 Hello everybody, I am Mr. Keshav Valase from Mechanical Engineering Department, Valchian Institute of Technology, Solapur. In this video, we will be discussing about EOQ that is Economic Order Quantity, its simple model and what things are required for the derivation of the formulae. At the end of this session, students are expected to understand basic inventory related costs and economic order quantity and the minimum inventory cost related basics. Referring the same slide from earlier video wherein we discussed about why we need to maintain inventory or why we need to have inventory control. If we look to this graph here as the quantity increases on vertical axis we have inventory related cost and horizontal axis we have inventory quantity as the quantity increases this holding cost increases the straight line indicates holding cost or inventory carrying cost. End element of a cost this one is a setup cost or ordering cost as quantity increases this setup cost or ordering cost decreases. Now adding these two we get total cost. If you look to this total cost we are basically interested in this particular Lormust point wherein to the left of this cost increases as well as to the right of it cost increases. Hence to balance between holding cost and setup cost we need to maintain inventory or we need to have inventory control. To talk about different types of costs related to the estimation of EOQ that is though there are many types of costs we are talking about three cost elements which are required to derive the formula for economic order quantity. The first one here is holding cost or also called as carrying cost inventory carrying cost. This includes all the cost elements towards holding the inventory item in the stock. All of your expenditures or expenses towards stores, stores record maintaining inventory items salary of your watchman towards store your warehouse all such elements of cost are added together to get this holding cost. Now the unit for the holding cost is say suppose example here we mentioned C1 as the symbol for holding cost then unit of holding cost is rupees per unit item per unit time. This is specified for single item of inventory and for a unit time. Different industries express their holding cost proportions on annual consumption and holding basis and then coming back to second cost that is a shortage cost which is also called as stockout cost. This is related to a situation of having a demand but not having the item for consumption or utilization symbol for this is C2 and it includes all the elements towards not fulfilling the demand so wherever we have a demand but we cannot fulfill more or we have expenditure towards that. These cost elements will be included in this shortage cost. Its unit is again same as C1 rupees per unit item per unit time. Third cost element is ordering cost or setup cost. Normally while we have ordering type business that is if we purchase items from outside what we call as bought items like bearings and castings such things. Now for such bought out items normally we refer it as ordering cost and in case of manufacturing setups associated cost towards keeping machine setup ready we call them as setup cost. So for example in case of ordering the main element would be transportation cost and all expenditures towards giving purchase order, release of aid, reminders to your suppliers and whatever we have expenses they will be the part of this ordering cost element. Similarly in case of manufacturing to keep a machine ready for required manufacturing process that is for example suppose if we take CNC machines. In CNC machines we need to keep tooling ready for actual operation required so time spent on such toolings to be kept ready for machining would be a part of setup cost and such all items towards keeping things ready for machining they all included in setup cost. In all we use for this is say C3 and it is specified as rupees per order or per setup. Now here I would like you all to think up some industry and list down different cost items from that industry and possibly group them under these three types of costs. Then to next this graph gives you on vertical axis it is inventory cost and on horizontal axis we have inventory quantity we have discussed this earlier this line indicates holding cost this one ordering or setup cost both added together this curvature gives you total cost what we are adding here is this low most point we are interested in this particular low most point of the total cost curve. This point on horizontal axis if we project what are the quantity we get that quantity is economic order quantity and corresponding ordinate on this vertical axis represents minimum cost so from total cost curve even we can take a judgment here this point represents the minimum quantity the lowest quantity which is referred as economic order quantity in total cost curve and this particular point on the vertical axis represents the associated minimum inventory related cost. Now coming to a simple model of your Q a model in inventory comes up with certain set of assumptions now here a model we represent wherein on vertical axis we have got inventory quantity and on horizontal axis we have time. Suppose we operate with one particular cycle represented by this particular triangle from origin to this Q and down to T. Now this Q is our inventory quantity for this particular cycle and this T we refer as cycle time say for example if we take this quantity to be say 300 units and this time minute if we take one month of 30 days then this 300 quantity we are consuming over a period of 30 days wherein 300 by 30 that is Q divided by T is equal to R so this R the slanted line indicates our consumption rate which will be in this particular case if suppose Q we take 300 T we take 30 then R will indicate 10 units every day we are consuming. Now like this in a year we have suppose N cycle so N represents number of cycles like this one simple triangle like this N cycles in a year so for example if we have one month as a time period then in a year we can have 12 cycles so N will be 12. For this model we have different assumptions and as I said these assumptions will give us this particular model so R that is consumption rate is uniform there is a first assumption second one no shortages allowed that is from previous slide we have defined C2 as a shortage cost so C2 we assume to be 0. Next assumption is lead time is 0 or known exactly. Now lead time is the time between placing the order and getting the material lead time can be thought in different perspectives but here for our simplicity let us take that time between placing the order and getting the material and that is either known exactly or it is 0 and one more assumption we have here is we assume instantaneous replenishment that is at the end of this particular first cycle suppose while we reach to 0 the quantity reaches to 0 then for next cycle to begin we assume that this Q raises to Q this height the quantity in our hand will be raised to this particular level of a small Q so that is what is the assumption we call as instantaneous replenishment. Now further part of derivation we will talk in next video here I mentioned only two references of the books but we can have many more references for inventory control topic and EOQ derivation thank you.