4 Avg 216. 3 235. 4 254. 3 217. 6 SR 0. 937 1. 020 1. 101 0. 943 2012 Divide 216. 3 by 230. 9 = 0. 937 230. 9

2. Deseasonalize Year Quarter 2009 1 2 3 4 2010 2011 2012 Gaming Win Seasonal Relative Deseas 190, 098, 500 0. 937 202, 978, 936 211, 913, 667 1. 020 207, 841, 838 217, 227, 445 1. 101 197, 232, 693 185, 971, 111 0. 943 197, 212, 207 187, 016, 132 0. 937 199, 687, 717 198, 330, 968 1. 020 194, 520, 124 209, 608, 491 1. 101 190, 315, 028 175, 601, 589 0. 943 186, 215, 895 174, 138, 905 0. 937 185, 937, 972 192, 122, 889 1. 020 188, 431, 331 203, 912, 214 1. 101 185, 143, 066 175, 510, 911 0. 943 186, 119, 736 175, 417, 340 0. 937 187, 303, 030 183, 305, 632 1. 020 179, 783, 494 201, 825, 465 1. 101 183, 248, 392 166, 760, 853 0. 943 176, 840, 777

Period Deseasonalized 1 202, 978, 936 2 207, 841, 838 250 000 3 197, 232, 693 4 197, 319, 016 5 199, 687, 717 200 000 6 194, 520, 124 7 190, 315, 028 8 186, 316, 749 150 000 9 185, 937, 972 10 188, 431, 331 11 185, 143, 066 100 000 12 186, 220, 538 13 187, 303, 030 14 179, 783, 494 50 000 15 183, 248, 392 16 176, 936, 554 3. LR on Deseas data R 2 = 0, 8681 Washoe Win Deseasonalized Linear 2009 2010 2011 2012

4. Project trend line into future 250 000 200 000 150 000 Washoe Win 100 000 Deseasonalized Linear 50 000 - 2013 Q 1 = Period 17 204, 821, 292 + 17 * (-1, 675, 913) = 176, 330, 771 2009 2010 2011 2012 2013

5. Multiply by Seasonal Relatives Linear Trend Seasonal Period Q Line Relative 176, 330, 17 1 767 0. 937 174, 654, 18 2 854 1. 020 172, 978, 19 3 941 1. 101 171, 303, 20 4 027 0. 942 Seasonalized Forecast 165, 141, 344 178, 076, 517 190, 514, 933 161, 451, 313

Past Year Forecast Performance 250 000 200 000 150 000 Washoe Win Deseasonalized Linear Forecast 100 000 I was WRONG! Better than expected!! 50 000 2009 2010 2011 2012 2013

Summary 1. Calculate seasonal relatives 2. Deseasonalize 1. Divide actual demands by seasonal relatives 3. Do a LR 4. Project the LR into the future 5. Seasonalize 1. Multiply straight-line forecast by relatives