Customers, Products, and OM: Forecasting
1Introduction
Forecasting is vital to every business organization. Forecasts drive a wide variety of business decisions, from short-term personnel scheduling to long term facility design. Forecasts are the basis for budget allocations, funding of equipment, and long term strategy. Forecasts will determine a large number of operational decisions as for example the technologies used, the capacity of the facilities, the mix of services or products to make, and what are some areas of business opportunities.
Forecasting is both a science and an art. There are no perfect forecasts given the many factors that affect a business organization. Based on this premise, the objective of forecasting is to determine what forecasting method is the most appropriate for what is being forecasted, and to maintain a strict discipline of reviewing forecasts.
Forecasts are typically of two types, qualitative and quantitative. Qualitative methods are based on perception and knowledge and are typically used for long term planning and strategy. Quantitative forecasts are based on past data, mathematical models, and are typically used for medium to short term planning. In many cases a combination of both methods are used, where knowledge is used to modify quantitative forecasts and some data and mathematical models are used in the processes of qualitative forecasting.
2Product Demand
The demand over time for a specific product can be broken down into three main components: trend, season, and random. Figure 1 shows these three components. A trend is a linear relationship between demand and time. Trends often change, where a firm entering a market may experience rapid growth during the first year, and then taper off after that, with a slow growth trend. In some cases, recognizing changes in trends is one of the qualitative aspects of quantitative forecasting. The seasonal factor relates to periodic changes in demand that reoccur at a steady cycle. We all know about seasons here in SW Florida. The random component relates to variation that cannot be explained by the trend or seasonal effect.
There are models for product demand that are not time based. For example a product demand model can be based on product characteristics, size of the customer base, and other economic factors. For example, product price can have a significant effect on demand. Figure 2 shows the effect of price (competitor price/selling price) on product demand. This helps companies strategically price products to help manage demand. In seasons when demand is typically low, prices are reduced to increase demand (for example coupons are offered with special discount, i.e. 2 for 1 dinners), and on the period where demand is high, prices may be increased to both maximize sales and keep requirements within the organizations capacity.
Figure 1
Figure 2
3Forecasting and Small Businesses
Forecasting demand for a new business is typically a difficult task, as patterns have not been established. Given this, new businesses should establish procedures to track customer demand/needs and the characteristics of these customers. Establishing an understanding of the type of customers and the pattern of customer demand will help manage the operational processes. Marketing/ advertising and demand management (price structure) will play a significant role in demand. Qualitative forecasts will be more useful for small businesses until data can be obtained and analyzed.
4Qualitative Forecasts
There are two main types of qualitative forecasts, those driven by customer perceptions and those driven by field experts. Combining the results from both is a common and good practice.
Customer based forecasts
Customer perceptions of actual and future requirements are determined though interviews, focus groups, and/or surveys. These types of forecasts are driven in many cases by marketing organizations, and involve the use of market research techniques to find what customers want. Developing market surveys is not a simple task as the design of the questions may lead to wrong conclusions. Some of the most important characteristics of a good survey instrument are (Alreck and Settle, 1985):
Focus: Questions in a survey should only focus on a single specific subject.
Brevity: Brief questions are typically easier to understand, and therefore to answer.
Clarity: Questions should have little left to interpretation.
Expert based forecast
While many varieties exist of expert based forecasts, two good examples are the panel consensus method and the Delphi method. In the panel consensus method a group of individuals that could include customers, employees, and consultants meets in brainstorming sessions to develop a forecast. While in principle this method could be very effective, typically a few individuals dominate the meeting (consultants) and the voice of low level employees may be ignored. The Delphi method a group of individuals (could include all those mentioned above) are surveyed by mail (or some other method) about the future (forecasts). Once the responses have been received, they are summarized and based on the results, a new survey may be sent. In this method, the opinions of all surveyed is given an equal weight.
5Quantitative Forecasts: Time-Based Relationships
Quantitative forecasts are those where functions replace opinions. Quantitative forecasts are normally used for short term planning, although quantitative forecasts are used to calculate population figures 20-50 years into the future. Time based relationships reflect the connection between the passage of time and the “item” in question. The example shown in Figure 1 is such a case. This section will describe four time-based forecasting methods: Simple Moving Average, Weighted Moving Average, Exponential Smoothing, and Linear Regression.
