What is forecasting? + Forecasting is a a tool used for predicting future demand based on past and current demand information. + Common variables that are forecasted include demand levels, supply levels, and prices.What is forecasting? + Forecasting is an integral part of almost all business enterprises including Manufacturing firms that forecast demand for their products Service organizations that forecast customer artival patterns to maintain adequate customer! service, Secutity analysts who forecast revenues, profits, and debt ratios, to make investment recommendations. + Firms that consider economic forecasts of indicators (housing starts, changes in gross national profit) before deciding on capital investments.fa) a is a a ZZ ~ eB) rs | I What is hotel n Tete My ______} ee 'youtube.comiwatc! )-WLFSC-](a) ofl Why is forecasting important? Demand for products and services is usually uncertain. Forecasting can be used for + Strategic planning (long range planning) + Finance and accounting (budgets and cost controls) + Marketing (future sales, new products) + Production and operations pusness —— researct Sefa) What is forecasting all about? Demand for Mercedes E Class Dieteaaeca as sina oentae te Baan er ace Cone) ee) Peetind a Jan Feb Mar Apr May Jun Jul Aug @ | Actual demand (past sales) @ Predicted demanda 2 Short Term Forecasting: Needs and Uses Scheduling existing resources + How many employees do we need and when? * How much product should we make in anticipation of demand? nal resources * When are we going to run out of capacity? + How many more people will we need? * How large will our back-orders be? six months one year five years Determining what resources are needed * What kind of machines will we require? * Which services are growing in demand? declining? + What kind of people should we be hiring?Example: Mercedes E-class vs. M-class Sales Month | E-classSales | M-class Sales Jan 23,345 = Feb 22,034 = Mar 21,453 = Apr 24,897 = May 23,561 = Jun) 22,684 = Jul ? ? Question: Can we predict the new model M-class sales based on CUTERCP Tmt item e Hemel) Cor PASC eam VCO Co oct ROMO EST om Cena Mme) PLEAS LEN Kea LU MCcepTLEA OE14 Forecast Types Organizations often need to forecast variables other than demand. The most common forecast types are: demand, supply, and price forecasts. Demand Forecasts BAN NX Q) yy Supply Forecasts = Price Forecasts5 Fundamental Principles of ForecastingMain Steps in Forecasting Process See cae nee eo nearer Ce ene eu eit) Step 3 Select a forecasting technique Reason eu ce) Re Pc iey tec ke dee tdMajor Categories of Forecasts __|Quantitative Qualitative avercast https:/www.youtube.com/watch?\ |_9mLIbe&t=2sMajor Categories of Forecasts Qualitative methods — judgmental methods + Forecasts generated subjectively by the forecaster + Educated guesses Quantitative methods — based on mathematical modeling: | + Forecasts generated through mathematical modelingfa) _ Major Categories of Forecasts |__ Forecasting methods are classified into two groups 41. Characteristics Based on human judgment, Based on mathematics; |.) ‘opinions; subjective and quantitative in nature. I nonmathematical. 2. Strengths Can incorporate latest Consistent and objective; changes in the environment —_able to consider much and “inside information.” ‘information and data at i) ‘one time. 3. Weaknesses Can bias the forecast and Often quantifiable data are reduce forecast accuracy. not available. Only as good as the data on which they are based.fa) 20 ff Qualitative Methods Executive opinion Market research Delphi method A group of managers Good for strategic or One person's opinion meet & come up with new-product can dominate the a forecast forecasting forecast Uses surveys & Good determinant of It can be difficult to interviews to identify customer preferences develop a good customer preferences questionnaire Seeks to developa = Excellent for Time consuming to consensus among a forecasting long-term develop