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Forecasting the Demand Those who do not remember the past are condemned to repeat it George Santayana (1863-1952) a Spanish philosopher, essayist, poet and novelist

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Operations managers need forecasting for their Design tasks as well as their Operational tasks. We will learn Why do we need forecasting? What is forecasting? Qualitative (judgmental) forecasting. Quantitative forecasting. Time series analysis –Naïve method –Moving average –Exponential smoothing Regression analysis How to measure forecasting errors? Goals and Aims

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AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion MISIT/IS systems, services OperationsSchedules, MRP, workloads Product/service designNew products and services Uses of Forecast in Planning, Scheduling, and Decision Making

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Meaningful unit Written Easy to use Accurate Close to reality Close to actual data Reliable Accuracy over time Consistency in forecasts Timely To have enough time to make the required decisions based on forecasts Elements of a good forecast

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Forecasts rarely perfect because of randomness Forecast should be accompanied by a measure of forecast error Forecasts are more accurate for groups of items vs. individual items Forecast accuracy decreases as time horizon increases I see that you will get an A this semester. Common features of forecasts

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Judgmental - uses subjective inputs. Qualitative Time series - uses historical data to develop a function to forecast demand of our products over time. A relationship between demand and time. Regression - Create a relationship between demand of our products and value of one or more variables Types of Forecasts

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Executive opinions Sales force composite Consumer surveys Outside opinion Delphi technique Judgmental forecasts

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A questionnaire is send to individuals who have knowledge and ability in the area Responses are kept anonymous A new questionnaire is developed based on the information extracted from the previous questionnaire. The process starts over The process stops when they reach an consensus forecast Delphi technique

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One reason for using the Delphi method in forecasting is to avoid premature consensus (bandwagon effect)

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Find a relationship between demand and time Demand Time Time series analysis

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forecast variations Irregular variation Random variation Trend - long-term movement in data Seasonality - short-term cycles (seasons, weeks, days, hours) Cycles - Long-term variations (5 to 10 yrs) Irregular variations - caused by unusual circumstances Random variations - caused by chance

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Naïve forecasts Moving Averages Exponential Smoothing Techniques for time series forecasting

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We sold 250 wheels last week.... Now, next week we should sell.… A t : Actual demand in period t F (t+1) : Forecast of demand for period t+1 F (t+1) = A t Naive forecasts 250 wheels The naive forecast can also serve as an accuracy standard for other techniques

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Moving Average Three period moving average in period say 7 is the average of MA t 10 = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-9 )/10 MA 7 3 = (A 7 + A 6 + A 5 )/3 Three period moving average in period t is the average of MA t 3 = (A t + A t-1 + A t-2 )/3 Ten period moving average in period t is the average of

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Forecast Using Moving Average Forecast for period t+1 is equal to moving average for period t F t+1 =MA t n n period moving average in period t is the average of MA t n = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-n+1 )/n F t+1 =MA t n = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-n+1 )/n

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Actual data; taking into account Which one take into account more elements of the actual data,? a 4-period moving average or a 7-period moving average? MA t 4 = (A t + A t-1 + A t-2 + A t-3 )/4 MA t 7 = (A t + A t-1 + A t-2 +A t-3 + ….+ A t-6 )/7

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Moving Average, t to t+1 Suppose we are in period 20, and we have already computed 4-period and 7- period moving averages. The actual demand for period 21 is 800 unit. From now on, which one needs to write more data in a file or store more data on computer, 4-periods or 7-period MA?

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MA 4 20 = (A20+A19+A18+A17)/4 MA 4 21 = (A21+A20+A19+A18)/4 4 period moving average at period 20, and 21 MA 4 21 = (800+658+864+1110)/4=858 MA 4 20 = (658+864+1110+634)/4 = 816.5 The Actual Demand for period 21 is 800 The Actual Demand for periods 17-20 are

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4 period moving average at period 20, and 21 MA 4 21 = (800+658+864+1110)/4=858 MA 4 20 = (658+864+1110+634)/4 = 816.5 MA 4 21 = MA 4 20 +(A21- A17)/4 MA 4 21 = 816.5 +(800- 634) /4=858 MA 4 20 = (658+864+1110) /4 +634/4 = 816.5 MA 4 21 = 800/4 + (658+864+1110)/4 = 858

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7 period moving average at period 20, and 21 Actual Demand for period 21 is 800 MA 7 21 = (800+658+864+1110+634+855+738)/7=808.43 MA 7 20 = (658+864+1110+634+855+738+910)/7 = 824.14

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7 period moving average at period 20, and 21 MA 7 21 = MA 7 20 +(A21- A14)/7 MA 7 21 = 824. 14 +(800- 910)/7=808.43 MA 7 21 = (800)/7 + (658+864+1110+634+855+738)/7 = 808.43 MA 7 20 = (658+864+1110+634+855+738 )/7 + (910)/7 = 824.14 MA 7 21 = (800+658+864+1110+634+855+738)/7=808.43 MA 7 20 = (658+864+1110+634+855+738+910)/7 = 824.14

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Which One MA 4 21 = MA 4 20 +(A21- A17)/4 MA 4 21 = 816.5 +(800- 634) /4=858 MA 7 21 = MA 7 20 +(A21- A14)/7 MA 7 21 = 824. 14 +(800- 910) /7=808.43 Same Computations

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Actual data; storing Which one needs to write more data in a file or store more data in Computer, 4 periods or 7 period MA? MA t = MA t-1 +(A t - A t-n )/n MA t 4 = MA 4 t-1 +(A t - A t-4 )/4 MA t 7 = MA 7 t-1 +(A t - A t-7 )/7

