OPIM201BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Chapter 6: Forecasting 1. Introduction Forecasting is vital to every business organization and for every significant management decision. Forecasting is the basis of corporate long-run planning. In the functional areas of finance and accounting, forecasts provide the basis for budgetary planning and cost control. Marketing relies on sales forecasting to plan new products, compensate sales personnel, and make other key decisions. Production and operations personnel use forecasts to make periodic decisions involving process selection, capacity planning, and facility layout, as well as for continual decisions about production planning scheduling, and inventory. Bear in mind that a perfect forecast is usually impossible. Too many factors in the business environment cannot be predicted with certainty. Therefore, rather than search for the perfect forecast, it is far more important to establish the practice of continual review of forecasts and to learn to live with inaccurate forecasts. When forecasting, a good strategy is to use two or three methods and look at them for the commonsense view. 2. Types of forecasting Forecasting can be classified into four basic types: Qualitative: Qualitative techniques are subjective or judgmental and are based on estimates and opinions. Time series analysis: This is based on the idea that data relating to past demand can be used to predict future demand. Causal relationships: Causal forecasting, which we discuss using the linear regression technique, assumes that demand is related to some underlying factor or factors in the environment. Simulation: Simulation models allow the forecaster to run through a range of assumptions about the condition of the forecast. 3. Qualitative techniques in forecasting Grass roots: this method builds the forecast by adding successively from the bottom. The assumption here is that the person closest to the customer or end user of the product knows its future needs best. Forecasts at this bottom level are summed and given to the next higher level. This is usually a district warehouse, which then adds in safety stocks and any effects of ordering quantity sizes. This amount is then fed to the next level, which may be a regional warehouse. The procedure repeats until it becomes an input at the top level, which, in the case of a manufacturing firm, would be the input to the production system. Market research: Firms often hire outside companies that specialize in market research to conduct this type of forecasting. Market research is used mostly for product research in the sense of looking for new product ideas, likes and dislikes 1/20 OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- about existing products, which competitive products within a particular class are preferred, and so on. The data collection methods are primarily surveys and interviews. Historical analogy: In trying to forecast demand for a new product, an ideal situation would be where an existing product or generic product could be used as a model. There are many ways to classify such analogies--for example, complementary products, substitutable or competitive products, and products as a function of income. If you buy a CD through the mail, you will receive more mail about new CDs and CD players. Another example would be toasters and coffee pots. A firm that already produces toasters and wants to produce coffee pots could use the toaster history as a likely growth model. Panel consensus: In a panel consensus, the idea that two heads are better than one is extrapolated to the idea that a panel of people from a variety of positions can develop a more reliable forecast than a narrower group. Panel forecasts are developed through open meetings with free exchange of ideas from all levels of management and individuals. The difficulty with this open style is that lower employee levels are intimidated by higher levels of management. For example, a salesperson in a particular product line may have a good estimate of future product demand but may not speak up to refute a much different estimate given by the vice president of marketing. The Delphi technique overcomes this problem. Delphi method: this method conceals the identity of the individuals participating in the study. Everyone has the same weight. Procedurally, a moderator creates a questionnaire and distributes it to participants. Their responses are summed and given back to the entire group along with a new set of questions. This technique can usually achieve satisfactory results in three rounds. 4. Time series analysis Time series is just a fancy term for a collection of observations of some economic or physical phenomenon drawn at discrete points in time, usually equally spaced. The idea is that information can be inferred from the pattern of past observations and can be used to forecast future values of the series. 4.1. Components of demand In most cases, demand for products or services can be broken down into six components: average demand for the period, a trend, seasonal element, cyclical elements, random variation, and autocorrelation. See appendix for an example figure of these components. Cyclical factors are more difficult to determine because the time span may be unknown or the cause of the cycle may not be considered. Cyclical influence on demand may come from such occurrences as political elections, war, economic 2/20 OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- conditions. The cyclic variation is similar to seasonality. except that the length and the magnitude of the cycle may vary. More specifically. Methods for forecasting stationary series A stationary time series is one in which each observation can be represented by a constant plus a random fluctuation. and auto-correlative) are subtracted from total demand.2. Random variations are caused by chance events. cyclical. Simple moving average When demand for a product is neither growing nor declining rapidly.2. and if it does not have seasonal characteristics. If we cannot identify the cause of this remainder. what remains is the unexplained portion of demand. 