group of experts product demand, technologicala ai Qualitative forecasting methods JNAVADHI ‘wwnavedhcom 1. Market Surveys: are generally structured questionnaires submitted to potential customers in the market. They solicit opinions about products or potential products, and also often attempt to get an understanding of the likelihood of customer demand for products or services. od & 6 STEPS OF SUCCESSFUL Strength: If structured well and administered to a MARKET RESEARCH, representative sample of the defined population, PROCESS. © market surveys can be quite effective. Weakness: A major drawback is that they are expensive and time-consuming to perform."2. Panel Consensus: A qualitative forecasting technique that brings experts together to discuss and develop a forecast. | 3. Delphi Method: A qualitative forecasting technique in which experts work individually to develop forecasts. The individual forecasts are shared among the group, and then each participant is allowed to modify his or her forecast | based on information from the other experts. | This process is repeated until consensus is reached. Advantages: The advantage is that when done correctly, i ney do tend to be quite accurate. Disadvantages: These two methods tend to be quite expensive, primarily due to the time requirements from a group of experts in the “field. Such experts often charge fairly high fees for their ime and observations. ‘Steps of Delphi Method4. Life cycle analogy method is a forecasting technique that attempts to identify the time frames and demand levels for the introduction, growth, maturity, and deciine Ife cycle stages of a new product or service based on the observation that many products and services have a fairly well-defined lite cycle. ‘The major questions that arise include the follo 4 + How long will each stage last? + How rapid will the growth be? How rapid will the decline be? + How large will the overall demand be, especially during the maturity phase? £ Sales ‘invest Introduction] Growth ~ Effective if the new product or service is essentially replacing another in the market and targeted to the same population. Disadvantages: Not accurate, but a good starting point when no product demand history is available.Qualitative forecasting methods 5. Informed judgment is among the most common forecasting methods used, but unfortunately is also among the worst methods lo use. Example: A sales manager to ask each salesperson to develop a projection of sales for their area for some defined time period in the future. The sales manager then combines the individual sales projections into an overall sales forecast for the company. This method tend to be so poor due to several things that will | Potentially alter the judgment ofthe incividual, sometimes without them being consciously aware. For example: - Being optimistic - Being pessimistic Being affected by recent eventsfa) Quantitative forecasting methods 25a 26 fl Causal Models Causal models use statistical techniques to establish relationships between various items and demand Some of the key characteristics of these methods include: + This method is based on the concept of relationship between variables, or the assumption that one measurable variable "causes" the other to change in a predictable fashion. + The causal variable can be accurately measured. + The developers will gain additional significant market Knowledge during the process of developing the models. » These methods are seldom used for product, but more commonly used for entire markets or industries. + The methods are often time-consuming and very expensive to develop, primarily because of developing the relationships and obtaining the causal data. eCeC SC! Gausal Forecastingfa) 27 Causal Relationship: Some of the more common methods of causal forecasting are given as: input =y Input-output models om Simulation models G output Econometric models Regression_ Time Series + Time Series models predict future demand