Operations Management Dr. Ron Lembke 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: The forecast will always be wrong The farther out you are, the worse your forecast is likely to be. 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

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

Historical Analogy Video sales of Shrek 2 Shrek (2001) did $500m at the box office, and sold almost 50 million DVDs & videos Shrek2 (2004) did $920m 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: 40m by end Q1 March SEC filing: 33.7 million sold. Oops. May 10 Announcement: In 2nd public Q, missed earnings targets by 25%. May 9, word started leaking Stock dropped 16.7%

Lessons Learned Guaranteed Sales: flooded market with DVDs 5 years ago 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: 12.1m in first 3 days Far Far Away Idol Had to vote in first week

Quantitative Methods Math-based Relationships, patterns, trends, in previous data Associative or Causal models Prediction based on relationship to inputs Identify independent and dependent variables Time-Series Extrapolation – existing patterns will continue

New Housing Starts 1959-2015 Who cares? How predict?

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

Forecast Errors Error: 𝐸 𝑡 = 𝐴 𝑡 − 𝐹 𝑡

Naïve Forecast Error Avg Error (14 mos)= -0.4 Avg Error (55 yrs)= 0.02 Month Total Naïve Error Jan 1959 96.2 Feb 1959 99.0 2.8 Mar 1959 127.7 28.7 Apr 1959 150.8 23.1 May 1959 152.5 1.7 Jun 1959 147.8 -4.7 Jul 1959 148.1 0.3 Aug 1959 138.2 -9.9 Sep 1959 136.4 -1.8 Oct 1959 120.0 -16.4 Nov 1959 104.7 -15.3 Dec 1959 95.6 -9.1 Jan 1960 86.0 -9.6 Feb 1960 90.7 4.7 Avg Error (14 mos)= -0.4 Avg Error (55 yrs)= 0.02

Mean Error of 0 That’s good! not perfect. Just unbiased

Squared Errors No negatives No cancelling Large errors blow up One bad month and your method looks terrible MSE=303.25 Good? Bad?

Mean Absolute Error No negatives No cancelling Large errors do not blow up What’s a good score? MAD=12.99 Good? Bad?

Mean Absolute Percentage Error No negatives No cancelling Large errors do not blow up What’s a good score? MAPE=11.4% Good? Bad?

Evaluating Forecasts Mean Absolute Deviation Mean Squared Error Percent Error

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

Scenario 1-Livingston Medical Month Math Model Jury of Executive Opinion Actual Jan 13,128 12,500 12,480 Feb 12,009 13,000 11,568 Mar 12,649 13,500 13,244 Apr 16,387 16,000 15,560 May 16,190 16,034 June 23,002 24,000 23,400

Math Model - Forecast Errors

Jury of Executive Opinion- Forecast Errors

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

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 and quantify relationship Someone else has to forecast the x values for you

Causal Relationships

Computing Values

Linear Regression Four methods Fits a trend and intercept to the data. Type in formulas for trend, intercept Tools | Data Analysis | Regression Graph, and R click on data, add a trendline, and display the equation. Use intercept(Y,X), slope(Y,X) and RSQ(Y,X) commands Fits a trend and intercept to the data. R2 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.

Van Uses – 2,200 clients -22+(0.10363 * 2100) = 195.62=196 rides

Confidence?

Assisted Living Facility -22+(0.10363 * 2100) = 195.62=196 rides

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

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, 2N, 3N etc. number of periods

Moving Average Advantages: Disadvantages: 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

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.

Exponential Smoothing F10 = F9 + 0.2 (A9 - F9) F10 = 0.8 F9 + 0.2 (A9 - F9) At-1 Actual demand in period t-1 Ft-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 F1 = 1,050,  = 0.05, A1 = 1,000 F2 = F1 + (A1 - F1) = 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 A1

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, A2=115

Trend-Adjusted Ex. Smoothing Suppose actual demand is 120, A3=120

TAF6=S5+T5 F6 A5 S5

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

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 N1: Assume January sales will be same as December N2: 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 2011 2012 Avg Relative Spring 200 220 210 210/257.5 = 0.83 Summer 350 380 365 365/257.5 = 1.42 Fall 300 320 310 310/257.5 = 1.20 Winter 150 140 145 145/257.5 = 0.56 Total 1,000 1,060 1,030 Avg 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

Scenario 3a R2=0.000096

Deseasonalized Van Usage

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 Calculate seasonal relatives Deseasonalize the demand Find trend of deseasonalized line Project trend into the future Project trend line into future Multiply trend line by seasonal relatives.

