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Remember we're focusing on independent demand items here.

Items that a company would purchase from a supplier,

that's coming from outside.

And how much to order is typically based on

this model that is very popular called the Economic Order Quantity.

So this is the model for calculating the amount of

inventory in terms of how much you want to order.

Now this model is based on the principle of trading off two different costs.

One of these costs is the cost of ordering.

So if you think about the cost of ordering,

if you're thinking about that trip to the grocery store,

it's the cost of the time that you're spending to go to the grocery store.

It's the cost of the gas that you might be

consuming to get to that distant grocery store.

For a company, it might be order processing costs,

it might be costs of transportation.

It's the cost of getting a truckload and that might be

a fixed cost whether you get a full truckload or you get a quarter of a truckload.

It might be a fixed cost based on that,

so that would get counted under your ordering cost.

So it's based on the number of orders that you have in a year,

you're going to have an annual ordering costs from that.

The other costs that companies are principally concerned about and

that gets incorporated into

this economic order quantity model is the cost of holding inventory.

So, if you think about the costs of finance that's being invested in this inventory,

the insurance that you're paying on that warehouse,

the opportunity cost of the space in your warehouse,

all those things are figured into the holding cost for inventory.

And when you think about the economic order quantity model what you'll see

is you'll see that it's trying to trade off these two different costs.

We'll see in terms of how it's trying to trade off these two different costs.

Now, we are also going to talk about

when to order and we'll talk about that in a different lesson,

in this lesson we're going to focus on how much to order.

But when to order is going to be based on a reorder point.

So, it's going to be based on when the inventory reaches a certain level.

There's going to be a point that will be determined based on some analysis that we'll do,

that will say when it reaches a certain level of inventory,

that's when you place an order.

The question that we're trying to address here in this lesson is

how much to order and that's going to be your economic quarter quantity.

So let's take a look at some of the things that get

incorporated into this Economic Order Quantity model.

So the first thing that you want to get

a perspective of is the trade off between ordering and holding cost.

So if you think about this from a perspective of annual quantity that's being ordered,

If you order in smaller quantities you are going to order

many more times if you have the same annual quantity,

like you will order more frequently and you will have many more orders.

So if you have a fixed ordering cost,

your annual ordering cost will be very high because you've ordered many many times.

Now contrast this with the idea of ordering a large quantity at a time.

So here in this extreme example,

if this was the time of the year and you've ordered only two times in the year,

you ordered six months worth in a year,

your annual ordering cost is going to be based on just two orders,

it's going to be very small.

However, the cost of holding inventory,

the cost of how much investment you have in that inventory,

how much risk you are taking about that inventory getting obsolete or getting

spoiled is going to be much higher because you're buying six months worth at a time.

So that's the idea of ordering cost and holding cost and you can

get some sense of a trade off between these two costs and that's

what we're going to use in order to derive what is called

Economic Order Quantity in order to calculate what is called the Economic Order Quantity.

Now the Economic Order Quantity Model is based on a certain restrictive assumptions.

It's a simple model and whenever you have a simple model it's probably going to

have restrictive assumptions that are

simplifying it in order to get the calculations done quickly.

So what are the assumptions here?

The assumptions are that the demand rate is known and its constant.

Annual demand is something that we know,

we can forecast very well,

that's what we're assuming here however unrealistic it may be.

And we're also assuming that all demand is met that you're never telling a customer,

don't have enough, all demand is being met.

We're assuming a lead time of zero at this point.

When we get to reorder point,

we'll talk about incorporating lead time in

the reorder point but for the Economic Order Quantity we're assuming a lead time of zero.

So there's instantaneous replenishment.

You place an order, and you get the quantity delivered to you right on that date,

so you're never worried about running short.

The setup cost is fixed regardless of the quantity you order.

So again whether it's realistic or not what we're saying is

that every time you place an order you incur a fixed cost.

Whether that order is for a very small quantity or a very large quantity,

the cost of ordering is going to be based on simply the fact that you placed an order,

so it's a cost per order.

The unit price is constant over the years.

So over the period that you're calculating the economic order quantity,

the unit price remains constant and we're starting off

with a model that does not involve discounts of any sort,

so the unit price is constant in this case.