based on past history trends Itis the process of analyzing time series data using statistics and modeling to make. predictions and inform strategic decision- making. It's not always an exact prediction, when dealing with the commonly fluctuating variables in time series data as well as 2 factors outside our control. Examples of time series forecasting ___- Forecasting the closing price of a stock _ each day /__ - Forecasting product sales in units sold each day for a store 10 fie Frecean on New Date ‘ooo! aval = predicted 2200 3 E 2000 ‘ays an 212-Dec 2016)Time Series Patterns . Random pattern (Horizontal Pattern) A horizontal pattern exists when the data fluctuate randomly around a constant mean ovel time. Changes in a condition often result in a time series with a horizontal pattern to shift to a new level at some point in time Demand endo seges ation30 resriceaire rar desea ‘wend a |\ rane ocean werd ‘enioesr PX lerecaing versTime Series Patterns '3. Seasonal pattern oe ‘Sarpie seasonal {opal pater + It occurs when a time series is affected by seasonal factors such as the time of the year or the day of the week. “he ‘Seasonality is always of a fixed and known frequency.Time Series Patterns . Cyclic pattern It occurs when the data exhibit rises and falls g «»- that are not of a fixed frequency. gow. 5 The duration of these fluctuations is usually of be at least 2 years.33 | | Time Series Patterns If we were to put a random pattern together with a trend and a seasonal pattern, we could obtain a demand pattern that would look similar to the pattern experienced by many companies for their products or services. For example, a random, seasonal pattern with a linear increasing trend might look something like the figure below Demand Time| Time Series Forecasting Models 1. Naive (Last Period) Models _ The simplest time series model is a last period model, which uses demand for the current period “as a forecast for the next period. Stated formally: Fy =D, where: Fy, = forecast for the next period, t + 1 D, = demand for the current period, t"Consider the time series listed in below table and graphed. Suppose the director of the emergency care facility decides to use Naive(last period) forecasting model to predict the number of patients each week. 2 3 4 | yg 7 27 108 8 17 27 9 27 7 0 103 127 Zz 36 ie ae a i 12 36 36 ‘Week 3 26 % 14 101 36 As the results suggest, the main problem with a Naive 13 103 101 model is that it is based on only one observation. This | 109 makes it overly susceptible to unusually high or low values Naive (Last Period) Forecasting for an Emergency Care FacilityiE ‘Time Series Forecasting Models __ 2, Simple Moving Average (SMA) Model + It derives a forecast by taking an average of a set of recent demand values. By basing the forecast on more than one observed demand value, the moving average model is less susceptible to random swings in demand. The model is stated as follows: 2 Drei Aa F..1 = forecast for time period t + 1 Drst-i ctual demand for period t + 1 — i n = number of most recent demand observations used to develop the forecastQ) For example, using the data in the table, what is the forecast for week 16 using four-period simple | moving average (4 period-SMA) and two-period __ simple moving average (2 period-SMA)? Four-period simple moving average: The forecast for 16 is derived from the demand figures for the *: previous four weeks (weeks 12-15): . 