this is a lecture from open tuition to benefit from the lecture you should download the free lecture notes from open tuition com this is the second lecture on chapter 4 of the free lecture notes and we've looked at the economic order quantity and we found out in the last lecture in example 2 that the best the economic order quantity was 800 units that was the order quantity that minimized that total inventory costs over the year and they were minimized at a total of two thousand and we ignored the how much we were paying there are 40,000 units on the basis that it would be 25 dollars over the per unit however many who were ordering each time however I did say you could make it a bit more fun with what we call quantity discounts so look at example 3 if you would for the information given in example 1 so the example we did in the last lecture the supplier now officers discounts on purchase price as follows and the depends of the quantity we order each time so if we order between 0 up to a 5,000 units we get no discount but if we prepared to order from 5000 that when less than 10,000 each time they'll give us a discount of 1 percent on the purchase price and if we provided for that order 10,000 or more each time we'll get a one and a half percent discount on the purchase price now we already know that 800 units will give the minimum inventory costs if we order bigger quantities each time the inventory concept already are bound to be higher think back to the graph Andrew but it could be worth paying higher inventory costs if because of the discount the cost of buying the 40,000 units over the year was lower and so there's no quick way here as you'll see there's no more formula we've just got to cost out and one of the choices well we know the economic order quantity was eight hundred and if we order eight hundred units each time we already know the inventory costs in total were two thousand and we know that it's any other level that total will be higher but we now need to also consider the purchase cost over the year remember we're buying 40,000 units a year and if we order eight hundred there's no discount we'll pay the full twenty five dollars a unit which is how much one million and so the two together 1 million and two thousand we then say well what about this first level of discount of one percent together one percent discount we'd have to order at least five thousand each time and so let's try ordering five thousand and see what the total cost will be then again the inventory costs will be higher but of course the total purchase cost will be lower let's see if it's better or worse so normal costing but just watch one little thing as I go through first of all the inventory costs we've done this enough time so it should be getting pretty automatic the reorder cost 40,000 units a year we are the 5,000 each time we'll need eight orders and the costume placing each order was twenty dollars so total of 160 the holding cost we're ordering 5,000 each time so the average inventory will be 2,500 but be careful here the cost of holding one unit if you remember was ten percent of purchase price but the purchase price is no longer twenty five dollars it's one percent less so the purchase price will only be 99 percent of twenty five dollars now notice on the entirely different but even so we should do it correctly perfect because of the discount purchase price is only 99 percent 25 there's a 1% discount so what will be the total holding cost per unit 10 percent 99 percent 25 per unit it's now two point four seven five instead of two fifty two and a half thousand units I get six one eight eight so the total inventory' costs will be six three four eight which of course is higher a lot higher before it was only two thousand now at six thirty four eight but the total purchase cost will be lower we still need 40,000 units over the year but instead of paying twenty five a unit again a one percent discount the cost per unit will be slightly lower so what'll at Ogilvy I think mayor isn't Detroit I get nine hundred and ninety thousand now you can set up your workings differently doesn't matter but although the inventory costs have gone up a lot from two thousand two sixty three four eight the total purchase price has gone down a lot from 1 million down to nine ninety thousand and so the total of the to nine nine six three four eight it would be better to order five thousand units the discount is bigger than the extra inventory costs what about other levels though why don't I try 3000 units well that'd be silly surely because 3000 units remember the economic order quantity was 800 each time or the 3000 each time and the inventory costs are bound to be higher and the bin ohm discount so it couldn't possibly be cheaper why don't I consider 6,000 units well consider 6,000 units we get no extra discount and the inventory costs of me higher still it cannot be cheaper we only need to consider the economic order quantity and the levels at which we first get a discount and so on this question the only other order quantity that could possibly be cheaper would be 10000 units because although again the inventory costs will be a lot higher we get a bigger discount the purchase cost will be lower so let's try finally 10000 units the inventory costs well the order costs if you're ordering a 10,000 each time Nordia that's supposed to say 40 we only need place for orders and a $20 for each order that goes down a lot to only 80 the holding cost ten thousand each time means average inventory throughout the year of 5,000 units the cost of holding each units 10% of purchase price but again it's a tiny thing that's all getting right the motorist price was 25 but with a one and a half percent discount it'll only be 98 and a half percent of 25 per unit so the holding costs 5,000 units 10 percent of 98 and a half percent of 25 12 3 1 3 so as we expected the inventory costs are a lot higher at 12 3 9 3 but again it might be worth paying so much more because we're getting a bigger discount so finally what happens to the total purchase price over the year we're still buying 40,000 but the cost per unit falls to only 98 and a half percent to 25 so the total purchase cost nine 85,000 and so overall is it going to be better or worse inventory costs a lot higher purchase costs lower the two together nine nine seven three nine and three and as I explained a few minutes ago it's only those three levels that are worth considering economic order quantity and the levels at which we first get higher discounts here five thousand and ten thousand one of those three has to be the best and it could be any one of the three what is it here nine nine seven nine nine six it's this one which is how many five thousand two units five thousand now say it could be any one of the three there's no quick way there's no choice but to cost out each of the three alternatives okay that's it really for economic order quantity if you did pay math - you'll know an F - you were also tested on something called the economic batch quantity but that isn't tested at f9 it's simply the eoq you one tiny thing I better mention just to be saved sometimes you might see mention of what's called buffer or safety inventory but all this is if you think back to the beginning of the first lecture I said that if we ordered a thousand units each time inventory you'd start with a thousand it had Faulds zero then up to a thousand down to zero about two thousand and so on and the average inventory would be half the order quantity well that's fine but there is always a danger in real life that if you meant new inventory Faulds zero before getting the new order as always a risk something might go wrong you know there might be delay in the new world of being delivered and what happens if there was a delay in the new order being delivered you fall to zero but then if the new order wasn't delivered to a few days later even a few days when you've no inventory and that could mean that turning away customers and losing profit you know they may not wait a few days and so what we might decide to do it's just to be safe let's have an extra hundred units all year and that's what we mean by buffer a safety inventory it's where we hold extra units in inventory throughout the year to be safe now it doesn't affect the economic order quantity at all you know even if an example what we're doing even if I said all the carried safety inventory of hundred units for the eoq you it would be completely irrelevant the only relevant relevance is when doing the costumes and calculating of the holding cost for the year well REO q if you remember forget quantity discounts re okay was 800 units and so when we were costing we said it on the average in factories 400 at what's the cost well if you're in saved inventory you will add on the holding cost of the same convention the buffer of the safety so if I am if I told you we were having safety inventory of hundred units it's as though there's an extra hundred oh yeah we'd simply add on a hundred units and whatever the whole thing cost even it was okay that's not we having to have one I'm sorry inventory there's likely to be something in every exam it's just one to mark question however there's one other thing we do need to consider so I will have one more lecture on this chapter where there's no arithmetic involved but you can be examined you know what we mean by what we call the gist in time system so one more lecture and then we love them crack the champion