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Remember we're focusing on independent demand items here.

Â Items that a company would purchase from a supplier,

Â that's coming from outside.

Â And how much to order is typically based on

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

Â So this is the model for calculating the amount of

Â inventory in terms of how much you want to order.

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

Â One of these costs is the cost of ordering.

Â So if you think about the cost of ordering,

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

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

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

Â consuming to get to that distant grocery store.

Â For a company, it might be order processing costs,

Â it might be costs of transportation.

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

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

Â It might be a fixed cost based on that,

Â so that would get counted under your ordering cost.

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

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

Â The other costs that companies are principally concerned about and

Â that gets incorporated into

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

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

Â the insurance that you're paying on that warehouse,

Â the opportunity cost of the space in your warehouse,

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

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

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

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

Â Now, we are also going to talk about

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

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

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

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

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

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

Â that's when you place an order.

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

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

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

Â incorporated into this Economic Order Quantity model.

Â So the first thing that you want to get

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

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

Â If you order in smaller quantities you are going to order

Â many more times if you have the same annual quantity,

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

Â So if you have a fixed ordering cost,

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

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

Â So here in this extreme example,

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

Â you ordered six months worth in a year,

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

Â it's going to be very small.

Â However, the cost of holding inventory,

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

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

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

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

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

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

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

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

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

Â have restrictive assumptions that are

Â simplifying it in order to get the calculations done quickly.

Â So what are the assumptions here?

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

Â Annual demand is something that we know,

Â we can forecast very well,

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

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

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

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

Â When we get to reorder point,

Â we'll talk about incorporating lead time in

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

Â So there's instantaneous replenishment.

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

Â so you're never worried about running short.

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

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

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

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

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

Â so it's a cost per order.

Â The unit price is constant over the years.

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

Â the unit price remains constant and we're starting off

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

Â so the unit price is constant in this case.

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

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

Â You have time on the Y-axis,

Â you have the quantity that's being ordered,

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

Â your average inventory that you have at

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

Â So if you're ordering Q at a time,

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

Â simply because you start off with Q,

Â it goes down to zero,

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

Â So, the next thing that you want to

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

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

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

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

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

Â So simply stated what this is saying is that,

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

Â you're basically ordering five times in the year,

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

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

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

Â there being a constant demand rate

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

Â So, before we get to the Economic Order Quantity,

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

Â the only two costs that we have and calculate

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

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

Â We're not taking that into account,

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

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

Â it's going to be based on two components.

Â One of them is the ordering cost.

Â So what you need is the number of orders.

Â You need the number of orders in a year.

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

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

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

Â Now on the other hand you need your holding costs.

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

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

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

Â so that is your one component

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

Â to be determined by the average inventory that is held

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

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

Â you have the total number of orders in a year,

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

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

Â It could be setting up your machinery to

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

Â It could be the set up cost of your supplier,

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

Â And on the other side you have the holding rate,

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

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

Â It's going to have some component of

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

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

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

Â up with a total cost of inventory management.

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

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

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

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

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

Â in diagonal is your holding cost,

Â that increases the more you order at a time.

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

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

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

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

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

Â the total cost of the combination of those two is giving

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

Â So the optimal quantity Q * is what you want.

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

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

Â our total cost and that unique minimum of

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

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

Â It's EOQ or Q* is the square root

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

Â multiply that by two,

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

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

Â your total annual cost using that

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

Â square root of two times annual demand

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

Â times the holding rate that you have for your item.

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

Â