4. In a N-period simple moving average. it measures the degree of dependency among values of observed data separated by a fixed number of periods. when all the known causes for demand (average. Statistically. seasonal. trend. or sociological pressures. it is assumed to be purely random chance.1. we take the average of last N periods as our forecast for the next period. Example 1: Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Actual Demand 800 1400 1000 1500 1500 1300 1800 1700 1300 1700 1700 1500 2300 2300 2000 3-week 9-week 3/20 . 4. Autocorrelation denotes the persistence of occurrence. a moving average can be useful in removing the random fluctuations for forecasting. OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Although it is important to select the best period for the moving average. The main disadvantage with this method is that all individual elements must be carried as data because a new forecast period involves adding new data and dropping the earliest data. the best forecast is derived by using 40 percent of the actual sales for the most recent month.2. Therefore. 30 percent of two months ago. Another shortcoming of this method is it lags behind the trend. For example. But if there is a trend in the data – either increasing or decreasing – the moving average has the adverse characteristic of lagging the trend. 4. The longer the moving average period. a longer time span gives a smoother response but lags the trend. a department store may find that in a four-month period. The amount of data involved is significant. If actual sales experience was month 1 100 month 2 90 month 3 105 month 4 95 month 5 ? The forecast for month 5 would be F5 = Suppose sales for month 5 actually turned out to be 110. a weighted moving average allows any weights to be placed on each element. of course. Period Actual demand 3-period avg 6-period avg 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 4 10 6 12 8 14 10 7 16 12 9 18 14 11 20 16 13 22 18 15 24 20 17 Notice that both the 3-period and 6-period moving average forecasts lag behind the trend.2. Consider a demand process in which there is a definite trend as follows. providing. that the sum of all weights equals 1. there are several conflicting effects of different period lengths. Weighted moving average Whereas the simple moving average gives equal weight to each component of the moving average database. for a shorter time span. Conversely. the more the random elements are smoothed. 20 percent of three months ago. and 10 percent of four months ago. and that the forecast with a smaller N value follows the actual demand more closely. there is a closer following of the trend. Then the forecast for month 6 would be F6 = 4/20 . Prepare a 3-period moving average forecast. Which of the two forecasts is better? (use MAD to judge) 5/20 . weights should be established accordingly. What is the error on each day? b.3. the number of daily calls for repair of Speedy copy machines in 8 days has been recorded as follows: actual demand day 1 2 3 4 5 6 7 8 3-day moving avg Forecast error weighted moving avg Forecast error 92 127 103 165 132 111 174 94 a. and therefore. Prepare a 3-period weighted moving average forecast with w1=0. However. What is the error on each day? c. the most recent past is the most important indicator of what to expect in the future. w2=0. Bathing suit sales in July of last year should be weighted more heavily than bathing suit sales in December.5(most recent data carries heaviest weight). for example.2. Example 2: In Atlanta. As a general rule. if the data are seasonal.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Choosing weights: experience and trial and error are the simplest ways to choose weights. it should get higher weighting. and w3=0. if a firm produced a standard item with relatively stable demand. the higher the reaction rate should be. and it is widely used in ordering inventory in retail firms. it would be desirable to have a higher reaction rate.2. Exponential smoothing Exponential smoothing is the most used of all forecasting techniques. For example. and service agencies. However. 6/20 . The equation for a single exponential smoothing forecast is simply Ft = Ft-1 + α (At-1 – Ft-1) Example 3: Assume last month’s forecast was 1050. This smoothing constant determines the level of smoothing and the speed of reaction to differences between forecasts and actual occurrences. The more rapid the growth. to give greater importance to recent growth experience. the actual demand that occurred for that forecast period. perhaps just 5 or 10 percentage points. wholesale companies. and a smoothing constant alpha (α). only three pieces of data are needed to forecast the future: the most recent forecast.3. and 1000 actually were demanded.