# Quantity Discount Order Limits

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### EOQ Quantity Discount

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### Incremental Quantity Discouts

hello and welcome back to part two of,our discussion of the eoq you with,quantity discounts in the first video we,talked about the all units quantity,discount schedule which assumes that the,quantity discount applies to the entire,quantity to all student to all units in,our orders so if for example we were to,place an order for 500 units looking at,this schedule right here we would assume,that we will pay nine dollars for each,of those 500 units in our order now if,we conversely we assumed an incremental,quantity discount schedule we would have,to pay ten dollars per unit for the,first 399 units in our order of 500,units and the discount at one dollar per,unit would apply for all those units,that are in excess of 399 units or more,specifically we would have to pay three,hundred ninety nine times ten dollars,plus 100 times nine dollars so there,will be a difference in acquisition cost,and an average unit cost that will,course also affect our optimal order,quantity and our inventory,decision-making so what I want to show,you in this video is how we can take,this difference in quantity discount,schemes into account as we calculate,optimal cost minimizing minimizing order,quantities so what we see here in this,lower portion of our worksheet is a,total cost function that takes this,adjustment into account you see that,this total cost function differs from,our standard total cost function and,that we have these d sub I divided by Q,adjustments that are also reflected in,the AO q formula well this D sub I as it,turns out simply represents the,additional acquisition cost that we must,take into account because we are dealing,with incremental quantity discounts,rather than all units quantity discounts,so it is the cost that we have to pay,extra for those quantity increments for,which the quantity discount does not,apply now as we try to find the optimal,order quantity we will set up a table,like this where we will start with the,highest price break and then work our,way down to the lowest and of course,most desirable unit price so the first,thing we need to do to solve this,problem is we need to calculate the,value of C sub I now if we look at a,unit cost of \$10 what is the extra cost,we incur because this unit cost of 10,does not apply to the entire order,quantity now clearly as you can see this,is the highest cost and it applies for,any order quantity so regardless of,whether I order \$10 or 200 or 300 units,I will get this price is \$10 price for,all units in my order quantity so d sub,I will always be zero in the highest,quantity bracket or I should say in the,lowest quantity bracket at the highest,unit cost so moving on to the next,increment where we have a unit cost of,\$9 that applies for all incremental,quantities between 400 and 1,000 and 199,units in my order while I simply,realized that for the first 399 units I,will not get this price rather for the,first 399 units I will have to pay an,extra \$1 per unit and this is exactly,what D sub I represents

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### OM Calculation: EOQ and Quantity Discount

hello everyone in this session we will,show how to do the UQ model and the,quantity discount model calculations,through examples let's first take a look,at an example of UQ model now a local,distributor for an national tire company,expects to sell approximately 9600,steel-belted radial tires of a certain,size and treat design next year then,your carrying cost is \$16 per tire and,uttering cost is \$75 the distributor,operates 288 days a year first question,what is your Q now remember to calculate,yield Q the formula is straightforward,the UQ kinetic Q star equals to square,root of 2 d s divided by H now in the,formula we need to know few numbers D,which is the demand S is the ordering,cost which is adding cost per order and,H is the holding cost,now here we mentioned the demand t and,the holding cost need to be consistent,if what we use is annual demand then the,holding cost should be and your holding,cost if what we use is monthly demand,then the holding cost should be adjusted,it to monthly holding cost as well now,let's take a look at a question and see,whether or not the required numbers are,given here we see the sales is 9600 per,year carrying cost or holding cost is,\$16 per tire and uttering cost is \$75 so,all the three numbers the HS are giving,the question to calculate the e oq,quantity it is straightforward result,from substituting all these three,numbers into the formula,can do the calculation and get an,optimal order quantity or the ilq,quantity for this problem equal to 300,unit which means the dealer of the,distributor need to order 300 unit of,the specifying tire,every time one thing to remind you is,don't forget to take the square root of,the calculation this is one error I've,seen before,next how many times per year does a,store reorder which is how many orders,does a distributor need to place every,year so number of orders we place,basically is the result of the total,demand our total quantity we need to,order divided by the number of quantity,we order every time for example if over,the year we need to order 100 unit and,every time we only order 10 unit then we,need to place 100 divided by 10 which is,10 order per year so similarly in this,question we use a demand D divided by,the outer quantity the uq quantity which,is 300 and gallons 32 which means based,on our demand of 9600 unit per year and,our yoku quantity of 300 unit per order,we need to place 32 orders per year Part,C asks us to calculate the lens of an,order cycle so the lens of outer cycle,basically is the interval between two,orders between two consecutive orders so,from the time I place the order now till,the time that I place the next order,what will be the length of the interval,which is the lens of an order cycle now,this actually is determined by two,numbers which is well,what is the time interval we're talking,about second is how many orders we need,to place for example if we need to,operate 10 days and we need to place two,orders over these 10 days compared then,