8 8 | Two-period simple moving average: The forecast for 16 is derived from the demand figures for the previous two weeks (weeks 14-15): =105 3 | ‘Number of patients| Time Series Forecasting Models 3. Weighted Moving Average (WMA) Model | A variation of the moving average model is the weighted moving average model. In this case, he actual weights applied to past observations are allowed to differ: . Ra = Win iDear- W,41-i = weight assigned to the demand in period t + 1 — i " DM =1 a As the formulas suggest, the only real restriction is that the weights must add to 1.Q) Suppose we want to use a three-period weighted moving average (3 period- WMA) model with the following weights: | Weight given to the current time period = Wt = 0.5 Weight given to the last time period = Wt- 1 = 0.3 Weight given to the time period two periods earlier = W-2 = 0.2 / The different weights will place more emphasis on the most recent | observations. Using the data in the table, the three-period weighted moving average forecast for week 16 would be: 4 Fis = YWre-Dio-i = WisDis + WuaDiy + WD a = 0.5*109 + 0.3*101 + 0.2*86 = 102 pos co es} 84 aI 29 90 93 106 a7 n7 a7 103 96 96 a6 101 109Flavio’s Pizza has recorded the following demand history for each Friday night for the past 5 weeks. Develop forecasts for week 6 using a two-period moving average and a three period _ weighted moving average. The weights for the three-period moving average model are 0.4, 0.35, and 0.25, starting with the most recent observation. ia Solution: 1 . 2 The two-period moving average forecast would be: - Fez (60 + 73)/2 = 66.5 pizzas a The three-period moving average forecast would be: _ _ Fe= 0.4*60 + 0.35*73 + 0.25*55 = 63.3 pizzas —| Time Series Forecasting Models _ 4, Exponential Smoothing Model _The exponential smoothing model is @ special form ofthe moving average model in which the forecast for the next period is calculated as the weighted average of the current period’s actual _ value and forecast. The formula for the exponential smoothing model is: cy F,.1 = forecast for time periodt + 1 (e., the new forecast) R D, = actual value for time period t smoothing constant used to weight D,and F,(0 = a@ = 1) forecast for time period t (ic., the current forecast) R I42 Example Suppose the Emerald Pool Company has just started selling aboveground pools. In the first month, the company forecasted demand of 40 pools, while actual demand tured out to be 50. If we select an_ value of 0.3, the exponential smoothing forecast for period 2 becomes: Period Demand Forecast Fe= 0.3*D: + (1 - 0.3)Fi ' 5 0 = 0.3°50 + 0.7*40 = 15 + 28 = 43 pools 2 a 0.3 °50+(1-0.3)*40=43 / 52 0.3 * 46+ (1-0.3)* 43 = 43.9 Now suppose period 2 demand turns out to be 46 pools. The forecast for period 3 can now be calculated as: 4 03+s2+(1-03)"439 5 ay 03% 48+ (1-03)" 4633 = Fi .3*Ds+ (1 - 0.3)Fe .3*46 + 0.7°43 = 13.8 + 13.0 = 43.9 pools 6 03°47 +(1-03)* 46.83 =_ Example | Using the time series data the table, calculate an exponential smoothing forecast for periods 2 through 20, using a smoothing constant value of 0.8. The detailed calculations for F2 through F7 are as follows: F2 = 0.8°D1 +0.2*F1 = 0.810 + 0.210 = 10 F3 = 0.8°D2 + 0.2*F2 = 0.8°11 +0.2"10 = 10.8 F4 = 0.8°D3 + 0.2*F3 = 0.8*9 + 0.2°10.8 = 9.36 | F5 = 0.8°D4 + 0.2*F4 = 0.8°11 + 0.2*9.36 = 10.67 | F6 = 0.8°DS + 0.2*F5 = 0.810 + 0.2°10.67 = 10.13 FT = 0.8*D6 + 0.2*F6 = 0.8*8 + 0.2°10.13 = 8.43 "Forecasts for periods 8 through 20 are completed in a similar manner. 13 IB 21.t e- % 20 19.68 wo 1974 192075 200 tas mo om var “ose he res ld a5 10.ee oman graze elect poted wast Figures show the complete set of forecast values and graph. Because of the high value, the exponential | “smoothing model now reacts quickly to the increase in demand levels.ll Linear Regression + An approach to forecasting when there is a trend in the data is linear regression. + Linear regression is a statistical technique that expresses the forecast variable as a linear function of some independent variable. + In the case of a time series model, the independent variable is the time period itself.Linear Regression " Linear regression works by using past data to estimate the intercept term and slope coefficient for the followingline: . . , ¢ “) j=at bx R . oe forecast for dependent variable y independent variable x, used to forecasty estimated intercept term forthe line B = estimated slope coefficient forthe line | __ Gand Bare estimated wsing the raw time series data for variable» he dependent