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MA t = (A t + A t-1 +…………+ A t-n+2 + A t-n+1 )/n MA t-1 = ( A t-1 + A t-2 …......…... A t-n+1 + A t-n )/n Moving average The relationship between MA t and MA t-1 can be easily computed for any moving average

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MA t = (A t + A t-1 +…………+ A t-n+2 + A t-n+1 )/n MA (t+1) = MA t + (A t+1 - A t-n )/n MA t-1 = ( A t-1 + A t-2 …......…... A t-n+1 + A t-n )/n Moving average Moving average is then used to forecast for the next period. In moving average forecasting F (t+1) = MA t F 22 = MA 21

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Comparison If we are in period 20, and 4-period moving average in period 20 is Then our forecast for period 21 is If the actual demand in period 21 is 800, and the actual demand in period 17 was 634 F 22 = MA 21 MA 4 20 = 816.5. F 21 = MA 4 20 = 816.5 Our forecast for period 22 is F 22 = MA 21 = 858 MA 22 = 816.5+(800-634)/4 = 858.

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4 and 7 period moving average Which one create a more smooth forecasting curve? A 4 period or a 7 period moving average. Increase the number of periods; increase the smoothness of a forecast Decrease the number of periods; increase the responsiveness of a forecast

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Micro $oft Stock

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Exponential smoothing

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The president of State University wants to forecast student enrollments for this academic year based on the following historical data: 5 years ago 15,000 4 years ago 16,000 3 years ago 18,000 2 years ago 20,000 Last year 21,000 What is the forecast for this year using exponential smoothing with alpha = 0.4, if the forecast for two years ago was 16,000? Practice

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t 1 2 3 4 5 At 15000 16000 18000 20000 21000 Ft 16000 Forecast for last year F5 = (1-α)F4+ α(A4) F5 =.6(16000)+.4(20000)=17600 Forecast for this year F6 = (1-α)F5+ α(A5) F6 =.6(17600)+.4(21000)=18960 17600

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.2 .05 Smoothing constant

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Exponential smoothing and Moving Average Which one take into account more elements of the actual data,? a 100-period moving average, or an exponential smoothing?

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How many piece of data are involved in ES

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Exponential Smoothing α=.2 t At Ft 1 100 F1 Since I have no information for F1, I just enter A1 which is 100 A1 F1

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Exponential Smoothing α=.2 t At Ft 1 100 F2 =(1- α)F1 + α A1 F2 =(1-.2)100 +.2(100) F2 =80 + 20 = 100 A1 & F1 F2 A1 F1 A1 F2 2 100

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Exponential Smoothing α=.2 t At Ft 1 100 F3 =(1- α)F2 + α A2 F3 =.8(100) +.2(150) F3 =80 + 30 = 110 F2 & A2 F3 A1 F2 A1 & A2 F3 2 100 3 110 150

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Exponential Smoothing α=.2 t At Ft 1 100 F4 =(1- α)F3 + α A3 F4 =.8(110) +.2(120) F4 =88 + 24 = 112 A3 & F3 F4 A1 & A2 F3 A1& A2 & A3 F4 2 150 100 3 110 4 112 120

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Exponential Smoothing F3 =(1- α)F2 + α A2 F2 =A1 F3 =(1- α)A1 + α A2 F4 =(1- α)F3 + α A3 F4 =(1- α)[(1- α)A1 + α A2] + α A3 F4 =(1- α) 2 A1 + α(1- α) A2 + α A3 F4 =(.8) 2 A1 +.2(.8) A2 +.2 A3 F4 =(.64) A1 + (.16) A2 +.2 A3 F4 =(.64) 100 + (.16) 150 +.2(120) F4 =64 + 24 + 24= 112

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Error - difference between actual value and predicted value Mean absolute deviation (MAD) Tracking Signal (TS) Forecast accuracy

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MAD = ActualForecast n Mean Absolute Deviation (MAD)

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Ratio of cumulative error and MAD Tracking signal = ( Actual - forecast ) MAD Tracking signal = ( Actual - forecast) Actual - forecast n Tracking signal = ( Actual - forecast) Actual - forecast n

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Tracking signal UCL LCL Time Tracking Signal Detecting non-randomness in errors can be done using Control Charts (UCL and LCL)

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Tracking signal UCL LCL Time Tracking Signal

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Associative (Causal) Forecasting The primary method for associative forecasting is Regression Analysis. The term most closely relates to associative forecasting techniques is predictor variables The predictor variable in simple linear regression is the independent variable

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Computed relationship Regression method Least squares line minimizes sum of squared deviations around the line

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Regression method

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Regression: Tools / Data Analysis / Regression

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Regression: X and Y ranges

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Regression Output

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Multi-Variable Regression

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Tools/Data Analysis

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Regression

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Y Range

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X Range

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Check Boxes

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Regression Line^ y = 3.17+ 1.4 x 1 +.251 x 2 SALARY = 3.17 + 1.40 EXPER + 0.251 SCORE

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Conclusion Predictions are usually difficult, especially about the future. Yogi Berra The former New York Yankees Catcher

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Assignment 2: Problem 1 Given the following data (a)Plot the data (b)Forecast for Sep. using linear regression (c)Forecast for Sep. using 5 period moving average (d)Forecast for Sep. using exponential smoothing. Alpha is.2 and forecast for march was 19 (e)Forecast for Sep. using Naïve method (f)Compute MAD for naïve method and exponential smoothing. Which one is preferred? NM or ES.

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(a) Exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be 5 units larger than actual demand. The next forecast is 65. Compute ? (b) The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is 6 period moving average in month 7? Assignment 2: Problem 2

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