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### EOQ with Quantity Discounts

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### How to set quantity discounts on your ASINs | English

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### All Units Discounts

hello and welcome to this video in which,I would like to talk about an extension,to the basic lq model which takes,quantity discounts into account as you,may recall the basic lq model makes a,series of limiting assumptions regarding,for example the nature of demand and the,nature of the times but we also assume,that unit costs are actually independent,of the order quantity of the basic lq,model clearly in reality that will often,not be the case because we cannot expect,to get a better price at a better unit,basis the more we purchase at a given,time the purpose of this video is to,tell you how we can extend the basic e,lq model to take quantity discounts into,consideration now there are two,different kinds of quantities discount,schemes the first one is called an,all-units quantity discount which simply,means that the discounted price is for,the entire purchase quantity so in our,example here where we have a quantity,discount schedule shown in this little,table here if we purchase 4,800 units or,more we will pay eight dollars for each,of those 4,800 units on the other hand,if we purchase a very small quantity we,will have to pay a price of up to ten,dollars in this particular really video,we will discuss the alkaline discount in,a separate video I will talk about,incremental quantity discounts in the,case of incremental quantity discounts,the discount only applies to the,increment of the order quantity that is,beyond the respective thresholds however,for now let's focus on this upper,portion of this table we will compute,the eoq you taking into account the,existence of all units quanta quantity,discounts as usual we start out with our,basic parameters we know that a lambda,annual demand is 4800 units the cost of,placing an order is \$40 and the,inventory carrying charge is 25% and now,of course we see that the unit cost will,depend upon the quantity we order in,every single order as you can see the,cost ranges from about 8 dollars per,unit for a large order quantity up to 10,dollars per unit for small order,quantities if we were to plot out these,total cost curves for these prices we,would find that we do not have a single,total cost curve that we can simply,optimize the way we do in the basic lq,as it turns out we now have a series of,different cost curves for each of those,different price levels so we end up with,a discontinuous total cost function and,we'll have to be a little more careful,as we try to find the truly cost,minimizing point on this discontinuous,total cost function to do this we simply,start out by computing the eoq you for,each of those respective price breaks so,let's start out with the lowest price,break of 8 dollars per unit the oq of,course simply the square root as we know,at two times lambda times the cost of,place in an order divided by the,inventory holding cost per order now,remember this of course simply is I,multiplied with your respective cost per,unit which on our case right now is \$8,so that gives me in this case a

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### Inventory Quantity Discounts

this video will show you how to deal,with quantity discounts this is based on,economic order quantity if you can order,economic quantity that will give you the,best answer if you really understand,economic order quantity it's where we've,minimized the ordering cost and minimize,the holding cost where they're equal to,each other,and together that is the lowest cost for,inventory now here we have a trade-off,because if we order more we get a,reduction of price and so we basically,have to calculate the cost out the cost,of managing that inventory and violating,economic order quantity plus the cost of,the actual product and we are ordering,this from somebody else that's why we're,getting a quantity discount production,or a quantity doesn't come into account,at all here quantity discount is in,regards to ordering it from somebody,else and so we're gonna go ahead and do,economic order quantity just like we,showed you in the earlier video because,holding cost is constant and we want to,know what that is because that will give,us the best answer and so once again you,go back to the formula I'm going to do,it in pieces so let's just economic,order quantity here I'll probably end up,using 3 cells like I did in the past so,the top part of the equation was 2 times,the the annual demand and and times then,the setup or ordering cost in this case,it's 120 so that's the top part of the,equation now some that I failed to,mention here they gave you the demand in,monthly this is data from 12 2012 point,20 at the end of chapter 12 they talk,about the the monthly demand is 400 so I,simply took 400 times 12 and that gave,me my my annual demand of 4,800 so,that's the top part equation the bottom,part of the,then of course we we take this amount,and we divide it by our holding cost,which is is constant at 35 and then,remember the last part of this equation,is the square root and so just a,reminder this is on the formula sheet I,just use this this formula here because,this is economic or quantity and the,holding cost was constant as compared to,this one or the holding cost varies,depending on the price,remember this is production or quantity,now I'm actually going to calculate out,the the total cost I'm actually going to,use this lower one here because this is,the cost to manage the inventory plus,the cost of the product well let's go,back and look at our answer here so,economic order quantity is a hundred and,eighty one well look at this from 1 to,99 if i order one up to 99 units the,price is 350 by order from 100 to 199,the price is 325 and if I order over 200,the price is 300 well right now they're,telling us economic order quantity will,put us above this category so we would,never order less than a hundred and,eighty one units so we won't even,consider this one because they're,telling us the best possible in regards,to holding an ordering cost to minimize,those and make them equal to each other,is at least 181 so it falls into this,category so let's go ahead and calc

