Hi everyone. I'm. Welcome to the final session of week one. We learned about forecasting techniques in various settings in the past sessions. Forecasting methods were based on data from several past observations. To wrap up, I'm gonna talk about a specific setting based on the apparel industry. In this setting, we'll use the same forecasting tools to build a descriptive distribution based on data from several products. Hello welcome back to Week 1, Session 4 of Descriptive Analytics. In this week, Session 4, we're gonna be Forecasting New Products and we're going to look at how to fit distributions. We're going to look at a New Product Problem, Forecasting a new product. In the case of new products and new designs in the market, there is very limited demand data. How do you Forecast in such settings? Often times subjective techniques are used. Let's take a look at some of the subjective techniques. Subjective Forecasting Methods. Some of the Subjective Forecasting Methods we're interested in are through composites. For example, you can look at Sales Force Composites. This is, sales personnel demand data and they estimate, and they aggregate all the demand data. This aggregation of sales personal estimates makes your composite. Another method to collect data or to forecast demand is to use customer service. Or you could use a jury of executive opinion, where there is a committee of forecasters and they come up with the forecast and use that collective knowledge. One method that is often used is called the Delphi method. What Delphi method does is the following. Individual opinions are compiled and then you reconsider them over and over again until a group consensus has reached. All of the subjective methods are eventually based on gut feel and check. Let's look at a forecasting application. And we are looking at an outdoor wear company called Andes. Andes has the a product, a new men's hiking shoe design. Andes Inc has sold this particular design called the Drifter, for only one season. In the past season, they made a forecast of 1200 units. They made more than 1200 units, they made Q=1500 units, out of which, they sold 1397 units. As you can see, not much demand data is available. Now, how can Andes think about descriptive statistics for Drifter? That's a question we're going to be looking at. We're going to learn how to fit a distribution by tracking errors. If there is limited past demand data, like in the case of Andes for example, for new products, we start with subjective forecasts. However, we can do better than that with more data. If you think about it, often there is additional demand data from other products you have forecast in the past. That data is informative of how your forecast deviated from the true demand. We will use one approach on how to fit a normal distribution to such available data. We can use other similar approaches for other distributions. But we're going to look at normal distribution. We have data from Andes Inc for all their men's shoes. The table shows you all the products that they made in the last season, their forecast in the second column, the volume of production in the third column. The sales for those products in the fourth column, and the demand that they saw for all these products in the last column. For example, if you look at the product omega, the forecast was 2,400, they made 3000 shoes, they sold 2967 and the actual demand was also 2967, all of which they sold. Now, the subjective forecast for Drifter for the next season is 1000 pairs. What demand model should Andes use for drifter? If you look at the previous table that I showed you, you will notice that there is a difference between sales and demand. What is sales? Sales is nothing but censored demand. For example, if your demand was 1,000 units and you had only 800 units on the shelf, the sales is going to be 800 units. You cannot meet all demand. There are several examples where this happens. For example, popular music players, gaming consoles, are often sold out because there is limited inventory. For most operational problems such as the Newsvendor problem, we need the true demand distribution. We are interested in collecting the true demand distribution. In order to do that, one step we are going to take is to compare your forecast with the actual demand in the table. And here is a graph that shows you the forecast and the actual demand on a chart. On the x axis is forecast on y axis is the actual demand. For example, here is a product for which the actual demand was pretty close to the forecast. In general, you'll notice that some demands are higher than forecast on the upper triangle in the chart. And for some products, the demand was lower than forecast, for example look at this product, the demand was about 1,000 and the forecast was more than 3,500. This chart tells you how much typically the true demands deviates from your forecast. If your demand was exactly equal to your forecast, you will be on the diagonal line over here in the chart. Using the chart that we saw in the previous slide, we can measure forecast performance now. In order to measure forecast performance, I'm gonna generate another column, which has something called the A/F ratio. The A/F ratio column is nothing but the actual demand, stands for A, divided by your forecast. In the first example, we have 796 divided by 800 which is almost equal to 1.00. So we measure the forecast versus the actual demands, by calculating a ratio of the actual demand to the forecast and this is called the AF Ratio. We are interested in generating an empirical distribution function of our forecast accuracy, and remember that A/F ratio is useful in developing our understanding