variable) + and variable he idepeen variable where: | (5.9) = matched pais of observed (x. numberof paired observations “ Once the line in Equation (has been estimated, the forecaster can then plug in values for x, the independent variable, to generate the forecast values, .Mike Clem, owner of Clem’s Competition Clutches, designs and manufactures heavy-duty car clutches for use in drag racing. In his first 10 |_| months of business, Mike has experienced the demand as shown in the Table and Figure Using the month as the independent variable (x) to forecast demand (y), Mike wants to develop a | linear regression forecasting model and use the |__| model to forecast demand for months 11, 12, and 13. 40 Demand (y) 8 3 12 25 40 50 65 36 61 88 63The first step is to set up columns to calculate the average x and y values, as well as the sums of the x, y, x, and xy values for the first 10 months: | ca) | , 5 2 1 8 1 8 2 12 4 24 3 25 9 75 4 40 16 160 5 50 25 250 6 65 36 390 | 7 36 49 252 | 8 61 64 488 9 88 81 792 10 63 100 630 sum. 55 448 385 3,069 5.50 44.80Plugging these values into the equations gives the estimate of the slope coefficient, b: 3,069 — 2548 7 10 3,069 — 2,464 32 «3RS OLS 385 — — 10 and the intercept term, a: — bx = 44.80 — 7.33*5.50 = 4.49 The resulting regression line is: § = 449 + 7.33x By plugging in 11, 12, and 13 for x, we can generate forecasts for months 11, 12, and 13: Month 11 forecast: 4.49 + 7.33*11 = 85.12 clutches Month 12 forecast: 4.49 + 7.33*12 = 92.45 clutches Month 13 forecast: 4.49 + 7.3313 = 99.78 clutchesThe beside Figure plots the regression line forecasts _ for months 1 through 13 and the first 410 months of demand. The graph shows how the regression line captures the upward trend in the data and projects it out into the future. Of course, these future forecasts are good’ only as long as_the upward trend of around 7.33 additional sales each month continues. Demandy) 3 3 Bs € 8 o 1 2345 67 8 910 1112 13 ‘Month (x)51 ff How should we pick our forecasting model? The amount & type of available data * Some methods require more data than others Degree of accuracy required * Increasing accuracy means more data Length of forecast horizon * Different models for 3 month vs. 10 years Presence of data patterns ¢ Lagging will occur when a forecasting model meant for a level pattern is applied with a trend52 Selecting a Forecasting Method a |Forecast Errors + Forecasts are never perfect + Need to know how much we should rely on our chosen forecasting method + Measuring forecast error: Forecast error for period jis Ei= Di F, + Note that over-forecasts = negative errors and under-forecasts = positive errorsfa) Measuring Forecasting Accuracy Mean Absolute Deviation (MAD) measures the total error in a forecast without regard to sign Cumulative Forecast Error (CFE) Measures any bias in the forecast Mean Square Error (MSE) Penalizes larger errors Tracking Signal Measures if your model is working MAD = CFE = y (actual— forecast) MSE = TS CFE _ D jactual — forecast | ¥ (actual - forecast )* MAD 5455 Forecast error for period i( E) = D, ~ F, Mean forecast error (MFE) ‘Mean absolute deviation (MAD) = Mean absolute percentage error (MAPE) ad Tracking signal = AD where: ‘D; = Demand for time period Forecast for time period i S & = sum of the forecast errors for periods 1 through m a56 Several measures of forecasting accuracy follow — * Mean absolute deviation (MAD)- a MAD of 0 indicates the forecast exactly predicted demand * Mean absolute percentage error (MAPE)- provides a perspective of the true magnitude of the forecast error * Mean squared error (MSE)- analogous to variance, large forecast errors are heavily penalizedGea ACY fT Py EY rt 5 c 7 r 9 ct 1 cr Eg rr ro cd ry 50 rc ra Erzcd EAC Era Eee Eee ries) rere) reer ore) ray] rere) cry me Er oR) rary 5.94 eae ED pea MAD = 4.85fa) 58 Tracking signal Determines it torecast is within acceptable control limits. If the tracking signal falls outside the pre-set control limits, there is a bias problem with the forecasting method and an evaluation of the way forecasts are generated is warranted.Sumof — MAD RSFE Abs.Dev. Abs.Dev. (%Erront TS = REE 1 1,000 950 -50 -50 50 50 50 (5.26%) eal 2 1,000 1,070 +70 +20 70 120 60 (5.61%) 33 3 1,000 1,100 +100 +120 100 220 73.3 (6.67%) 1.64 4 1000 960-40 «18040. 