0:06

Now everything that we've been talking about so far has focused on looking at

Â forecasts as a particular estimate, a pinpoint estimate or the point estimate.

Â Well, really when we're making predictions, we're not just talking about

Â a single point estimate, we're talking about distributions.

Â And so, imagine your regression line.

Â If this is our regression line, imagine at a particular point

Â overlaying a normal distribution around that point.

Â And so, that normal distribution reflecting the range of values

Â potentially that we might expect to observe around that.

Â So if I were to get multiple observations with a value of X2,

Â I have my best guess, but I've got that entire range of

Â uncertainty around that and that's important to keep in mind.

Â That we're not just predicting a point, we're predicting overall how

Â much certainty do we have that it's going to fall within a particular range and

Â that's something that's going to come up in the example that we work through

Â a little bit later.

Â 1:13

Now, how well we built a nice regression model?

Â Did we really need it?

Â Could we have done something that easier?

Â Well, what if we used a Simple Moving Average model?

Â Or what if we used formulated it as in other regressive models saying,

Â let's use the new most recent weeks of observations and those are going to be our

Â predictors and we'll use those two data points to predict.

Â So if I look back one week, look back two weeks,

Â use that to predict what's demand going to be like in the current week.

Â It turns out, you're not going to do too poorly with that particular measure.

Â So our regression line for forecasting is in black, the purple line here giving us

Â that simple moving average based model, just using those two weeks of data.

Â And it looks reasonably similar, but the piece that I wanted to point out and

Â you can see it clearly in this case here as well that

Â the smoothing based approach where the auto-regressive model,

Â where we're relying just on those recent observations,

Â it tends to take longer to adjust than the regression-based model.

Â So any time there's that discontinuity, the end of a quarter, the end of a month.

Â Because I'm only looking back at the most recent two weeks,

Â it's not as quick to adjust as our regression-based model.

Â The other thing that we've gotta keep in mind is how far out into the future am I

Â trying to forecast?

Â Our regression includes a trend and month specific effect.

Â I can forecast a year out, no problem.

Â But with our simple moving average model,

Â what do I do if I want to go beyond a two-week period?

Â I actually need to keep on forecasting to produce those X variables, and

Â I'm actually going to have to resort to a simulation-based procedure to take into

Â account the amount of variation that I'm going to observe and

Â be able to forecast out that four-year period.

Â 3:11

If we look at measures such as the average absolute error,

Â our regression based model's doing better there.

Â The farther out into the future that we're trying to forecast,

Â keep in mind the more uncertainty that we're potentially going to observe.

Â So this will, I pulled off stock forecasts.

Â For Google and just comparing the amount of uncertainty, the bounds on this

Â simulation procedure, looking out one month, two months, one year.

Â Notice how much variation we observe if we try to predict out a year,

Â whereas if we're just going out a couple of months,

Â the amount of uncertainty that we have is much smaller.

Â And so whenever you're using methods that rely on the most recent observations as

Â inputs into your forecasts, you're going to have, there's this uncertainty that's

Â going to keep on growing the further out you try to make those predictions.

Â 4:10

So, let's discuss the Excel exercise that we're going to work through next.

Â We're going to do a demand planning scenario.

Â So David's Retail, Art and Trade Shop.

Â I've got to make some orders for the holiday season,

Â determine how much I'm going to order based on historic consumer demand.

Â Now suppose that our forecasts are too high, well, let's order a lot of products.

Â Well, now we've got inventory that's gone unsold.

Â We're going to have to get rid of it, maybe we can return it,

Â maybe we've got to liquidate it.

Â What if I don't order enough?

Â Now I'm leaving money on the table, because I have consumer demand and

Â I don't have the inventory to meet that demand.

Â 4:55

So based on the historic demand,

Â we're going to figure out what is the right quantity to be ordering

Â where here is some of the constraints that we are dealing with.

Â Order quantity is going to be placed in,

Â quantities are going to be ordered in 25 unit increments.

Â We're going to assume that we're going to sell it at a price of $15, so

Â we haven't changed the price over time.

Â How much does it cost us?

Â Well, how much it costs us depends on how much we order.

Â And if we're ordering less than 100 units, it's going to cost us $12.

Â If we're ordering between 101 and 200 units, the first 100 units

Â are going to cost us $12, the next 100 units would cost us $10 a piece.

Â And ordering above 200 units, $12 for the first 100 units.

Â $10 for the next 100 units.

Â $8 for each unit above an beyond that and we do have a value that we can salvage,

Â any merchandise that's left over we'll be able to get recouped $5 a month for it.

Â So we don't completely waste our money, but

Â we're not going to get the $15 if we have unsold merchandise.

Â And so, here's the problem that we have is what's the right quantity for

Â us to order where our objective is profit maximization.

Â And so if I order too little, potentially if the money on the table.

Â If I order too much, there is a chance that I don't sell it and

Â that I end up spending too much money, because I don't get all of my money back

Â for the excess, for the merchandise in excess of the demand quantity.

Â 6:26

So for each month, we want to know what's the number that we need to order and

Â we want to know how much confidence do we have of profit falling into a particular

Â range?

Â So what is the range that contains centered around our best guess,

Â centered around our estimate for profit?

Â What's the range that we're 50% confident, 75% confident and

Â 95% confident that profit's going to fall into?

Â 6:53

As far as deconstructing this problem and

Â how do we approach it, we're going to start by building a forecasting model,

Â just like the regression models that we've been looking at so far.

Â Once we have our forecasting model, we know what the baseline level of demand is.

Â We're going to know what the variation looks like say, from month to month.

Â And we're going to be able to predict, what is demand going into the future and

Â how much uncertainty do we have in those estimates?

Â 7:36

So then for whatever quantity we decide to order, we're going to simulate out what

Â the different levels of demand are using the results from our forecasting model.

Â And based on that stimulation for each time we run that simulation,

Â we're going to be able to construct what's the revenue?

Â What are the costs that we incur?

Â And ultimately,

Â what's that profit if we knew exactly what the demand was going to be?

Â Well, we're going to simulate out a bunch of different levels of demand based on our

Â forecasting model and then we're going to take the average across them that's

Â going to give us our expectation for profit.

Â We're also going to use those simulations to characterize those ranges we were

Â looking for.

Â So what's the range on 50% sure of profit falls in the range of 75% sure, 95% sure?

Â So that Excel spreadsheet with the data we're going to be working with is up on

Â the course website.

Â So, we'll turn to that next.

Â