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 4. The value for the constant is determined both by the nature of the product and by the manager’s sense of what constitutes a good response rate. the reaction rate to differences between actual and forecast demand would tend to be small. perhaps 15 to 30 percentage points. Exponential smoothing methods have become well accepted for six major reasons: Exponential models are surprisingly accurate Formulating an exponential model is relatively easy The user can understand how the model works Little computation is required to use the model Computer storage requirements are small because of the limited use of historical data Tests for accuracy as to how well the model is performing are easy to compute In the exponential smoothing method.05. It is an integral part of virtually all computerized forecasting programs. if the firm were experiencing growth. What is the forecast for this month? Use α = 0. substituting into the above equation yields Ft = α At-1 + α (1.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- The following is some supplementary info for you to understand why we use the term “exponential”. we can fit the continuous exponential curve α exp(-αi) to these weights. which is why the method is called exponential smoothing. The smoothing constant α plays essentially the same role here as the value of N does in moving averages. 7/20 .α) At-2 + (1. more weight is placed on the current observation of demand and less weight on past observations. Notice that Ft-1 = Ft-2 + α (At-2 – Ft-2). You can skip it if you are not interested.α )2 Ft-2 We can substitute for Ft-2 in the same fashion. exponential smoothing applies a declining set of weights to all past data. If α is large. In fact. which results in forecasts that will react quickly to changes in the demand pattern but may have much greater variation from period to period. If we continue in this way we obtain the infinite expansion for Ft: ∞ Ft = ∑ α (1 − α ) i At −i −1 i =0 Hence. 1. If the actual for the next period turned out to be 120.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 4. Trend-based methods Both moving average and exponential smoothing forecasts will lag behind a trend if one exists. The latter is a method that fits a straight line to a set of data.3. and a delta of 0. the forecast always lags the actual occurrence. a trend of 10. 4. and Tt = Tt-1 + δ (Ft – FITt-1) To get the equation going. This initial trend value can be an educated guess or a computation based on observed past data.3.2. calculate the forecast including trend for the next period. A smoothing constant delta (δ) is introduced. an alpha of 0. then what is the forecast including trend for the second next period? 8/20 . Enhanced exponential smoothing with trend Note that in simple exponential smoothing. Example 4: Assume an initial starting forecast of 100. The former is a type of double exponential smoothing that allows for simultaneous smoothing on the series and on the trend. If actual demand turned out to be 115 rather than the forecast 100.3. This can be somewhat corrected by adding in a trend adjustment. the first time it is used the trend value must be entered manually. In this section we consider two forecasting methods that specifically account for a trend in the data: enhanced exponential smoothing with trend and regression analysis. The equation to compute the forecast including trend (FIT) is FITt = Ft + Tt Where Ft = FITt-1 + α (At-1 – FITt-1). Solution: x y xy 1 600 2 1550 3 1500 4 1500 5 2400 6 3100 7 2600 8 2900 9 3800 10 4500 11 4000 12 4900 x2 9/20 . y ∑ x − nx 2 2 Example 5: A firm’s sales for a product line during the 12 quarters of the past three years were as follows: Quarter 1 2 3 4 5 6 Sales 600 1550 1500 1500 2400 3100 Quarter 7 8 9 10 11 12 Sales 2600 2900 3800 4500 4000 4900 The firm wants to forecast each quarter of the fourth year—that is. b is the slope. The least squares method is used to fit the line to the data. Linear regression refers to the special class of regression where the relationship between variables forms a straight line. where a is the Y intercept. It is used to predict one variable given the other.3. The parameters of the line are given by a = y − bx b= ∑ xy − nx.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 4. Linear regression analysis Regression can be defined as a functional relationship between two or more correlated variables. quarters 13 through 16. This method tries to minimize the sum of the squares of the vertical distance between each data point and its corresponding point on the line. The linear regression line if of the form Y = a + b x.2. We restrict our attention to this case as it is the usual experience. Seasonality There are several ways to represent seasonality. Essentially. Seasonal forecasts are generated by adding a constant (say. this says that the larger the basic amount projected. This implies that the seasonal pattern depends on the level of demand. Following are the quarterly demand data from the past four years: 10/20 . week to week. This gives seasonal factors for each season. seasonal factors are multiplied by an estimate of average demand to arrive at a seasonal forecast. with a peak in the third quarter and a trough in the first quarter. Seasonal factor (or index): a seasonal factor is the amount of correction needed in a time series to adjust for the season of the year. then obtain the final forecast by multiplying the seasonal factor by the average demand per season. Additive seasonal variation simply assumes that the seasonal amount is a constant no matter what the trend or average amount is.1.4.