To finish this module, we're going to go back to something that we discussed in the introduction. This has to do with the idea of creating prediction models using average values. It seems reasonable to believe that if we use the average value for an uncertain input, we should get the average value for an output. While this might be true in some cases, it is not universally true for all models. This phenomenon is known as the Flaw of Averages. Let's examine this idea on a very well-known situation called the news vendor problem. The news vendor problem applies to many practical situations where a one time purchase decision must be made in the face of uncertain demand. Department store managers must make purchasing decisions for seasonal items well in advance of the beginning of the the season. For example, ski jackets are typically ordered in the summer. The name of the problem comes from the scenario where a news vendor needs to make a decision about the number of newspapers to purchase to sell the next day. If she doesn't know enough, then there is an opportunity cost, and if she orders too many, then the leftover papers go to the recycling bin. The input of a news vendor model consists of demand, selling price, cost and salvage value. The quantity to purchase is a decision and the output is the total profit. In this model, the selling price is larger than the cost and the cost is larger than the salvage value. Let's take a look at the news vendor model in Excel. Locate and open the Excel file News Vendor. This workbook contains two models for a hypothetical ski apparel store that must order ski jackets for the next season. The jackets cost $54 and can be sold for $145. The salvage value of a jacket is $45. The historical average demand is 80 jackets. Before examining the model in the workbook, let's turn on the interactive simulation of the ASP. Click on the Analytic Solver Platform tab and then click on the simulate ball in the Solve Action group. Let's take a look at the average volume model. Cell B10 contains a decision on the number of jackets to purchase.. This cell is colored yellow to indicate that is a decision. In this case we are saying that the manager is going to purchase the historical average of 80 jackets. The model assumes that the demand is going to be the historical average demand. So there is an 80 in cell B11. This means that the model assumes that all the jackets that were purchased will be sold and there will be no surplus. The total revenue is calculated in cell B14. The cost is in B15, and the profit in B16. Since the model doesn't consider any of the uncertainty, the average profit in cell B17 is the same as the profit in cell B16. The estimated profit is $7,280. Now, let's take a look at the simulation model. We're going to assume the store would purchase the historical average of 80 jackets. The demand value in cell E11 is in green, the color that we have been using to indicate that this is a uncertain value. If we double click on this cell, we can see that we are making an assumption that the demand follows a Poisson distribution with an average of 80 jackets. The rest of the formulas to calculate the profit are the same as in the average value model. The profit is the simulation output. So cell E16 includes the psi output function. The average profit is calculated using the PsiMean function. The difference between the average model and the simulation model is that we have added uncertainty in the demand. The uncertainty was modeled using a Poisson distribution. If the assumption is correct that the demand follows a Poisson distribution, which could be verified by analyzing historical data, then the simulation model shows that the average value model is over-estimating the expected profit. This tells us that using an average value for an uncertain input, the demand in this case, does not necessarily result in the correct estimate for the average output value. What is happening here is that every time the demand is larger than 80, the profit it stays at $7,280. However, when the demand is less than 80, the profit drops because there will be some loss associated with selling jackets at their salvage value. The average value model is not able to capture this. To conclude, I hope that I have been able to convince you of the benefits of simulation as a predictive analytics tool that enables you to incorporate uncertainty in decision making models. In this example, we show how average values might result in misleading information. But this is just one of several important insights produced by various types of analysis that we have discussed throughout this module.