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So, the reorder point is going to be based on two important things.

Two essential things that you're going to figure in.

One, is going to be the probability distribution of demand.

What does that mean? It means that you're going to figure

in the standard deviation of demand.

You're going to say, well, I expect my demand during the lead time to be

40 units but it could be as high as 50 or 60 units.

So, that's what I want to cover because

my demand during lead time could be between 40 and 50 or 60 units.

So, I want to cover all the way up to 60 units.

The other thing that you want to figure in is,

what kind of service level do you want to give your customers?

Now, what that means in terms of inventory,

is how much are you okay with running out at any point in time.

Are you okay to run out 10% of the time?

In which case, you are saying you want a 90% service level.

You don't run out for approximately 90% of

the time but you're okay with running out 10% of the time.

And, if you want a 95% service level,

what you're saying is that you are okay with running out 5% of the time.

So, that's the managerial decision that you have to make.

What is the service level that you want to maintain.

And then, you have to incorporate

the probability distribution of demand and come up with a reorder point based on that.

So, two things we're going to include in coming up with the reorder point.

So, you have the service level for the customer

on the basis of which you have a stock out probability.

And then, you also have the probability distribution of demand.

And what you see over here is what is used a

lot when you are using any kind of statistical calculations.

And this is your normal distribution.

So, we're going to base the calculation of the reorder point on the bases,

we're going to base it on the normal distribution.

We're going to take the properties of the normal distribution and

use it to come up with a reorder point.

So, you have a certain stock out probability,

you have the average demand during lead time which

is going to be the center of this distribution,

which is basically saying,

if you maintain inventory at this average level,

you are saying you're okay with running out 50% of the time.

Because 50% of the data and

this distribution is to the left and 50% of the data is to the right.

So, if you're averaging,

if you're keeping average demand,

you're okay with running out 50% of the time.

But if you're not okay with running out 50% of the time,

you are adding some kind of a safety stock.

And, that's going to be based on your stock out probability and the standard deviation

of demand that you would have got from the data that you have on your demand.

So, let's go through the calculations for

a reorder point here and then we'll go through an example to see how this works out.

So, reorder point is based on the demand during

lead time which if we didn't have any safety stock,

it would simply be, let's take whatever lead time we have.

Let's calculate the demand for that and that gives us demand during lead time.

The safety stock is based on something that we called a z score.

Now, if you remember this from statistics,

a z score comes from a standard normal distribution and it's

based on the probability that is to the left and the right of that point.

So, we'll take the z score, based on that.

And in the case of this lesson, what we'll do is,

we'll just look at a table that's going to give us

the different z scores for different probabilities running out.

So, we'll take a look at that in a minute.

So, for now, let's just call it a z score.

And then, we multiply it by the standard deviation of demand during lead time.

Right? So, we might have a standard deviation per period and we

convert it to a standard deviation for demand during lead time.

And what you see on the bottom of the screen there,

is you're calculating the standard deviation for

demand during lead time by taking the standard deviation per period,

multiplying it by the square root of the lead times.

Square root of LT, is a square root of the lead time and that's giving

you your standard deviation for demand during lead time.

Right. I promised you that we would see a table that's giving you

all the different factors of

a service and all the different z values for those factors of service.

So, here you have that table which says 75% service level translates into a 0.67 z value,

going all the way up to 99.99%,

translates into a z value for 3.72.

So, what this is saying is that if you want a certain service level,

you enter the z value,

the corresponding z value from this table.

And for those of you who are familiar with statistics,

this is something that can be calculated or

taken easily from an Excel function based on norms inverse.

So, you put in the probability into that function and you get the z value based on that.

So, you can do this easily for any probability that you want to look at.

Now, let's take this idea of reorder point and apply it in an example.

So, what you have here is average daily demand of 100 units.

Standard deviation of 30.

Lead time of three days.

The cycle service level that is expected is 92%.

So, you're okay with running out 8% of the time.

The z value is given to you as 1.41 for that service level.

And you're asked to compute the reorder point.

So, go ahead and use the formulation that we had earlier to compute

the reorder point and we'll come back and see what you find.

All right.

So, the reorder point is going to be based on the demand during lead time and

then the safety stock factor which is going to be based on the standard deviation,

the z score that you're going to get based on the service level.

And we can calculate the standard deviation based on the lead time,

square root of lead time that we're going to multiply it with.

So, here is your reorder point for this particular problem.

It's going to be 100 units of average demand per day times three days of lead time.

To that, we will add the z score which is 1.41.

Multiply that by 30,

which is a standard deviation.

And multiply that by the square root of 3

in order to convert the standard deviation for lead time.

To convert the standard deviation into standard deviation for lead time.

And this gives us a reorder point of 373.

So, what is this telling us?

It's telling us that every time your inventory reaches a level of 373,

if you're using the continuous replenishment system for inventory management,

you will place an order which is going to be equal to the economic order quantity.

So, you reach a level of 373,

you place an order of economic order quantity.

And here, you have the solution,

a complete solution, given to you in clear type.

So, 373 is your reorder point.

Right. Now, we looked at what is called a

continuous replenishment system as the system that we focused on for the calculations.

There is, however, an alternative system that you can use.

And you may be familiar with the system.

When we describe it,

you'll probably see that you're familiar with the system.

It's called a Periodic Review System.

And the main difference there,

is that in the Periodic Review System,

the time between replenishments is fixed.

So, when I said you may be familiar with this,

let's think of the vending machine that you might have in your building,

in your office building or in your school,

that is being replenished at fixed intervals.

There's somebody who comes there every week or every four days,

whatever that fix period is,

and replenishes the inventory in there.

What you also notice about about that replenishment system,

is that the time period is fixed but the quantity that needs to be

replenished for every product is going to be different every time it gets replenished.

So, if you have 10 slots for M&M candies in that particular machine,

on some days that the person comes back to replenish,

all of those slots might be empty.

In which case, the replenishment quantity becomes 10 units.

Some days, only two of those might have been used up,

so the replenishment quantity becomes two.

Some days none of those might have been used up and the quantity is zero.

So, to contrast this with what we learnt about in the continuous replenishment system,

in the continuous replenishment system you are having a fixed order quantity.

We came up with the EOQ.

That was the fixed order quantity.

The time between orders is going to be

different based on when you reach the reorder point.

In the Periodic Review System,

the time between orders is fixed,

the quantity is not fixed.

It's based on that particular target inventory level.

It's the number of slots for the M&Ms that you

have in that machine that becomes the target inventory level.

You want to build it up to 10 and that

determines how much quantity you would be replenishing at any point in time.

So, these are the two main types of

inventory replenishment systems that get commonly used in all your inventory systems.

And these are in place when you look at

a larger ERP system that's making decisions for inventory.

These are the basic ideas that are in place there.

This basic EOQ formula that we learned about in

the basic continuous replenishment system that we learned about can

be looked at from

a more sophisticated perspective if you were to relax some of the assumptions.

So, if you remember, we started off with saying there are

no discounts for any item in terms of the price.

The annual demand is constant.

And we can take all of those restrictions and

relax them and it gets to be a more and more complex kind of model,

for which the calculations obviously get more complex.

But this is the model that we did look at,

it is the basic model on which all of those other models are based.