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### Operations Research--The Quantity Discount Problem ILP Model Formulation

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### Special Price & Qty Break/Volume Discount

so I've had a question from a customer,wants to set up a price on a customer,but it's a price where there's a minimum,order quantity so essentially they want,to set up a business partner special,price and set a better price with the,customer orders more than a certain,minimum quantity so that's just let's,just look at say the special prices in,the system so we can go to a business,partner call up the partner right click,on their account and then go to special,prices for the business partner this,business partner happens to have a list,price already set against them and if we,we want we can just go there and change,that as I'm making this that too without,a price list the objective here then is,that it allows me to call up a specific,stock item against that business partner,in this instance we're not referring to,any of the existing price lists on that,account and we're simply going to set a,price that we want this customer to be,charged for their item so in this,instance we're setting it to 55:29,that's fine if we do that we can just,add that item and it means that business,partner will forevermore Ragesh and that,that special price for that product we,go back in here however we can also then,double click on this role and that,brings up a second window which in this,case is titled period discounts and this,means that from a certain date perhaps,up to a certain date we will be charging,them perhaps a different price so this,could be for like some special offers,running for you know a week a month,three months whatever happens to be or,we can just leave that as it is and,double click on that rule and it opens,up a third window which allows us to set,or the system referred to as a quantity,break price or volume discount as we,have here,so not instance we set what the minimum,order quantity is in order to achieve,this lower or this better and unit price,so I'm just going to say it's ten for,the moment and if we offer or if they're,if they order more than ten they guess,they're it's like a lower price so just,update on that and we update all the way,back so if we go to a sales document,users pick up a sales quotation when I,call up that customer and that stock,item the system brings back the price in,blue indicating that there is a special,price available on it and we'll see it's,the higher price at the moment and any,quantity I put in up as far as nine who,attract that price once I put in ten the,price will revert or drop to the,quantity break price available for the,customer from there I can process the,transaction

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### Quantity Discount Model

this video will discuss how to set up,and solve a quantity discount model,problem using Excel and salt in this,problem we have a vendor for which we,have a fixed ordering cost of ten,dollars per quarter an annual holding,cost percentage of forty forty percent,based on the unit purchase cost there's,no storage cost per unit for this,product although we'll build a model,where we have the flexibility to include,this we have annual demand of 2400,working days during the year of 240 and,Ally time of five days we have a,quantity discount schedule with six,price levels for example the unit,purchased cost is \$35 we order between 1,and 49 units of the product if we we pay,a lower price we must order more units,of the product for example to purchase,for 32 dollars and thirty-five cents we,would have to order a minimum of 150 or,as many as 299,the unit holding costs is based on the,purchase cause so the unit holding costs,will be the purchase cost times the,holding cost percentage and I'll put the,dollar signs as absolute references on,the holding cost percentage plus the,storage cost per unit the storage cost,per unit would be a component of the,holding cost that does not change with,the purchase price in this particular,problem we don't have that type of cost,but when we're setting up this model,gives us the flexibility to incorporate,this,copy that formula all the way across and,you can see that the holding cost,decreases as the purchase cost increases,the last maximum quantity is just an,arbitrarily large number in reality if,we buy any number of units five hundred,or over the cost will be thirty dollars,and seventy-five cents we just put an,arbitrarily large number here because,this will make the references within,solver and sister we need to solve this,problem for each price level separately,to do so one way we can bring in the,correct values that are associated with,the right price level is the H look up,for me VH look up will first reference,to lookup value that will be the price,level analyzed right now we have one but,we'll change this any any number between,1 and 6 i'll hit f4 the function key to,put the dollar signs in the table array,is going to be all of the purchase costs,quantity and holding cost information,for each price level of at the f or,function key to put in the dollars in,the row index number tells us the row in,this table we want to look up and place,on this lawn the unit purchase cost is,on Row 2 of the horizontal table so,we'll put to the last element in the age,look up formula is a cell that tells us,whether we want an approximate match or,an exact match and we'd like to have an,exact match,so we double-click on pulse type the,closed parentheses to test this formula,we want to enter the other price levels,and make sure that the unit purchase,cost changes,for instance right now I have price,level 6 we can see that the unit,purchase cost is thirty dollars and,seventy-five cents if we enter a number,like seven we get an error becau

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