10th ed. I see that you will get an A this semester. Forecasting

FORECAST: A statement about the future value of a variable of interest such as demand. Forecasting is used to make informed decisions. Long-range Short-range Generally, the responsibility of preparing forecasts falls on marketing and sales rather than on operations. Most operations generated forecasts deal with inventory, resource needs, and other areas that require managing operations (e.g., for obtaining materials, facilities, and employment levels to meet the sales demand forecast that was developed by the marketing department). The formal forecasting procedures (or forecasting models) which you read about in the assignment are a means of making informed decisions. It beats pure guessing. Short term forecasts covering a day or week are common in operations. Long term forecasts can extend out to several years, and are generally employed in strategic management (as strategic forecasting).

Features of Forecasts Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases

This illustrates the fourth bullet of the previous slide This illustrates the fourth bullet of the previous slide. Note that error seems to increase exponentionally with time, which illustrates the problem with long term forecasting.

Uses of Forecasts Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing MIS Operations Product / service design

Examples of Forecasting Uses Accounting Cost/profit estimates Finance Cash flow and funding Human Resources Hiring/recruiting/training Marketing Pricing, promotion, strategy MIS IT/IS systems, services Operations Schedules, MRP, workloads Product/service design Timing of new products and services Regardless of your area of business, you are likely to make and/or use forecasts. Overall, your job (as well as the job of the organization that you work for) is likely to depend on your firm’s ability to forecast.

Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use Of course, these are goals. In reality, you hope that your organization’s ability to have good forecasts is better than that of the competition. This relates in not only meeting customer demand, but also in better utilization of your organization’s resources. Good forecasts relate to good scheduling of employment levels and good inventory control, both of which are two high cost activities in the area of operations.

Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Obtain, clean and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast” This slide would be very helpful to you if you have to do forecasts in any cases you are given in courses such as Strategic Management (MHR 410 or TOM 411). However, we will not have such a case in our course.

Types of Forecasts Judgmental - uses subjective inputs (e.g., sales force estimates). Time series - uses historical data assuming the future will be like the past. Time could be in weeks, months, years, etc., and is based on t=1,2,3,… Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households. Recall what we mean by a series– e.g., movie series such as Rocky, Rocky II, Rocky III; Rambo, Rambo II, Rambo III; Back to the Future, Back to the Future II, Back to the Future III. Note that Naked Gun and Naked Gun “One and a Half” are NOT the proper way to label a movie series. We will not have enough time to cover judgmental forecasts and associative models. We will discuss some aspects of simple and econometric associative models if time permits. No formal problems will be assigned on associative models.

Judgmental Forecasts Executive opinions Sales force opinions Consumer surveys Outside opinion Delphi method Opinions of managers and staff Achieves a consensus forecast The Delphi Method usually involves experts going several rounds in making and sharing their forecasts with each other, until they move toward a consensus.

Time Series Forecasts Trend - long-term movement in data Seasonality - short-term regular variations in data Cycle – wavelike variations of more than one year’s duration Irregular variations - caused by unusual circumstances that are not random Random variations - caused by chance Random variations cannot be predicted, while there is some predictability for the other bullets on the slide above. For example, an irregular variation could be a snowstorm predicted by the weather bureau that is expected to result in late shipments to the manufacturing department. As such, it can be incorporated in a forecast.

Forecast Variations Trend Cycles Irregular variation 90 89 88 Seasonal variations

This slides shows the variations as components that make up a time series forecast.

This slide shows what happens when the random component is so large that the other components are masked by it. Hence, this time series forecast is useless. Later in the course, we will cover what companies do when they cannot generate a useful forecast because of high volatility in demand.

Some Common Time Series Techniques or Time Series Forecasting Models Naïve forecasts Moving average Weighted moving average Exponential smoothing

Naive Forecasts The forecast for any period equals the previous period’s actual value. This was probably how forecasts were done at the time man invented the greatest invention of all time– the wheel.

Naïve Forecasts Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy This approach, as indicated above, cannot provide high accuracy, unless demand is very stable.

Formula for Naïve Forecasts Ft = At-1 Note that t=1,2,3,…….. Note that t is always a positive integer. Sometimes, t=0 is permissible. We will have examples of this in the homework. This is the forecasting that is the most responsive to changes in the past actual demand.

Moving Average Formula Moving average – A technique that averages a number of recent actual values, updated as new values become available. Weighted moving average – More recent values in a series are given more weight in computing the forecast. At-n + … At-2 + At-1 Ft = MAn= n Note that n equals the number of past time periods when the actual demand is known for each of those time periods. For example, for n=3, we assume a three month moving average, and we assume we know the actual demand for the past three months. Also, note that all the weights in a weighted moving average must sum to 1. A one month moving average is equivalent to the naïve forecast. Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1

Simple Moving Average At-1 + At-2 + … At-n Ft = MAn= n MA5 MA3 Actual Demand MA5 MA3 Note that the 3 month moving average is more responsive to changes in the actual demand than the 5 month moving average. Also, note that both moving average forecasts tend to lag in changes to the actual data. This is true for all simple averaging techniques. Ft = MAn= n At-1 + At-2 + … At-n

Exponential Smoothing Ft = Ft-1 + (At-1 - Ft-1) Weighted averaging method based on previous forecast plus a percentage of the forecast error A-F is the error term,  is the % feedback This is an easy to use formula because you only have to carry demand for one period back, along with the last period’s forecast.

