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

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

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

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

Â in the standard deviation of demand.

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

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

Â So, that's what I want to cover because

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

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

Â The other thing that you want to figure in is,

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

Â Now, what that means in terms of inventory,

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

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

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

Â You don't run out for approximately 90% of

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

Â And, if you want a 95% service level,

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

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

Â What is the service level that you want to maintain.

Â And then, you have to incorporate

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

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

Â So, you have the service level for the customer

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

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

Â And what you see over here is what is used a

Â lot when you are using any kind of statistical calculations.

Â And this is your normal distribution.

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

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

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

Â use it to come up with a reorder point.

Â So, you have a certain stock out probability,

Â you have the average demand during lead time which

Â is going to be the center of this distribution,

Â which is basically saying,

Â if you maintain inventory at this average level,

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

Â Because 50% of the data and

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

Â So, if you're averaging,

Â if you're keeping average demand,

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

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

Â you are adding some kind of a safety stock.

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

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

Â So, let's go through the calculations for

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

Â So, reorder point is based on the demand during

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

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

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

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

Â Now, if you remember this from statistics,

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

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

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

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

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

Â the different z scores for different probabilities running out.

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

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

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

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

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

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

Â is you're calculating the standard deviation for

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

Â multiplying it by the square root of the lead times.

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

Â you your standard deviation for demand during lead time.

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

Â all the different factors of

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

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

Â going all the way up to 99.99%,

Â translates into a z value for 3.72.

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

Â you enter the z value,

Â the corresponding z value from this table.

Â And for those of you who are familiar with statistics,

Â this is something that can be calculated or

Â taken easily from an Excel function based on norms inverse.

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

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

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

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

Â Standard deviation of 30.

Â Lead time of three days.

Â The cycle service level that is expected is 92%.

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

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

Â And you're asked to compute the reorder point.

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

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

Â All right.

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

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

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

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

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

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

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

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

Â Multiply that by 30,

Â which is a standard deviation.

Â And multiply that by the square root of 3

Â in order to convert the standard deviation for lead time.

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

Â And this gives us a reorder point of 373.

Â So, what is this telling us?

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

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

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

Â So, you reach a level of 373,

Â you place an order of economic order quantity.

Â And here, you have the solution,

Â a complete solution, given to you in clear type.

Â So, 373 is your reorder point.

Â Right. Now, we looked at what is called a

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

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

Â And you may be familiar with the system.

Â When we describe it,

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

Â It's called a Periodic Review System.

Â And the main difference there,

Â is that in the Periodic Review System,

Â the time between replenishments is fixed.

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

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

Â in your office building or in your school,

Â that is being replenished at fixed intervals.

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

Â whatever that fix period is,

Â and replenishes the inventory in there.

Â What you also notice about about that replenishment system,

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

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

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

Â on some days that the person comes back to replenish,

Â all of those slots might be empty.

Â In which case, the replenishment quantity becomes 10 units.

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

Â so the replenishment quantity becomes two.

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

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

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

Â We came up with the EOQ.

Â That was the fixed order quantity.

Â The time between orders is going to be

Â different based on when you reach the reorder point.

Â In the Periodic Review System,

Â the time between orders is fixed,

Â the quantity is not fixed.

Â It's based on that particular target inventory level.

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

Â have in that machine that becomes the target inventory level.

Â You want to build it up to 10 and that

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

Â So, these are the two main types of

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

Â And these are in place when you look at

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

Â These are the basic ideas that are in place there.

Â This basic EOQ formula that we learned about in

Â the basic continuous replenishment system that we learned about can

Â be looked at from

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

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

Â no discounts for any item in terms of the price.

Â The annual demand is constant.

Â And we can take all of those restrictions and

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

Â for which the calculations obviously get more complex.

Â But this is the model that we did look at,

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

Â