Simple Moving Average
This method is appropriate when there is not a significant trend (fast up or down trend) or seasonal characteristics. It is useful only to smooth out randomness of the data. This method is very simple to compute and requires one decision: the number of time periods to consider n. The larger the number of time periods considered, the smoother the forecast.
w = 1/n
Ft = w(At-1 + At-2 + ….. + At-n)
Where
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
Example
A small retail store owner wants to know how many T-shirts will be sold per month. The owner has tracked T-shirt sales for the last 7 months and needs a forecast for August. The data is shown in Figure 2 and the forecasts are shown in the table below.
Figure 2. T-shirt Sales per Month
Month / Period / Sales / n = 2 / n = 3 / n = 4January / 1 / 712
February / 2 / 733
March / 3 / 689
April / 4 / 738
May / 5 / 688
June / 6 / 654
July / 7 / 709
August / 8 / 1/2(709) + 1/2(654) = 681.33 / 1/3(709) + 1/3(654) + 1/3(688) = 683.55 / 1/4(709) + 1/4(654) + 1/4(688) + 1/4(738) = 697/16
Weighted Moving Average
This forecasting method is similar to the Simple Moving Average, but it allows the decision-maker to place more emphasis on recent (or past) data. The computations are also simple and require two decisions: the number of time periods to consider n, and the weight for each period x, wx. Note that the sum of all weights must be equal to 1. While there are no rules to select weights, typically a larger weight is given to more recent data.
w = forecaster’s decision (0 to 1)
Ft = w1 At-1 + w2 At-2 + ….. + wn At-n
Where
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
w1 = Weight for the actual demand period t - 1
w2 = Weight for Actual Demand period t - 2
wn = Weight for Actual Demand period t - n
sum all w’smust be equal to 1
Example
Using the data from the above example and investigating three cases; n = 2, and w1 = 0.7, w2 = 0.3, n = 3, and w1 = 0.7, w2 = 0.2, w3 = 0.1, and n = 4, and w1 = 0.7, w2 = 0.1, w3 = 0.1, w4 = 0.1 we get the following forecasts.
Month / Period / Sales / n = 2,w1 = 0.7, w2 = 0.3 / n = 3,w1 = 0.7, w2 = 0.2, w3 = 0.1 / n = 4,w1 = 0.7, w2 = 0.1, w3 = 0.1, w4 = 0.1January / 1 / 712
February / 2 / 733
March / 3 / 689
April / 4 / 738
May / 5 / 688
June / 6 / 654
July / 7 / 709
August / 8 / 0.7(709) + 0.3(654) = 692.26 / 0.7(709) + 0.2(654) + 0.1(688) = 695.66 / 0.7(709) + 0.1(654) + 0.1(688) + 0.01(738) = 704.06
Exponential Smoothing
Exponential smoothing is another forecasting technique that is also simple to compute. In this case, past data and forecasts are used in the generation of a forecast for the next period. This method is widely used in practice, but it has some of the same problems as simple moving average (not useful when there are significant trends and seasonal effects). The computations are simple and require one decision and a forecast number for the period before the forecast period in question: the smoothing constant . Note that the smoothing constant, , has to be greater than 0 and less than 1. The smaller the , the less reactive the forecasts will be.
Ft = Ft-1 + (At-1 -Ft-1)
Where
Ft = Forecast for the coming period t
Ax= Actual Demand for period x
= Smoothing Constant
Example
Using the data from the above example and investigating three cases; F1 =700, = 0.8, F1 =700, = 0.4, and F1 =730, = 0.8 we get the following forecasts.
Month / Period / Sales / F1 =700, = 0.8 / F1 =700, = 0.4 / F1 =730, = 0.8January / 1 / 712 / 700 / 700 / 730
February / 2 / 733 / 700 + 0.8(712 - 700) = 709.6 / 700 + 0.4(712 - 700) = 704.8 / 730 + 0.8(712 - 730) = 715.6
March / 3 / 689 / 709.6 + 0.8(733 - 709.6) = 728.6 / 704.8 + 0.4(733 - 704.8) = 716.2 / 715.6 + 0.8(733 - 715.6) = 729.8
April / 4 / 738 / 697.3 / 705.5 / 697.5
May / 5 / 688 / 729.9 / 718.5 / 729.9
June / 6 / 654 / 696.4 / 706.3 / 696.4
July / 7 / 709 / 662.5 / 685.4 / 662.5
August / 8 / 699.4 / 694.7 / 699.4
Linear Regression
This is a mathematical tool used for many purposes and you probably remember it from the introductory statistics class. This technique is especially good for the forecasting of products with a clear trend (growing or decreasing).