Exponential Smoothing Formula Ft = Ft-1 + (At-1 - Ft-1) Premise--The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods when forecasting. The symbol “α” is the Greek letter “alpha.” Alpha is called the smoothing constant. Note that alpha varies from zero to one. Note that t is the period of the forecast (e.g., t=3 could be March, and t=t-1=3-1=2 could be February). Also, alpha varies from zero to one. Note that when alpha is one in the above formula, we have the naïve forecasting formula.

Exponential Smoothing The above shows the exponential smoothing formula in an expanded form. Note the weights decay because of the increasing exponent. In reality, the exponential smoothing formula is a weighted moving average. You are not responsible for fully understanding this slide. It is shown only for you edification.

Picking a Smoothing Constant  .1 .4 Actual Note the lag for both values of alpha, and that the higher alpha is more responsive to changes in the actual demand than the lower alpha, which is why the lower alpha has a smoother plot.

Again, this is another example of the difference of a higher alpha compared to a lower alpha. Of course, in selecting an alpha, we want the one that best fits our data. Which one do you think is best for the above? Why?

Homework Problem Referring to page 118 in the text, do problems 2a and 2b, but skip problem 2b(1) which asks for a linear trend equation. Complete and partial solutions of homework problems are found on the slides at the end of this session. For this problem and for all homework problems, do not go to the solutions until you have made a strong effort to solve the problems.

Linear Trend Equation Ft = Yt = a + bt Ft = Forecast for period t t = The time period being forecasted a = Value of Ft at t = 0 b = Slope of the line This is actually the same as the straight line equation, y = mx + b. However, the slope is now b, where b is also the “trend” in this application, and the vertical intercept is a. Note that y = mx + b is common in algebra, while the formula in the above slide is a more common form found in statistics books.

Calculating a and b Yt = a + bt b = n (ty) - t y 2 ( t) a  where b and a follow from the following formulae: b = n (ty) - t y 2 ( t) a  Recall the summation sign. The value of “n” is the number of paired observations of t and y. Note the application in the next slide.

Linear Trend Equation Example Calculations of b and a are from the sums given in the table on the left. Ft = Yt = a + bt n = 10 Note the ten paired observations of t (for period) and y (for sales) as given above in the table, where n=10. The sums are given in the last row of the table. Also, we expressed t2 as “t squared” in the table. This demonstrates the formula for linear trend given in the previous slides. All you have to do is plug in the data from the above table into the linear trend formula, where b is the slope and a is the vertical intercept of the straight line equation, or in this application, the linear trend equation. The line that we obtain is the best fit line for the given data (i.e., the best fit line for the 10 observations of t and Y in the first two columns of the table). Ft = Yt = a + bt = 67.78 + 5.79t

Plot of Previous Slide Y t

Homework Problem Referring to page 118 in the text, do 2b(1), which asks for a linear trend equation. Also, do problem 2c. However, change problem 2c to read as follows: “Which method seems MOST appropriate? Why?”

Associative Forecasting Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households This description of associative forecasting is identical to that of an earlier slide.

Example of an Associative Forecast: Using x to Predict y Computed relationship In the above slide, assume x is per capita income and y is the demand for stoves. The relationship in the graph between x and y suggests that as per capita income goes up, demand for stoves goes up. Note that this is not a time series forecast. It is a forecast where the forecasted item (stoves) is associated with per capita income. The associative model as described in our Stevenson textbook uses the same formula as the linear trend equation, except x is substituted for y (i.e., change y=a+bt to y=a+bx). However, there will not be sufficient time to assign you problems using the associative forecasting model formulae. Therefore, while you need to know what associative forecasting is, you will not have to do any assigned problems in associative forecasting. Hence, word problems on associative forecasting will not be on the quizzes or exams since none were assigned. A straight line is fitted to a set of sample points.

Example of an Associative Forecast Equation for Automobiles (with several variables, and nonlinear) This is an example of an associative model that could be a real world equation. You may have to enlarge it to see the details. Note that it consists of a complex equation with positive and negative exponents. This is an illustrative example. This type of problem will not be on a quiz or exam.

Forecast Accuracy Error - difference between actual value and predicted value Mean Absolute Deviation (MAD) Average absolute error Mean Squared Error (MSE) Average of squared error

Some Measures of Forecasting Accuracy  Actual  forecast MAD = n MSE = Actual forecast) - 1 2   n ( The top formula represents the average error per period, and is referred to as the mean absolute deviation (MAD). The second formula represents the average squared error per period, and is referred to as the mean squared error (MSE). Note that the errors are taken for each of the past n periods where the actual demand is known.

