 Hello everybody, I am Dr. Keshav Valasi from Walchand Institute of Technology, Sohla. In this session, we will further discuss about how different inventory models are formed based on the set of variables assumed. At the end of this session, students will be able to understand basically what are the variables in defining any inventory model and types of deterministic inventory models. Their overall idea of four models, we are focusing only on deterministic inventory models. Now in earlier slide, we have discussed these points, we will just revise fast here. Any inventory model, basically we intend to determine quantity and time, that is cycle time. So, it is a policy decision for any industry, management or the authorities and they need to take this on controlled variables which like are represented mathematically or symbolically by Q and T as discussed in earlier session also and here we will talk about how the models come up based on the assumptions and these assumptions are nothing but consumption rate, how it is, lead time, production rate whether it is finite, infinite, zero, known, unknown. So, based on these assumptions, we get different inventory models. At this point, I would expect you people to think of quantity and cycle time relations for any industry particularly say for example, here we can consider machine tool manufacturing industry. Just to think of how the quantity and time requirements may be related for all inventory items for machine tool manufacturing industry. If you see the classification of inventory models, broadly I would classify them in these three groups. First is deterministic models, second probabilistic models and third models with the discounts. If you see different books and different authors, you may find different styles of defining these models but I would prefer to group these inventory models in these three groups as mentioned here that is deterministic models, probabilistic models and models with discounts. In deterministic models, the demand and some parameters in this there, you can determine them. They are not dependent on probability as it is in second case. Here some parameter to be determined like demand particularly is based on probability, probabilistic state is there. And in third case, some organizations they offer you discounts on bulk purchases. So, inventory models can be of these three types but here we are focusing particularly on deterministic models, we can find our discussions to deterministic inventory models only. Now, let us talk about different variables that we need to assume while defining any inventory model. Shortage cost, if we denote suppose with symbol C2, are shortages permitted or not permitted that is whether C2 is 0. If we do not permit shortages means C2 will be 0. If C2 is not 0 means inventory mathematically will be taking a negative quantity and how to deal with that we will talk in allied derivation. Different variable is production rate if we denote as symbol K, this production rate are we assuming it finite or infinite that is instantaneous replenishment or gradual replenishment instantaneous replenishment refers to K to be infinite whereas gradual replenishment refers to some finite rate of production is we are manufacturing the quantity items and then consuming. Next parameter is consumption rate are whether it is uniform or non uniform. Then lead time L if we denote it is 0 or it is known exactly what are we assuming then the first stock be it is 0 or known exactly like this there can be still many more variables. Thus what is the state of these types of variables we are assuming that defines your inventory model. So, I repeat here again any inventory model depends upon how we are assuming these types of variables in inventory control. Now coming to little concise discussions here as I have said we are focusing on deterministic models again to make it easy I would focus more on these two parameters that is shortage cost and production rate K. Major variation happens mathematically because of the assumptions we have for these two variables basic graphic representation and allied things the variation of any inventory model particularly again in deterministic type of model depends on how we are assuming these two parameters broadly. For example C2 this you can take as inventory models with and without shortage cost and this category would tell you inventory models with the K as a finite or infinite. These two variables with two decision making conditions under age would give us four combinations and the way we assume the different variables the set that we have assume for different variables will define our inventory model and its graphical representation also will change. Let us talk of the first model here C2 is 0 that is shortages are not permitted we are not considering shortages and secondly K that is production rate we are assuming infinite or instantaneous replenishment. This model representation is basically with the Q on a vertical axis that is quantity on vertical axis and time on horizontal axis with this set of assumptions this particular line which starts from this Q and moves down to this point 0 this R represents the consumption rate at what rate we are consuming this quantity Q. So, the simplest inventory model coming to second model here C2 is not 0 the moment we change the assumption graphic representation and allowed mathematical derivation part it changes. Here shortages permitted means negative quantity now this line is x axis anything above this line would represent positive quantity and anything below this line that is this one this indicates negative quantity that is a shortages we have a demand but we are not fulfilling the demand. So, this particular vertical line corresponds to the shortages. So, this model will be the EOQ model with the shortages permitted. So, here if you see the symbols Q represents the overall quantity that we order Z represents the physical holding of the stock above 0 there is a positive quantity and Q minus Z that is quantity ordered minus holding that represents the shortage that represents the shortage cost. Coming to third model here C2 is 0 and shortages are not permitted shortages not permitted means we do not have quantity below horizontal line and the main difference is K is finite. So, if you see here from point O along this line OA we are manufacturing certain quantity during time period T1 while we raise it to this capital Q this quantity raise to capital Q we stop the manufacturing and we consume it along this line. So, T1 is the time period of manufacturing as well as consumption and T2 is the time period of only consumption this is how we get model 3 wherein C2 is 0 and K is finite. This is the fourth model wherein C2 is not 0 means shortages are permitted and K is also finite. So, if we see here again T1 is the time period wherein along this we build the inventory as well as consume we manufacture and consume along this line from point A to B we consume the quantity from B to C we build the shortages we have demand, but we are not fulfilling. Then at C again we start the manufacture and C2D we manufacture the quantity, but we are just recovering the shortages sense we are not building the quantity to positive level. Thus there are the four models basically from deterministic inventory models and I recommend these two books on operations research by S.D. Sharma and Hiragopta. Thank you.