Linear regression is based on the linear relationship between time (for example days, weeks, or months) and the variable to be forecasted (T-shirt sales for example). This relationship is formulated in the familiar Y = mX + b format, where Y is the variable to be predicted, X is the time factor, m is the slope of the line, and b is the constant. This text will not present the details of how this equation is formulated/calculated given this is covered in other courses and texts and in practice, the regression equation can be easily computed using spreadsheet software such as Excel or statistical software such as SPSS.
To forecast using regression analysis it is necessary to enter the data into the software and obtain the regression equation. At this time it is important to examine the resulting r value; a high r value means the regression equation is a good predictor of the data. If the r2 value is low, the data may be graphed and analyzed to remove outliers, or it may be determined that linear regression is not the best technique. The equation will then be used to predict the period of interest.
Example
The data from the T-shirt example does not show a trend, does applying the linear regression method is not a good option. However, sales for New Age CD's seemed to have a trend (sales are decreasing). The data is shown in Figure 3.
The data was entered in Excel and using the data analysis tool, the following regression equation was obtained: sales = 134.28 - 11.21 * (period), thus sales for August are forecasted by
F8 = 134.28 - 11.21 * (8) = 44.6
Figure 3. Graph for New Age CD sales
It is important to note that the r2 value for this equation was 0.90, which is good. Other examples and the use of Microsoft ® Excel will be presented during class.
6 Seasonal Effects
In many environments and for many products, there are clear seasonal effects to product demand. Here in Southwest Florida, a strong seasonal pattern is felt during the months of December through April given a large influx of tourists. Other regions and products may have other seasonal patterns, such as the demand for air travel to some destinations; high season during summer and winter, low season during spring and fall. Forecast accuracy will be greatly enhanced by taking into account seasonal effects in the forecasting process.
To determine seasonal effects, the decision-maker should first estimate the seasonal breakdown and the time periods. For example, seasonal effects can be calculated in a monthly basis or in a tri-monthly basis. It is rare to encounter seasonal effects smaller than one month. Special occasions such as Thanksgiving travel are not typically considered seasons.
To determine seasonal effects, we must have data from previous years including all seasons. At least three years of data are recommended to get reasonable accurate seasonal effects. The process is as follows:
1)For each year calculate the total average per period.
2) For each value of actual sales, divide the sales by the average per period. This is the ratio for that period for that year.
3) Add all the ratios for a similar period and divide by the number of ratios. This is the seasonal effect for that period.
While other options exist, we will use linear regression to determine the average per period forecast that will allow to develop a forecast for the next year. Even if the regression coefficient is not acceptable, the regression will provide an estimate for average sales.
Example
The owner of the retail store believes there is a seasonal effect in Souvenir sales. After spending three hours looking through old papers, data for the last three years was obtained for actual sales. The owner estimated four seasons, High: January - March, Summer: April-June, Summer B: July-September, and Fair: October-December. The data and the process to determine seasonal effects is shown below.
Figure 4
(Step 2)Season / 1996 / 1997 / 1998 / 1996
(ratio) / 1997
(ratio) / 1998
(ratio) / Average Ratio (Step 3) = Seasonal Index
High / 1856 / 1977 / 2133 / 1.29 / 1.36 / 1.34 / 1.33
Summer A / 1327 / 1344 / 1450 / 0.92 / 0.93 / 0.91 / 0.92
Summer B / 835 / 815 / 983 / 0.58 / 0.56 / 0.62 / 0.59
Medium / 1739 / 1672 / 1780 / 1.21 / 1.15 / 1.12 / 1.16
AVERAGE (Step 1) / 1439 / 1452 / 1587
Once the ratios for each period are calculated (Step 2), an average ratio per period is calculated; the seasonal index (Step 3). This effect will be used to modify the forecast for the period average for 1999. The linear regression equation for the data above is: 1345.3 + 73.6, thus the average sales for 1999 is 1639.8.
(from above - Step 3) / (Step 4) / (Step 5)Season / Seasonal Index / Estimated Average for 1999 / Forecast per Season
High / 1.33 / 1639.8 / 2184.2
Summer A / 0.92 / 1639.8 / 1509.7
Summer B / 0.59 / 1639.8 / 962.7
Medium / 1.16 / 1639.8 / 1903.3
7Forecasting Errors
As discussed in the previous sections, there are many methods to develop quantitative forecasts. For the T-shirt example, we have at least six possible forecasts for the month of August. The question now is, what method is the best and what are the best parameters? While it will be impossible for anyone to evaluate all the possible options (for example all the possible set of weights in a weighted moving average), the evaluation of forecasting methods is based on comparing a few pre-selected options for a specific data set.