Some Characteristics of MAD and MSE Easy to compute Weights errors linearly MSE Squares error More weight to large errors

Sources of Forecast errors Model may be inadequate Irregular variations Incorrect use of forecasting technique

In-class assignment The next two slides ask some basic questions about forecasting, and give some examples of measuring forecasting error. These slides make up an in-class assignment. You can try to answer the questions on the slides. However, if you have difficulty with all or some of the questions, we will do them in class. At least become familiar with the questions before the next class. If you find the next two slides difficult to read, simply magnify the size of the slides. If you can, please try to print a hardcopy of the next two slides and bring them to class. If you can set the resolution of your printer, it is suggested that you set it to a high resolution for the best printed copy.

Choosing a Forecasting Technique No single technique works in every situation Two most important factors Cost Accuracy Other factors include the availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon Managers in the real world can find some excellent articles on forecasting in the journal Harvard Business Review. Overall, if you have some idea of how different forecasting methods best match a given situation, you can seek out experts to build the forecasting model on the computer, rather than trying to do it yourself.

Good Operations Strategy Understand that forecasts are the basis for many decisions Work to improve short-term forecasts Understand that accurate short-term forecasts have benefits for the following: Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility The above is only a partial list.

Supply Chain Forecasts Sharing forecasts with suppliers can Improve forecast quality in the supply chain Lower costs Lead to shorter lead times It is interesting to note that many supply chains are designed to try to avoid forecasting, particularly in industries with a high level of volatility in demand (e.g., the semiconductor industry).

Common Nonlinear Trends Parabolic Exponential Growth Note that you could use many linear trend equations over short time periods to approximate a forecasting model for all the above curves. This can be done by drawing many tangent lines along the nonlinear curves, with small sections of the tangent lines approximating the curves. As time permits, we may be able to discuss this in class. You will not to be questioned about this slide on the exam or on a quiz.

Exponential Smoothing The next three slides show that you can solve problems with the software on the DVD which came with your textbook. These three slides are for illustration purposes only. You will not be subject to quiz or exam questions about the DVD or its software. However, you could use this software on your own and compare the results with your homework or with solved problems in the text.

Linear Trend Equation

Simple Linear Regression

Homework Problem Solutions 2a Month Sales F M A M J J A S 20 It is suggested that you complete the above graph by taking a “good guess” for the September forecast. (This will help us in solving Problem 2c.)

For the September forecast, t = 8, and Yt = 16.86 + .50(8) = 20.86 To solve this problem, we need to plug the appropriate values into the equation Ft = Yt = a + bt t Y tY t2 1 19 2 18 36 4 3 15 45 9 20 80 16 5 90 25 6 22 132 7 140 49 28 542 Hence, n = 7, t = 28, t2 = 140 Note that the bottom row in the table are the sums. Therefore, Yt = 16.86 + .50t For the September forecast, t = 8, and Yt = 16.86 + .50(8) = 20.86

2b(2)

Ft = Ft-1 + (At-1 - Ft-1) 2b(3) Month Forecast = F(old) + .20[Actual – F(old)] April 18.8 = 19 .20[ 18 – 19 ] May 18.04 = 18.8 .20[ 15 – 18.8 ] June 18.43 = 18.04 .20[ 20 – 18.04 ] July 18.34 = 18.43 .20[ 18 – 18.43 ] August 19.07 = 18.34 .20[ 22 – 18.34 ] September 19.26 = 19.07 .20[ 20 – 19.07 ] In order to use the exponential smoothing formula, we need the August forecast. However, the problem gives us the March forecast of 19 (or 19,000). Hence, we have no choice but to use the March forecast to get the April forecast, the April forecast to get the May forecast, etc., until we get to the August forecast. Once we have the August forecast, the slide above shows the last calculation giving 19.26, the September forecast. Because the problem gave us the March forecast rather than the August forecast, we had to do all that extra work to finally get the August forecast. Answer is 19.26 (or actually, 19,260 units).

2b(4) Ft = At-1 Hence, the answer is 20 (or 20,000 units) This formula is telling us that the forecast in period t is simply the actual demand for period t-1, or simply, the actual demand of the previous period. For the September forecast, the answer would be the actual demand in August. Hence, the answer is 20 (or 20,000 units) Note that t=1,2,3,…….. Note that t is always a positive integer. Sometimes, t=0 is permissible. We will have examples of that in the homework.

Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1 2b(5) = .6 (20) + .3(22) + .1(18) = 20.4, (or 20,400 units) Note that the more recent actual demand values are usually given more weight in computing the forecast.

2c Change this problem to read “which method seems the most appropriate?” To logically find the answer, go back to the plot in 2a, and make your best guess as to where the September actual demand might be on the plot or graph. Hence, you need to see a pattern on the plot. Once you have September on the plot, find the method from part b of the problem which comes the closest to your guess on the plot. The answer should be the linear trend equation.

See you next class