The implication of product variety goes beyond the production settings and beyond just simple setup times. Product variety will also impact the distribution system of our operations. The more we will segment demand into smaller and smaller segments, the harder will it be to accurately predict demand. Consider the following example. How many shirts, in blue, of size L, will the Gap here in Philadelphia sell tomorrow morning? One, two, three, four, or five? I'd be surprised if we would get this forecast right, even within 50 to 100%. Now ask yourself, how many shirts across all colors, sizes, stores, will the Gap sell in all of the next quarter? Probably, we can get that forecast within 10 to 20% of the real number. The reason for that is the more we aggregate a forecast, the aggregate uncertainty, the uncertainty starts behaving following the laws of statistics, and it becomes easier to plan. This will be the focus of this session. To make distribution decisions, we typically need the forecast of demand. The problem with demand forecasts is they're not always right. We face what is called demand uncertainty. When we describe demand uncertainty, we think of demand as the distribution drawn from some underlying distribution. Now think of a running shoe company. The running shoe company has two models, model 1, and model 2. It makes forecasts for model 1 and model 2 by thinking about the mean or the expected amount of shoes that they're going to sell. It is common in operations and statistics to use the Greek symbol mu to capture this, and the standard deviation of that demand, which we going to call sigma. [SOUND] Now we might think about sigma as the amount of uncertainty that the firm faces. However, sigma alone, the standard deviation alone, is not a good proxy for the amount of variability or uncertainty in demand. A thousand running shoes standard deviation, is that a big number or a small number? That really depends on the mu, on the mean. If I'm having 1,000 standard deviation for an expected demand of 2,000, we would call this probably a lot of statistical variation. However, if it's 1,000 standard deviation for a million shoes, that would be relatively little. With this in mind, we define the coefficient of variation, also CV, coefficient of variation as a ratio between the standard deviation and the mean. Now consider a competitor of our running shoe business that has somehow managed to combine shoes 1 and 2 into one model. Think of this as, again, shoes for men and shoes for female runners, whereas this company has just one common shoe for everybody. Let's assume for the sake of argument that the demand for the female running shoes and the demand for the male running shoes are independent of each other. Moreover, let's assume that the market sizes are roughly similar and the market uncertainties are also roughly similar. In other words, the mu1 is equal to the mu2, and the sigma 1 is equal to the sigma 2. Now, what's going to be the demand for company 2 over on the right? The expectation is simply going to be mu1 + mu2, which is equals to, assuming that they are the same, 2 times mu. How about the standard deviation? To find the standard deviation of the combined demand, I have to look at the square root of sigma one squared, plus sigma two squared, plus two times the covariance between demand 1 and demand 2. We assumed independence, and so this fellow here is going to be equal to zero. And we also assume that sigma 1 is equal to sigma 2 ,which leaves us here with the square root of 2 times sigma 1 or sigma 2 squared. I can simplify this and write this is the square root of 2 times sigma. Now, how about the coefficient of variation? Again, I have already computed now the standard deviation, so the standard deviation divided by the mean, which is 2 times mu is going to be equals to 1 over the square root of 2 times sigma, divided by mu. You notice that the firm here to the right is facing a lower variability of demand than the firm here on the left. We see that by combining demand, I'm able to reduce the demand variability as measured by the coefficient of variation. Or put differently, is I'm combining demand, the standard deviation of this combined demand goes up slower than the underlying mean. This effect is called demand pooling. Pooling demand, or aggregating demand is a way for us to reduce uncertainty that will make it much easier for us to get the right amount of orders in the right place. Notice that pooling does not always require independence. It works out nicely mathematically if the two demands are independent but even if there is a mild amount of correlation between the demand of product 1 and product 2, pooling still offers tremendous benefits. In this session, we went from the left to the right, and asked ourselves what would happen if I could combine the two products. Now just put this argument on its head. Ask yourself, what would happen if I'm a company offering one running shoe and thinking about customizing it now and offer more variety of the product for the male runners and the female runners. You notice that as we are fragmenting the demand, so pooling goes this way, here we're fragmenting demand. As we're fragmenting demand, I'm increasing the amount of demand uncertainty. Now let's go back to our comparison of McDonald's and Subway that we started in the module on process analysis. We said that McDonald's follows a make to stock strategy. Make to stock means that they make the burgers before having the orders. In contrast, we said that Subway produces make to order. Why that? Let's think about this. At McDonald's, the choice of burgers is limited. You can have the cheeseburger, you can have the hamburger, or the Big Mac but you cannot have the sandwich customized your way. This limited set of offering keeps the demand variability relatively low and lets McDonald's come up with reasonably good forecasts of demand. At Subway and Subway's customization strategy, this does not work. There's so many versions in which you can have your Subway sandwich made, that it would be impossible for Subway to hold one in inventory for every possible offering. Notice that we observe the same two strategies in the computer industry. We have the Dell model that is basically playing the Subway strategy. We are taking the orders of customers in through the website, and make the computer to order. Apple, on the other hand, plays the McDonald's strategy. They offer a handful of variants that are so popular that customization is typically not necessary. That allows them to reduce demand variability and gets the match to supply between supply and demand reasonably correct. In this session, I introduce the concept of demand pooling. By pooling the demand across multiple items in a product line or multiple locations in a distribution network, I can decrease the demand uncertainty. In other words, I can tame the uncertain demand. This is a direct consequence of the laws of statistics. By reducing the demand uncertainty, I'll also reduce the supply/demand mismatches. I have fewer customers that are disappointed because they couldn't get the shirt, and size, and model that they wanted and vice versa, I have fewer shirts that nobody wanted to buy. Pooling is probably one of the most powerful insights and concepts in operations management. We will see it again and again in the remainder of this course.