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 4. the seasonal pattern lasts a week. the larger the variation around this that we can expect. begin by estimating the average demand per season for next year.4.2. To calculate each season’s forecast for next year. 4. The carpet cleaning business is seasonal. and the seasons are the days of the week. Note that this is different from the popular usage of the word season as a time of year. The peaks and valleys are more extreme when average demand is high. In this case. For example. which is referred to as the length of the season. Here we examine tow types of seasonal variation: additive and multiplicative. 4.4. In multiplicative seasonal variation. Compute the overall average per season from all the data Find the average demand for the same season Divide each seasonal average by the overall seasonal average. the demand for haircuts may peak on Saturday. Seasonal factors for stationary series Now we present a simple method of computing seasonal factors for a time series with seasonal variation and no trend. Example 6: The manager of the Stanley Steemer carpet cleaning company needs a quarterly forecast of the number of customers expected next year. Methods for seasonal series A seasonal series is one that has a pattern that repeats every N periods for some value of N. 50 units) to the estimate of average demand per season. OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------Quarter 1 2 3 4 Year 1 45 335 520 100 Year 2 70 370 590 170 Year 3 100 585 830 285 Year 4 100 725 1160 215 The manager wants to forecast customer demand for each quarter of year 5. we divide the original data by the seasonal factor. we need to identify and separate the time series data into these components to obtain better forecast. Now let’s see how to decompose a time series using least squares regression. Step 3: develop a least squares regression line for the deseasonalized data. Step 5: create the final forecast by adjusting the regression line by the seasonal factor (re-seasonalizing). Decomposition of a time series When demand contains both seasonal and trend effects at the same time. This is called decomposition of a time series.3. The general procedure involves 5 steps: Step 1: determine the seasonal factor Step 2: deseasonalize the original data. The purpose is to develop an equation for the trend line. Solution: Overall Avg quarterly sales in past years = Avg quarterly sales for next year = avg past sales seasonal factor forecast for next year Quarter 1 Quarter 2 Quarter 3 Quarter 4 4. Step 4: project the regression line through the period(s) to be forecasted. To remove the seasonal effect on the data. Example 7: 11/20 .4. based on her estimate of total year 5 demand of 2600 customers. 600 8 2.900 9 3.500 5 2. = avg seasonal factor Spring Summer Fall Winter Quarter Sales 1 600 2 1.000 12 4.500 4 1.500 11 4.900 deseasonalized demand Quarter Trend-based forecast Final forecast 13 14 15 16 12/20 .100 7 2.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Use the same data given in example 5. What are the forecasts for the quarters 13 through 16? Solution: Overall quarterly avg.800 10 4.550 3 1.400 6 3. Suppose the seasonal factor is given by the average for the same quarters in the 3year period divided by the general average for all 12 quarters. but now we consider the seasonal effect. Another measure of forecast accuracy is known as the mean absolute percentage ⎡1 n e ⎤ error (MAPE) and is given by MAPE = ⎢ ∑ i ⎥ * 100 . and use only the earlier time periods to develop and test different model.1. some analysts prefer to use a holdout set as a final test. is given by 1. It is independent of the ⎣ n i =1 Ai ⎦ magnitude of the values of demand. as is generally assumed. managers recognize that the best technique in explaining the past data is not necessarily the best to predict the future. an estimate of the standard deviation of the forecast error.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 4. However. then they are tested again with the holdout set. given by the following formulas: MAD = 1 n ∑ ei n i =1 MSE = 1 n 2 ∑ ei n i =1 Note that the MSE is similar to the variance of a random sample. The MAD is often the preferred method of measuring the forecast error because it does not require squaring. To do so.2. 4.5.5.25 times the MAD. Measures of forecast error Define the forecast error in period t. 13/20 . σe. et. Evaluating forecasts 4. as the difference between the forecast value for that period and the actual demand for that period: et = Ft – At Two common measures of forecast accuracy during n periods are the mean absolute deviation (MAD) and the mean squared error (MSE). Once the final models have been selected in the first phase. they set aside some of the more recent periods from the time series. Furthermore.5. For this reason. when forecast errors are normally distributed. Criteria for selecting time-series methods The criteria to use in making forecast method and parameter choices include Minimizing bias Minimizing MAD or MSE Meeting managerial expectations of changes in the components of demand Minimizing the forecast error last period. availability of qualified personnel. excess capacity. 14/20 . If one variable changes because of the change in another variable. o A good forecast is more than a single number. In the linear regression method. Causal relationship forecasting Linear regression technique is used in causal relationship forecasting. Concluding remarks In selecting a forecasting method to use. size of forecasting budget. when the dependent variable (usually the vertical axis on a graph) changes as a result of time (plotted as the horizontal axis). data availability. o The longer the forecast horizon. Ways to cope with forecast errors: buffer—safety stock. Characteristics of forecasts: o They are usually wrong.