 Hello everybody, I am Dr. Kesha Wallase from Walton Institute of Technology, Sohlapur. In today's session, we will be talking about basic inventory models, how the inventory models are formed, basically pertaining to the variables in defining the model. At the end of this session, students will be able to understand the basics of inventory control, its variables in inventory control and more importantly, different variables which we need to consider while defining any inventory control model. Now, these things are discussed in earlier video, we will briefly revise it. What is inventory? Now inventory is basically the stock of goods required in manufacturing, the final product of any manufacturing industry. Here I repeat, we are not considering, these things are discussed in earlier video, I again repeat here, we are only considering inventory items which go into manufacturing the product and not the items like stationery, furniture etc. Then inventory control refers to optimizing the levels of all these inventory items so that the inventory related costs will be kept to a minimum level. Next is, there are basically three types of inventories, raw material, work in process and finished goods. Coming to the variables is a main part of our discussion today. All the variables related in inventory control are grouped in two areas or two groups, one is controlled or controllable variables, second is uncontrolled variables. Now controlled variables are like quantity and time, any inventory model cycle if we consider that basically constitutes of quantity on vertical axis and time on horizontal axis. Of course, there are additional parameters or variables also but basically quantity and time they define the inventory model and uncontrolled variables are like different inventory related costs such as holding cost or also called as inventory carrying cost, shortage cost or also called as stock out cost and set up cost or ordering cost. Next point is the demand, not demand in the market for any product is always unpredictable that you can never control and one more parameter is the lead time. Lead time is the time between placing the order for certain material and getting the material. So, now there are so many parameters which control the lead time hence it is very difficult to control these three categories of variables and hence they fall under uncontrolled variables that is inventory costs, demand for the items and the lead time. So, these are the major uncontrolled variables in inventory control. At this point of time I expect the viewers to list down different activities for automobile industry but particularly pertaining to different types of inventory costs. For example like watchman salary and allied types of activities and under which cost type they come that is what I want you people to think for a while. Now coming to the main area of our today's discussions that is how inventory models are formed. As we have discussed controlled variables they become the strategic decision making part of any industry and they are determined, they are derived from a set of assumption of certain variables uncontrolled variables and other parameters like production rate. Now whatever you assume like for example shortage is permitted not permitted or what is a consumption rate or which is production rate what do you assume are they zero are they infinite are they permitted not permitted. So, based on the set of assumption of such variables we get the model as a set of assumptions changes the model will be changing thus symbolically if we discuss q if we represent as the quantity inventory quantity and t as a cycle time then this q and t are the major variables of interest in defining any inventory model and other variables that we need to assume may include variables such as consumption rate r or it can also be called as annual demand then lead time l production rate k whether this production rate is finite or infinite like this we have a set of many more variables to be assumed here and assumption of such a set of different variables will give us a particular inventory control model as the set of assumptions changes the variables how we assume they changes then the inventory model definitely will be different. Let us discuss brief procedure a common standard procedure for derivation of economic order quantity just to make the process easy to remember very first is we calculate holding cost now this holding cost is calculated on annual basis wherein we consider the unit holding cost this unit holding cost normally is specified as rupees per unit item per unit time hence we multiply this unit cost by number of quantity items or units that we are holding in the stock and again it is multiplied by cycle time. So, while we multiply this unit holding cost by quantity items we are holding in stock and the cycle time we get the holding cost for a cycle and if that is multiplied again by number of cycles in a year all together we get this as the annual holding cost. Now, coming to shortage cost this also moves exactly on same line like holding cost what changes here is here we consider unit shortage cost and unit for this the specified measurement unit is again rupees per unit item of shortages and per unit time. So, in upper case we consider holding quantity here we are considering shortage quantity. Hence, unit shortage cost we multiply by number of shortage units shortage quantity and cycle time. So, this will give per cycle shortage cost multiply by number of cycles will give us the annual shortage cost thirdly set up cost normally it is specified as rupees per set up per cycle per order. Now, that we multiply simply by number of cycles we get set up cost for the year thus all these three cost elements that we have calculated we have determined here if we add them all together if we sum it up here that gives us the total inventory cost. Coming to further steps cost equation that we got as discussed in earlier slide that is a function of parameter q that is quantity it is a function of still many more parameters. But, now as we intend to know q we can partially differentiate that cost equation with respect to q for cost to be minimum I repeat the total cost to be minimum that cost equation we need to partially differentiate with respect to q and equate it to 0. While we simplify this and get ultimately what is q is equal to small q is equal to then that relation what we get is nothing but economic order quantity. So, this how we get the total cost equation we differentiate that with respect to q and solving it for q we get economic order quantity. This economic order quantity if we put back into the cost equation then that cost what we get will be the minimum inventory cost associated with economic order quantity. Now, in this graph we will see how it is graphically represented here this graph represents inventory cost on vertical axis and quantity items inventory items on horizontal axis. Now, as the quantity increases holding cost increases that is indicated by this particular straight line. Similarly, as the quantity increases this setup cost curve this particular line this setup cost decreases. Now, as quantity increases one cost increases other cost decreases if we see this particular summation then to the left of this point cost increases and again to the right of this point again the cost increases. Hence, we have our interest in determining this particular point which represents E O Q that is economic order quantity on horizontal axis and associated minimum cost is represented on vertical axis. Thus, this reason of optimizing inventory quantity and minimizing associated inventory cost and that is a reason why we need to maintain inventory look into inventory control. Thus, I recommend these two points two books one is by S. D. Sharma and second by Hira Gupta. Thank you.