of forecast accuracy. A/F ratio is just the ratio of actual demand to the forecast. We evaluate these actual demand to the forecast ratio of the A/F ratio for all past observations. A/F ratios measure how much the actual demand deviated from the forecast. If your A/F ratio was 0.8, this means that your actual demand was 80% of the forecast. The A/F ratios help us pin down the uncertainty around the current forecast. We're going to learn how to choose a normal demand distribution and fit it on our data. We start with an initial forecast. This comes from a subjective method, lets say hunches, guesses, committee forecast etc. We use the initial forecast, let's assume the initial forecast is 1,000 units. Then we calculate the A/F ratios in the historical data. And recall, A/F ratio is just the ratio of actual demand to forecast for all the products that we forecasted. Now how do we fit in the mu and the sigma, that is the mean and the standard deviation of the normal distribution? We set the mean of the normal distribution to the following value. We calculate the expected A/F ratio and multiply it by the Forecast and that's your mean of the normal distribution. For the standard deviation of the normal distribution, we calculate the standard deviation of the af ratios and multiply it by the forecast. Let's look at an example. In our example, we had a forecast of 1,000. We calculated the A/F ratios. The mean A/F ratio is 1.01 and the standard deviation of the actual A/F ratios is .31, so when we multiply these by the forecast we get the mean demand is 1,010 and the standard deviation of the actual demand is 310. So for our descriptive data, we can fit a normal distribution with mean 1010 and standard deviation 310 to represent our demand. Note, if you wanna predict demand for predictive purposes, we need to update the demand distribution. We can update the normal demand distribution as follows. Mean, we can just keep the same, which is 1,010, and the standard deviation needs to be corrected. The standard deviation will be corrected in this data set from 310 to 390. If you wanna look at how the standard deviation is corrected for predictive purposes, we can go back to Session 2 and look at the video where I corrected using our moving averages method. We just calculated the descriptive statistics for our data, and we have the normal demand model. Here is the normal demand distribution for our data. For Drifter, we use a normal demand distribution with mean 1010 and standard deviation 310. This comes because we knew our forecast, we knew how good our forecast was, which helps us measure how your forecast will deviate from the true demand, and that helps us calculate the standard deviation. And this is a good demand distribution model. Even though we had very limited data for a new product, we used our forecasting process in the past to come up with some demand distribution that helps us understand how the uncertainty in the future looks like. Our techniques are very broadly applicable. For example, they can be used for understanding GDP forecasts, Gross Domestic Product for our country or foran economy. And we compare the forecast with the actual observations and be confident about our forecasting process. For more details, you can look at Nate Silver's book on The Signal and the Noise, particularly the Chapter 6 on Drowning in 3 feet of water. Another example that I will briefly mention is a company called Sport Obermeyer. The forecasting process used in Sport Obermeyer also measures errors. You can find out more about this in a paper by Fisher and Raman. The paper is on Reducing the Cost of Demand uncertainty through Accurate Response to Early Sales. So far we looked at how to generate a demand distribution when there is limited data. The technique that helped us is how to measure forecast errors. Keeping track of forecast errors informs us how good and reliable our forecasts are. In turn, this information is useful in characterizing the demand uncertainty, how your demand is distributed in the future. Figuring out what's casual and what's correlated is a hard thing to do. The tools I have covered leverage the past data into coming up with a predictive model for future demand. That's it for Descriptive Analytics, let's recap. We started with the Newsvendor Problem, we introduced Random Variables and we looked at Demand Distributions. We learned how to forecast demand, we leaned how to forecast with Past Historical Data. We looked at Forecast Errors and Biases in Forecasts. We looked at two techniques, moving averages and exponential smoothing. We learned how to generate Descriptive Statistics, particularly mean and standard deviation. We learned how to adapt them for future predictive purposes. We looked at Trends and Seasonality. Finally, we learned how to forecast new products and how to fit demand distributions. That's it for Descriptive Analytics. We'll cover more tools in the weeks to come, and in those weeks we'll be continuing on to prescriptive and predictive analytics. It's been an exciting week. We saw a fundamental operations problem called a newsvendor problem that deals with supply-demand matching in uncertain settings. We learned how to describe our data in such settings. We learned how to forecast in stationary settings. We learned how to describe trend and seasonality as well as how to forecast in such settings. Using Excel examples, we explored how to implement these toolkits and techniques. The descriptive analytics that we have learned, forms a basis for your future learning in this course. We have review material, slides for some advanced material and example templates available. We hope you find them useful.