The evaluation process is based on the average error of a method given historical data. Therefore, we look at multiple data points, determine what the forecasting method would have calculated and determine the error. IF the forecasting method does not work for past data, we can guess it will not work in generating forecasts.
For each data point (where there is historical data and a forecast value) and forecasting method we calculate an absolute deviation.
Dt = Absolute value of (Ft - At )
The mean absolute deviation (MAD) is the average measure of error, and the basis to make a decision regarding what is the best forecasting method. The MAD is calculated by:
MAD = SUM 1..g(Dt ) / g
Where
g = number of periods where there is a forecast and actual data.
Example
The owner of the store wants to know which is the most accurate forecast for the month of August, and which method should they use to forecast T-shirt sales every month. To determine this we calculate the forecasts for all possible periods. Lets evaluate the simple moving average forecasts under our three parameters.
Month / (Period) / Sales / n = 2 / n = 3 / n = 4 / Dt / Dt / DtJanuary / 1 / 712
February / 2 / 733
March / 3 / 689 / 722.7 / 33.3
April / 4 / 738 / 711.4 / 711.6 / 26.6 / 26.4
May / 5 / 688 / 713.7 / 720.3 / 718.2 / 25.7 / 32.3 / 30.2
June / 6 / 654 / 713.0 / 705.1 / 712.2 / 59.0 / 51.1 / 58.2
July / 7 / 709 / 671.0 / 693.3 / 692.4 / 37.7 / 15.3 / 16.3
August / 681.3 / 683.6 / 697.2
MAD / 36.4 / 31.3 / 34.9
Using 3 periods (n=3) results in the lowest MAD, thus 683.6 is the so far the best estimate for August (and the best forecasting method for T-shirt Sales). Let's now look at the weighted moving average forecasts. Option 1 = (n = 2, w1 = 0.7, w2 = 0.3); Option 2 = (n = 3, w1 = 0.7, w2 = 0.2, w3 = 0.1) and Option 3 = (n = 4, w1 = 0.7, w2 = 0.1, w3 = 0.1, w4 = 0.1).
Month / (Period) / Sales / Option 1 / Option 2 / Option 3 / Dt / Dt / DtJanuary / 1 / 712
February / 2 / 733
March / 3 / 689 / 727.0 / 37.5
April / 4 / 738 / 702.6 / 700.5 / 35.4 / 37.5
May / 5 / 688 / 723.4 / 727.8 / 730.1 / 35.4 / 39.8 / 42.1
June / 6 / 654 / 703.0 / 698.1 / 697.7 / 49.0 / 44.1 / 43.7
July / 7 / 709 / 664.2 / 669.2 / 669.3 / 44.5 / 39.5 / 39.3
August / 692.3 / 695.7 / 704.1
MAD / 40.4 / 40.2 / 41.7
The three options of the weighted moving average resulted in MAD's that were higher than 31.3, thus the simple moving average with 3 periods (n = 3) is best estimate for August. Let's now look at exponential smoothing.
Month / (Period) / Sales / F1 =700, = 0.8 / F1 =700, = 0.4 / F1 =730, = 0.8 / Dt / Dt / DtJanuary / 1 / 712 / 700 / 700 / 730
February / 2 / 733 / 709.6 / 704.8 / 715.6 / 23.8 / 28.6 / 17.8
March / 3 / 689 / 728.6 / 716.2 / 729.8 / 39.2 / 26.8 / 40.4
April / 4 / 738 / 697.3 / 705.5 / 697.5 / 40.7 / 32.5 / 40.5
May / 5 / 688 / 729.9 / 718.5 / 729.9 / 41.9 / 30.5 / 41.9
June / 6 / 654 / 696.4 / 706.3 / 696.4 / 42.4 / 52.3 / 42.4
July / 7 / 709 / 662.5 / 685.4 / 662.5 / 46.2 / 23.3 / 46.2
August / 699.4 / 694.7 / 699.4
MAD / 39.0 / 32.3 / 38.2
The second option of the exponential smoothing method resulted in a lowest MAD for this method, but still, the simple moving average with three months results in the lowest MAD (31.3). Therefore the forecast for August is 683.6 and simple moving average with n = 3 is selected as the forecasting method. If we had used a linear regression equation, the process would have included a MAD analysis for the regression forecasts.
7The Forecasting Process for Time Based Relationships
Just like everything else, a good forecast is based on a good process, experience, good data (garbage in – garbage out) and luck. The first one will be covered next, the second one will depend on your job, the third one depends on a good data collection system and in your ability to determine if the data represents reality, and the fourth is up to? The steps to forecast are below and illustrated in Figure 5.