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This has to do with the idea of creating prediction models using average values.

Â It seems reasonable to believe that if we use the average value for

Â an uncertain input, we should get the average value for an output.

Â While this might be true in some cases, it is not universally true for all models.

Â This phenomenon is known as the Flaw of Averages.

Â Let's examine this idea on a very well-known situation

Â called the news vendor problem.

Â The news vendor problem applies to many practical situations where

Â a one time purchase decision must be made in the face of uncertain demand.

Â Department store managers must make purchasing decisions for

Â seasonal items well in advance of the beginning of the the season.

Â For example, ski jackets are typically ordered in the summer.

Â The name of the problem comes from the scenario where a news vendor needs to make

Â a decision about the number of newspapers to purchase to sell the next day.

Â If she doesn't know enough, then there is an opportunity cost, and

Â if she orders too many, then the leftover papers go to the recycling bin.

Â The input of a news vendor model consists of demand,

Â selling price, cost and salvage value.

Â The quantity to purchase is a decision and the output is the total profit.

Â In this model, the selling price is larger than the cost and

Â the cost is larger than the salvage value.

Â Let's take a look at the news vendor model in Excel.

Â Locate and open the Excel file News Vendor.

Â This workbook contains two models for

Â a hypothetical ski apparel store that must order ski jackets for the next season.

Â The jackets cost $54 and can be sold for $145.

Â The salvage value of a jacket is $45.

Â The historical average demand is 80 jackets.

Â Before examining the model in the workbook,

Â let's turn on the interactive simulation of the ASP.

Â Click on the Analytic Solver Platform tab and

Â then click on the simulate ball in the Solve Action group.

Â Let's take a look at the average volume model.

Â Cell B10 contains a decision on the number of jackets to purchase..

Â This cell is colored yellow to indicate that is a decision.

Â In this case we are saying that the manager is going to purchase

Â the historical average of 80 jackets.

Â The model assumes that the demand is going to be the historical average demand.

Â So there is an 80 in cell B11.

Â 2:48

This means that the model assumes that all the jackets that

Â were purchased will be sold and there will be no surplus.

Â The total revenue is calculated in cell B14.

Â The cost is in B15, and the profit in B16.

Â Since the model doesn't consider any of the uncertainty,

Â the average profit in cell B17 is the same as the profit in cell B16.

Â The estimated profit is $7,280.

Â Now, let's take a look at the simulation model.

Â We're going to assume the store would purchase the historical

Â average of 80 jackets.

Â The demand value in cell E11 is in green,

Â the color that we have been using to indicate that this is a uncertain value.

Â If we double click on this cell, we can see that we are making an assumption that

Â the demand follows a Poisson distribution with an average of 80 jackets.

Â The rest of the formulas to calculate the profit

Â are the same as in the average value model.

Â The profit is the simulation output.

Â So cell E16 includes the psi output function.

Â The average profit is calculated using the PsiMean function.

Â The difference between the average model and

Â the simulation model is that we have added uncertainty in the demand.

Â The uncertainty was modeled using a Poisson distribution.

Â If the assumption is correct that the demand follows a Poisson distribution,

Â which could be verified by analyzing historical data, then the simulation

Â model shows that the average value model is over-estimating the expected profit.

Â This tells us that using an average value for

Â an uncertain input, the demand in this case,

Â does not necessarily result in the correct estimate for the average output value.

Â What is happening here is that every time the demand is larger than 80,

Â the profit it stays at $7,280.

Â However, when the demand is less than 80, the profit drops because there

Â will be some loss associated with selling jackets at their salvage value.

Â The average value model is not able to capture this.

Â To conclude, I hope that I have been able to convince you

Â of the benefits of simulation as a predictive analytics tool

Â that enables you to incorporate uncertainty in decision making models.

Â In this example,

Â we show how average values might result in misleading information.

Â But this is just one of several important insights produced by various types

Â of analysis that we have discussed throughout this module.

Â