260 65(677%) 1.2 5 1000 1,090 +490 +170 90 350 70(642%) 2.4 6 1,000 1,050 +50 +220 50 400 66.7 (6.35%) 33 “Overall, MAD = 400 + 6 = 66.7. MAPE = (5.26 + 5.61 + 6.67 +6.77 + 6.42 + 6.35)6= 6.18% ‘Tocking 4 3 2 1 sign gValue forecast. error —_ertor®2 Month ‘a)MSE? forecast for month 10 2 b)MSE ? forecast for month 10 ? c) Which method appears better? Value forecast error error’? 1 2 2 Fy R 2144 3 2B 6 36 4 23? 16 7 49 5 1a" 1775 3.75 14.0625 6 wo ° °o 7 wa 7 49 8 ww ° a7. 25 625 using the most recent value as forecast using the avg of available data as forecasta ol i Week _ Snes 10005 of USD) Exponential fneast (a= 0.1) enor __ABS(encs) enor'2_Sverror_ ABS ene) 7 2 a m0 100 100100435 6 10 410 410681 22.78% 22.78% is ne 369 3691362 20508 20508 2 a2 168168282708 7.30% 2 nas 049 odd 028-2 2K 0 na 4a dak 39.71 262% 262% 2 no 200 «20402 TIN 2 7120080 080065 365% su 2 72a 00720523298 3.29% ias3 5938 0% [Weck _ Sales (10005 of USD) i frecast(a=02) eror _ABS(enoe) cor’? _% cor eo 2 » mo 1 L.A ASK 1s mm 40 © 420 «sk 2K ARN. 18 213-2 2351129 1K ON. B 20s 231 2a 5.35 105% 105K. a1 2s ais ats, om OK ON. "7 mn 42 42 1698 2am DEH. 2 2030270270731 176% ML T6N. 2 post 116116138208 SDD 207 oss ass os 4K ADIN 1998 6180 amrWeek _ Snes 10005 of USD) Exponential fneast (a= 0.1) enor __ABS(encs) enor'2_Sverror_ ABS ene) 2 rt ee — a at a ois i Mik l= 3 ——— t= ——— #4 —— eo — —— 3 a —e ale Be ae ue, at ——— ———— == t—# ———— rt % a t—$ ae = ae ee + —# Se aa a z eee “ ~ ea,Qa ef Moving Average Forecasts Weighted Moving Average Forecasts Period) Sales Moving Average Forecasts Weighted Moving Average Forecasts | Error Absolute Deviation Squared Eror| Error Absolute Devitlon ‘Squared Eror 130 2 208 47 30.33383533 30.83533333 3.333338 3.333399833 11.a1n1i111|-3.833833 3.833385333 14 69eaaaas 5s 48 2933333333 29.16666667 43466667 14.66666657 215.1111131|24.833333 1483332333 2200277778 6 oa 34.66666667 365 -13,66667 12.66666667 186.7777778| -15 155 240.25, 79 30.66665667 29.65656667 8.333333 8339333333 69.4adaaaaa]|9.3393333 9.333339333 @7.11111111 8 34.66665667 338322333 9.566667 e.6se666667 75.11111131|-7.923333 7.932332323 6136111111 soa 28,66666667 295 7.866667 7.666666667 58.77777778| 85 as 7225 Pomme 28.66565667 25.65656667 2.333333 2339333333 S.anaqaaaaa|5.3333333 9.333333333 2aaqaaaaae uoo3 26 26.83333333 7 7 49 |6.1666667 6.166656667 3802777778 pv 2 2,33333333 30.33333333 0.666667 o,6s6666657 o.asacasaga|-1.333333 | 1.3333333331.777797778 aon 3 30.65556667 cre map mse | cre Map se YY Compare the accuracy ofthe forecasts using MAD. Please indicate whch forecast appears tobe most accurate. Compare the accuracy ofthe forecast sing MSE lease indicate which forecast appears tobe mos accurate, Compare the accuracy ofthe forecasts srg the cumulative error. Pleas ndcate which forecast appears tobe most accurate,64 | COMPUTER-BASED ORECASTING PACKAGES Spreadsheets * Microsoft Excel, Quattro Pro, Lotus 1-2-3 + Limited statistical analysis of forecast data Statistical packages * SPSS, SAS, NCSS, Minitab * Forecasting plus statistical and graphics Specialty forecasting packages * Forecast Master, Forecast Pro, Autobox, SCAfa) | COLLABORATIVE PLANNING, FORECASTING, AND REPLENISHMENT (CPFR) - CPR is a set of business processes, backed up by information technology, in which supply chain partners agree to + mutual business objectives and measures, + develop joint sales and operational plans, + and collaborate to generate and update sales forecasts and replenishment plans. What distinguishes CPFR from traditional planning and forecasting approaches is the emphasis on collaboration. - The increased