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 5. Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 Permits 18 15 12 10 20 28 35 30 20 Sales 13000 12000 11000 10000 14000 16000 19000 17000 13000 Suppose that there are 25 permits for houses to be built in 2000. safety lead time. Example 8: The Carpet City Store in Carpenteria has kept records of its sales (in square yards) each year. this is a causal relationship (such as the number of deaths from lung cancer increasing with the number of people who smoke). What is the forecast for sales in 2000? 6. etc. it is time series analysis. along with the number of permits for new houses in its area. a firm should consider many factors including time horizon to forecast. accuracy required. o Forecasts should not be used to the exclusion of known information. o Aggregate forecasts are more accurate. the less accurate the forecast will be. 4 weeks ago Monday 2200 Tuesday 2000 Wednesday 2300 Thursday 1800 Friday 1900 Saturday Sunday 2800 3 weeks ago 2400 2100 2400 1900 1800 2 weeks ago 2300 2200 2300 1800 2100 last week 2400 2200 2500 2000 2000 2700 3000 2900 Make a forecast for this week on the following basis: A. B. with the forecast made in c. Period 1 2 3 4 5 6 7 8 Actual demand 300 540 885 580 416 760 1191 760 15/20 .and under-production because of forecasting errors.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 7. The following data are its demand in dozens of doughnuts for the past four weeks. using a simple four-week moving average.4. Suppose. C. It has been experiencing over. prepare a forecast for the upcoming year using decomposition.1? D. this week’s demand actually turns out to be 22500. What would the new forecast be for the next week? Question 2: Here are quarterly data for the past two years. Doughnuts are made for the following day. Sunrise is also planning its purchases of ingredients for bread production.1 for the past four weeks. for example. using a weighted average of 0. what would Sunrise’s forecast be for this week using exponential smoothing with alpha = 0. Daily. 0. 0. so Friday’s production must satisfy demand for both Saturday and Sunday. and so forth. Sunday’s doughnut production is for Monday’s sales. Daily. Exercises: Question 1: Sunrise Baking Company markets doughnuts through a chain of food stores. From these data. If bread demand had been forecasted for last week at 22000 loaves and only 21000 loaves were actually demanded.3. The bakery is closed Saturday. Monday’s production is for Tuesday’s sales.2. 0. 000 825. and Mar. is experiencing a decline.000 pieces of mail to sort next week. Month Jan Feb Mar Sales 890.2. Generate forecast for Feb. B. 16/20 . The following table shows the actual sales history for Jan. If the postmaster estimates that there will be 230.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Question 3: The demand for Krispee Crunchies. a favorite breakfast cereal of people born in the 1940s. FJan.000 Question 4: The Northville Post Office experiences a seasonal pattern of daily mail volume every week. was 900000 and the trend. The trend-adjusted exponential smoothing method is used with alpha = 0.000 800.1 and delta=0. At the end of December. was -50000 per month. TJan. the January estimate for the average number of cases sold per month. Mar. The following data for two representative weeks are expressed in thousands of pieces of mail: Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday total week 1 5 20 30 35 49 70 15 224 week 2 8 15 32 30 45 70 10 210 A. and Apr. The company wants to monitor demand for this product closely as it nears the end of its life cycle. forecast the volume for each day of the week. Calculate a seasonal factor for each day of the week. Feb. 3*2300+0.987 0.79 789.5272 0.99 564.6.4*2400)/4 = 2350 doz Tue: 2160 Wed: 2400 Thu: 1900 Fri: 1980 Sat & Sun: 2880 C. we have: period trend forecast 9 857.4 10 897.64 Therefore.9573 1.529 0.2*2400+0.1*(21000-22000) = 21900 D.957 1.5287 0.92 587. Monday: (2200+2400+2300+2400)/4 = 2325 doz Tue: 2125 Wed: 2375 Thu: 1875 Fri: 1950 Sat & Sun: 2850 B.08 770.OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Answer Key Question 1: A.527 0.529 0.0 11 936.987 final forecast 452.3 seasonal factor 0.6 12 976.1*2200+0.957 1. b=39.0 858. Ft = Ft-1 + α (At-1 – Ft-1) = 22000+0.9867 deseasonalized demand 568.09 578. we obtain the parameter values: a = 500.1*(22500-21900) = 21960 Question 2: Period 1 2 3 4 5 6 7 8 Avg Actual demand 300 540 885 580 416 760 1191 760 679 period avg 358 650 1038 670 seasonal facto 0.91 779. Ft-1 = 21900 + 0.9 963.7 1431.21 Run a regression in Excel using deseasonalized demand.3 17/20 .01 793. Monday: (0.527 0. 548 32.5 47 70 12.816 74.565 1.5 17.258 0.516 2.000 1.403 forecast 6.5 31 32.249 18/20 .OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- Question 3: Feb: 804800 Mar: 755024 Apr: 714125 Question 4: Day week 1 Sunday Monday Tuesday Wednesday Thursday Friday Saturday total 5 20 30 35 49 70 15 224 week 2 8 15 32 30 45 70 10 210 daily avg 6.210 0.447 49.857 34.048 1.889 18.5 31 seasonal factor 0.194 13. OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 8. Appendix 19/20 . OPIM201 BUSINESS PROCESSES -------------------------------------------------------------------------------------------------------------------------------------------- 20/20 .