So let's work towards coming up with the Economic Order Quantity here.

So we said it's a constant demand rate on the X-axis.

You have time on the Y-axis,

you have the quantity that's being ordered,

so when you have a constant demand rate and an annual demand of D,

your average inventory that you have at

any point in time is going to be based on Q divide by two.

So if you're ordering Q at a time,

your inventory is going to be based on Q divide by two,

simply because you start off with Q,

it goes down to zero,

starting and ending inventory are Q and zero and the average is Q divide by two.

So, the next thing that you want to

see is that the time between orders is going to be determined by

the quantity that you order every time you place an order divide by

the annual demand or D. And if you take the opposite perspective of this,

the number of orders in a year is going to be based on

the annual demand divided by the quantity that you order every time you place an order.

So simply stated what this is saying is that,

if you have an annual demand of 10,000 units and you order 2,000 at a time,

you're basically ordering five times in the year,

so that's number of orders is five in a year based on 10,000 being

the annual demand and 2,000 being the order that you order every time you place an order.

So this picture is reflecting the assumption of there being instantaneous replenishment,

there being a constant demand rate

and we're keeping these assumptions in mind going forward.

So, before we get to the Economic Order Quantity,

let's take the perspective of our ordering costs and holding costs as being

the only two costs that we have and calculate

what would be the total annual cost of managing the inventory.

So we're keeping the cost of the item aside.

We're not taking that into account,

we're simply looking at the total cost of managing the inventory.

So, when you look at the total cost of managing inventory,

it's going to be based on two components.

One of them is the ordering cost.

So what you need is the number of orders.

You need the number of orders in a year.

And the number of orders in the year is going to be determined by

the annual demand divided by the quantity that you order every time you place an order,

and that's going to give you your annual cost of ordering.

Now on the other hand you need your holding costs.

You're holding cost is going to be determined by how much you hold at any point in time.

So your average inventory which is Q by two is going to determine your holding cost.

So the ordering cost is going to come from the number of orders,

so that is your one component

and the other main component is going to be the holding cost and that is going

to be determined by the average inventory that is held

based on the fact that you're ordering Q at a time.

So, if you were to take those two components and try to come up with the total cost,

you have the total number of orders in a year,

you multiply that by the cost of ordering every time you place an order and we

call that S here because S stands for ordering costs or set up cost.

It could be setting up your machinery to

make an item in which case you're going to call it your set up cost.

It could be the set up cost of your supplier,

in which case you're going to use set up costs as the cost of ordering.

And on the other side you have the holding rate,

so that's going to be like an interest rate that's going to be calculated like

an interest rate but it's going to have some more components than simply the investment.

It's going to have some component of

how much percentage do you expect to be added for a product to get spoiled,

to get obsolete and those sorts of things might go into a holding rate.

So that would give you the total cost of holding inventory and ordering inventory coming

up with a total cost of inventory management.

So if you take these two costs and you look at the trade off between these two costs,

that's what's being represented on this picture over here.

On the X-axis you have order quantity as the order quantity

goes from left to right as it increases so the more you order at a time,

the holding costs, the straight line going from left to right

in diagonal is your holding cost,

that increases the more you order at a time.

At the same time, the costs of ordering or set up costs go

down and that's the curve that's going down from

left to right showing that the set up cost is going to be

less if you order more at a time simply because you have fewer orders.

And the total cost curve which is a combination of the holding costs and the setup cost,

the total cost of the combination of those two is giving

you the total cost based on adding up both of these costs.

So the optimal quantity Q * is what you want.

It's the quantity at which your total cost is going to be at its absolute minimum.

So there's going to be a unique minimum for this in terms of

our total cost and that unique minimum of

total cost is going to come from a optimal quantity Q*,

which can be computed based on this Economic Order Quantity formula.

It's EOQ or Q* is the square root

of your total demand or your annual demand times your ordering cost,

multiply that by two,

divide that by holding cost and take the square root and that gives you your EOQ.

Once you have your EOQ given to you by Q*,

your total annual cost using that

EOQ can be calculated by the formula that you have on the bottom of the screen,

square root of two times annual demand

times set up cost for every time you place an order,

times the holding rate that you have for your item.

So that's the way you would be calculating your total annual cost if you are using EOQ.