communication among partners means that when demand, promotions, or policies change, managers can adjust jointly managed forecasts and plans immediately, minimizing or even eliminating costly after-the-fact corrections.66 SUMMARY + Forecasting is a critical business process for nearly every organization. + There are four basic patterns of data: level or horizontal, trend, seasonality, and cycles. + Forecasting methods can be classified into two groups: qualitative and quantitative + Different measures of forecast error, such as MAD, MSE, MAPE, MFE and TS. + There are four factors to consider when selecting a forecastng model: amount and type of data available, degree of accuracy required, length of forecast horizon, and patterns present in the data.o7 i Exercises68 ff Problem #1 Below are monthly sales of light bulbs from the lighting store. ‘Month Sales gen 258: Fe 298 Mar 357 Aor 319 May 360 dune Forecast sales for June using the following 1. Naive method 2.Three- month simple moving average: 3. Three-month weighted moving average using weights of 5, 3 and 2 4, Exponential smoothing using an alpha of 2 and a May forecast of 350.1.360 2. (397 +519 + 560)/3=3453 3.360 x 5-319 x3 +357 x.2=3471 4,350 + 2(860 - 350) = 35270 ff Problem #2 Demand for aqua fit classes at a large Community Centre are as follows for the first six ‘weeks of this year. Week Demand 1 162 2 18 3 we 4 190 5 162 6 m 7 ‘You have been asked to experiment with several forecasting methods. Calculate the follow- ing values: 1a) Forecast for weeks 3 through week 7 using a two-period simple moving average 2.b) Forecast for weeks 4 through week 7 using a three-period weighted moving average: with weights of 6, Sand 1 3.¢) Forecast for weeks 4 through week 7 using exponential smoothing. Begin with a ‘wook 3 forecast of 130 and use an alpha of 3al (962 +158) /2= 160 (osa.+ 138) /2 148 (938 +190) /2 = 164 (990 + 162) /2= ras 992.4177) /2= 195 138 x.6+ 198% 5 +162x 121464 190x 6+ 158 x.3~ 158 x a=1m2 162.6 + 190x.3 + 38x 3=180 17.6 + 182% 3+190x i 8) 130 150 + 3x (138-150) 124 152.4 = 3 x (190 182.4) =497 V9.7 + 3x (182- 14997) = 159.4 1594 + 3x (177-1894) 2166.7 32179872 ff ‘Demand for aqua fit classes at a large Community Centre are as follows for the first six weeks of this year. 162 188 we 190 vez wr You have been asked to experiment with several forecasting methods, Calculate the follow- ing values: 1. a) Forecast for weoks 3 through week 7 using a two-period simple moving average 2. b) Forecast for wooks 4 through woek 7 using a three-peried weighted moving average with weights of 6, 3 and 1 3.) Forecast for weeks 4 through week 7 using exponential smoething. Begin with a ‘week 5 forecast of 180 and use an alpha of 3182 7 (062 +158) /2 160 (058 +138) /2 148 (138 +990) / 166 (090+ 182) / 186. e249) /2= 1795 >) 138 x 6+ 158.3 +162 121464 190 x 6 +138 x 3+ 158x yea 182.6 + 190%.3 4188x 1=180 W7x 6+ 182x 3 +190x 11798 130 130 + 3x (138-130) = 124 152.4 + 3% (190-1524) =497 497 + 3x 1a2~ 1497) =159.4 1994 + 3x (177-189.4) 166.7 73 |74 ff Problem #3 Sales of a new shed has grown steacily rom the large farm supply store. Below are the sales from the past five years. Forecast the sales for 2018 and 2019 using exponential smoothing h an alpha of 4 In 2015, the forecast was 360. Calculate a forecast for 2016 through te Year Sales Forecast 2015 348 $60 2016 372 2017 3 2018 371Forecast Year 2015 2016 2007 2018 2019 2020 3583 + 4x (365-3533) = 3580 Sales 348, a m 365 360 360+ 4 « (348-360) = 355.2 3552+ 4 x(872-3552)= 3619 3619 + 4x (SM 3619) = S416 ALG + 4x (571-3416) = 3533 7576 ff Problem #4 Bolow is the actual demand for X-rays at a medical clinic. Two methods of forecasting were sed. Calculate a mean absolute deviation for each forecast method. Which one is more accurate? “Week Actual Demand Forecast #1 Forecast #2. 50 56 5s es Beas saasForecast #1 letron Forecast #2 lertort 50 2 60 2 55 wo 86 9 60 2 55 3 70 9 65 6 Mean Abs Mean Abs Deviati 575 Deviation: .