Washoe Gaming Win, 1993-96 Looks like a downhill slide Silver Legacy opened 95Q3 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

1989-2007

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

BTW

2003-2014Q2 SR 2003-2014

1.Compute Seasonal Relatives 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Avg Q1 240.1 231.6 245.8 244.6 227.9 190.1 187.0 174.1 175.4 179.5 172.1 209.5 Q2 259.3 259.8 269.2 269.7 273.5 237.0 211.9 198.3 192.1 183.3 191.8 191.1 228.1 Q3 279.8 297.4 294.8 284.7 259.0 217.2 209.6 203.9 201.8 207.2 250.0 Q4 246.1 259.6 257.0 257.2 246.4 206.2 186.0 175.6 175.5 166.8 174.6 213.7 Average 225.3 Avg SR Q1 209.5 0.930 Q2 228.1 1.012 Q3 250.0 1.110 Q4 213.7 0.948 Divide 209.5 by 225.3 = 0.930

2.Deseasonalize 0.930 1.012 1.110 0.948 Year Quarter Gaming Win Seasonal Relative Deseas 2009 1 190,098,500 0.930 204,462,607 2 211,913,667 1.012 209,348,089 3 217,227,445 1.110 195,779,857 4 185,971,111 0.948 196,079,317 2010 187,016,132 201,147,331 198,330,968 195,929,832 209,608,491 188,913,148 175,601,589 185,146,174 2011 174,138,905 187,297,082 192,122,889 189,796,912 203,912,214 183,779,283 175,510,911 185,050,567 2012 175,417,340 188,672,118 183,305,632 181,086,403 201,825,465 181,898,566 166,760,853 175,824,912

3.LR on Deseas data Period Deseasonalized 1 204,462,607 2 209,348,089 195,779,857 4 196,079,317 5 201,147,331 6 195,929,832 7 188,913,148 8 185,146,174 9 187,297,082 10 189,796,912 11 183,779,283 12 185,050,567 13 188,672,118 14 181,086,403 15 181,898,566 16 175,824,912 17 193,041,432 18 189,508,450 19 186,699,574 20 184,133,867 21 185,087,867 22 188,770,074 3.LR on Deseas data

4.Project trend line into future Q3 is 23rd point in series 199,533,125 +23*(-839,033) = 180,235,371

5.Multiply by Seasonal Relatives Period Q Linear Trend Line Seasonal Relative Seasonalized Forecast 23 3 176,330,767 0.937 165,141,344 24 4 174,654,854 1.020 178,076,517 25 1 172,978,941 1.101 190,514,933 26 2 171,303,027 0.942 161,451,313

Housing-Selecting Data A>F A<F

1. Seasonal Factors 2009 2010 2011 2012 2013 2014 2015 Avg SF Jan 31.9 38.9 40.2 47.2 58.7 60.7 73.0 50.1 0.776 Feb 39.8 40.7 35.4 49.7 66.1 65.1 61.9 51.2 0.794 Mar 42.7 54.7 49.9 58.0 83.3 80.2 79.7 64.1 0.993 Apr 42.5 62.0 49.0 66.8 76.3 94.9 108.5 71.4 1.107 May 52.2 56.2 54.0 67.8 87.2 92.5 99.6 72.8 1.128 June 59.1 53.8 60.5 74.7 80.7 87.3 112.7 75.5 1.171 July 56.8 51.5 57.6 69.2 84.0 101.0 112.3 76.1 1.179 Aug 52.9 56.3 54.5 69.0 80.4 86.2 66.6 1.032 Sept 52.6 53.0 58.8 75.8 78.4 94.2 68.8 1.066 Oct 44.5 45.4 53.2 77.0 92.0 1.009 Nov 42.3 40.6 62.2 83.8 59.6 0.924 Dec 36.6 33.8 63.2 67.6 73.4 0.820 64.51

2. Deseasonalize Month Starts SF Deseas Jan 2009 31.9 0.776 41.1 Feb 2009 39.8 0.794 50.1 Mar 2009 42.7 0.993 43.0 Apr 2009 42.5 1.107 38.4 May 2009 52.2 1.128 46.3 Jun 2009 59.1 1.171 50.5 Jul 2009 56.8 1.179 48.2 Aug 2009 52.9 1.032 51.3 Sep 2009 52.6 1.066 49.3 Oct 2009 44.5 1.009 44.1 Nov 2009 42.3 0.924 45.8 Dec 2009 36.6 0.820 44.6

3. Linear Regression

4. Project Forward F(t) = 36.98 + t*0.69

5. Seasonalize

Summary Calculate seasonal relatives Deseasonalize Do a LR Divide actual demands by seasonal relatives Do a LR Project the LR into the future Seasonalize Multiply straight-line forecast by relatives