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Classical EOQ Model | Dr. Tridib R. Sarma - YouTube
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[Music]
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hello everybody let me tell you a story
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about my own my life during my school
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days I had a dilemma I had an
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opportunity and a dilemma now
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opportunity I wanted to do business
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I wanted to business of small pants or
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buying pants from the factory and then
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selling it to my friends I expected that
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I'll be having about 300 customers every
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year would in my schoolmates where I'll
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purchase pain at a price of 2 rupees per
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item and then sell it off at 5 will be a
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spy item fantastic business opportunity
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with my limited resources I've decided
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to buy pens and in small lakhs I'll go
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to the factory equipped I'll buy those
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pen and then sell it off with my friend
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and I expected a bonanza but there was a
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problem the problem is every time I went
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to purchase pen the factory they decided
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to impose a ordering price ordering cost
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of 20 rupees per order something which I
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was not very comfortable with so what do
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I do
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I use the number of orders so let me
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order a whole lot in one single shot and
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I'll store all the pens in my own
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warehouse so that's my option I had a
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brilliant idea I'll buy all of them I'll
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store it in my own location in a
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commercial space but again there's a
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hitch the hitch is those people who are
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giving me storage spaces they are
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charging one rupees per pen per year
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again it's a robbery so now I need to
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make a compromise between these two how
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many times do I buy every time I buy how
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many do I buy I need to make a
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compromise on that I was in a dilemma I
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need to have the best economic return
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within this so I needed a solution where
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the total cost over the whole year is
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minimum
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and her idea when to order my next cloth
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and most importantly how many pens to
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order every locked
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I needed a solution for damped let's go
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into a technical solution this is my
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dilemma let's see what we can get out of
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it we have the classical yo Q situation
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out here the model a classical model for
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economic order quantity we shall
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developed a classical yo Q solution with
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a certain set of assumptions number one
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stock level delivery is instantaneous
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number two demands power consumption is
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known and constant number three lead
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time is known and constant number four
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inventory related costs are lone and
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constant number five low price discount
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on volume number six safety stock or
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buffer stock is not to be there with all
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these assumptions let me explain them
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one by one
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in a set of three the first one stock
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delivery is instantaneous
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number two demand for consumption is
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known and constant and number three lead
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time is known let's explain how is it to
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be done or x-axis will take time on a
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y-axis we take quantity
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it's a time now at time zero i order a
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lot it will deliver instantaneously one
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of our assumptions so I have the whole
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lot and that I define as Q this is going
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to be consumed over the next time next
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set of time which is that time it is
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consumed over that period of time T it
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is constantly consumed now on that
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particular date I get the next log
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delivered and it continues for a next
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cycle so we are having these cycles over
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and over again
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where T is
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10 Q is constant and the consumption is
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constant we have a lead time which is a
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time required for placing order of the
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next log when we will be getting
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delivery of the next log that is the
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lead time now how much quantity it gets
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reduced from that point Q till the lead
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point is the reorder level and this time
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we get a horizontal line there is the
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reorder level which is constant fine we
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call it R that is the average quantity
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which is stored at every point of time
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the max and the min divided by 2 we have
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the average level of quantity which is Q
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by 2 that is the average inventory level
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we call it a V the next set of
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assumptions inventory related cost
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unknown and constant no price discount
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on volume and there is no safety stock
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no baha stock how this is to be
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explained we have the inventory related
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cost as annual purchase cost which is d
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multiplied by C where B is the annual
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demand C is the average purchase cost
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per unit
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the next cost is in an ordering cost
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which is given by D divided by Q which
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gives the number of orders per year
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multiplied by ordering cost or the
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set-up cost which is given by s and a
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third one is a wholly cost where the
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amount held every amount held over to
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here is Q by 2 multiplied by the holding
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cost age so Q by 2 multiplied by H gives
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the third cost which is the annual holy
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cost let's combine all this 3 which
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gives us the annual total cost the
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addition of all those three annual
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purchase cost and we're ordering cost
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and annual hauling cost we get this tree
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combined together we get that total cost
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next we go to the next stage we need to
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find out
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where it is the minimum displayed on a
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graph it gives a flat line like a
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purchase cost because you don't have a
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discount over volume if that is the
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volume we don't have a discount no
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matter how many items we purchase we
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have the cost and a cost is flipped so
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the price per item is flat next we have
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the ordering cost which comes down if we
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order more items per order in a first
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case we have less items per order so
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number of orders every year will be high
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it gradually comes down and takes a
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flattened off the third one is the
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annual holding cost which is zero if we
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have dough holding and it goes
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proportionally up that's the holding
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cost combining these three we have the
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total cost which follows a curve and
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this one is the total display of all the
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costs we need to find out the minimum
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out there and a minimum is that point
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which is the minimum cost next we put it
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down and we hit upon a quantity which
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will mark it with a kuester that is the
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quantity which we need to find out how
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do I find out this is the graph let's go
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into something which is very basic for
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finding the total minimum cost we use
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some basic calculus where we take
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derivative of total cost with respect to
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Q remember Q is the item which we need
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to find out and the total cost is
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dependent on Q okay so what do I do
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so did i dt c of DQ the c calculus the
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first factor is doesn't have a cube so
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it becomes zero the second factor
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becomes minus DS divided by Q squared
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and the third factor becomes H by 2 we
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are of all these three and then we
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equate this to 0 because we need the
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bottomless position the minimum of the
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curve
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and simplifying what you we get a
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formula this is the formula we are
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looking for the Q which is under root of
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2 D s divided by H and this Q we tap it
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with a star we call it the economic
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order quantity we get the yoku out here
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the classical economic order quantity Q
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star is independent of purchase price if
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you notice carefully there is no C
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factor out here the cost of the item is
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not present out here has the reorder
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level simply as R equal to DL where D is
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the average daily demand and L is the
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lead time has the optimal interval
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between orders as T star is Q divided by
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D that's the interval in days and the
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number of orders per year and star is
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given by now if you remember my dilemma
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we are trying to find a solution for
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that now my dilemma was what is the
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amount which I have to purchase every
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time I purchase my D is 300 so Q star is
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square root of 2 into 300 into 20
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divided by 1 so which we get 109.5 for
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pins the nearest good number is 110 so
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that is my number which I need to order
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every time I place my order so every
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time I place my order I have to place
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order of 110 which will give me the
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least
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annual cost so with the purchase of
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every pending in rupees to my annual
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expense is going to be 879 3.19 that is
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going to burn my expense and my revenue
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I am selling it at rupees 5 so 300 into
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5 is 1500 which makes a cool profit of
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72% for me on my business
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not bad I guess how decision was good
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help for you in subsequent sessions we
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shall take up some morning miracles I
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had given you only one example of my own
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subsequently we will develop other
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models for Q system namely yo Q it price
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break
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remember those assumptions we'll try to
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break us assumptions one by one and then
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we will try to make it into a reality
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next we'll build up a model for yo q
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next we will have an inventory model
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with plan shorties and then continue for
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the pset where the predict review system
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will be given and then the hybrid system
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will be given we'll try to find out this
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in my subsequent sessions till then have
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a nice day thank you
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