 I am Dr. Keshav Valase from Walton Institute of Technology, Solapur. In this session, we will briefly talk about the methodology in operations research. Talking about the learning outcomes of this particular session, at the end of this session, students will be able to understand what is the basic methodology of operations research, as well as briefly they will be able to understand the applications of this particular methodology of OR. These are the major steps in the methodology of OR. If you see different books, you'll find one or two steps here and there. But by and large, these five activities are in common. And some of the activities some authors may combine. So the very first step here is we need to formulate the problem. That is, we need to really define the problem, what exactly we are going to do about the given situation. So we have to take up a particular case, take up a particular situation from industry. And industry could be manufacturing or service type. Any organization OR has got its applications in all the fields. So which are the field you want. You select that domain, you select that particular area. And in that, you focus on a particular problem. You define the problem, what exactly you want to do. For example, maybe if you're considering a mobile manufacturing company, then you may think of how can you increase the profit of that mobile manufacturing company? How many models you can have and what profit margins from each model you can have? And selling of these models, how much profit you can get? And how can you maximize? Or it could be some cost-related things. So that particular problem you have to define, what exactly you want to do. Second is constructing a model. For a given situation, you can think of which model suits more. And the data available, the precision of the data available, the nature of data available, is it known exactly? What part of it is deterministic? That's known exactly or what depends on probability. So considering all these aspects of the data availability, you can then decide on a particular model and convert your real-life situation into that OR mathematical form that we call as constructing a OR model in mathematical relationship form. Now maybe if you take a case of, again, the profit maximization case we just discussed, then you can think of formulating objective function from profit-related data. And subsequently from resource-related data, from maybe raw material, or man-machine material, or the data from market survey, you can think of developing the relationships of these variables which basically restrict, which put the limitations. And in all with these relations, you can formulate what is called as LPP model. We'll see in detail in next video what it is. But this is how you can convert the real-life data into a mathematical form. So this conversion is called as construction of an OR model. Next is deriving the solution from the model. Now once you have a particular model, then there are standard ways of solving these mathematical problems. And solving those problems we have converted, we have to get the solution. And across the globe, for a particular model, mathematical model, solution will be unique. This is the perfect mathematical thing. So it's a perfect science. So you get the solution to the problem. And next stage is you have to test it, testing the model and the solution. How far that the solution we have got? How far it is feasible? How far it is realistic? How far it is implementable? Are there any problems in infrastructural changes or training to be given to the people concerned? What are the difficulties? Are the variables considered were defined properly? And while implementing in next stage, was it OK, the time dimensions and the reliability of the data collected from market research? See, whenever you have data collected from market research, in some cases, like forecasting techniques and all that if you are using, sometimes the reliability of the technique may be questioned. So with that, the results that you have come out with, the solution that you have derived, that you need to really test in your particular case, is it feasible, is it implementable? And then in last stage, you have to implement. So in implement, yes, you need to really think of what are the infrastructural changes you have proposed or maybe if you have proposed some buying of new machines, then is it feasible, the money investment? So many things are there. Are you required to provide a training? Suppose you are buying some CNC machines, then what operators or which engineers need to be trained on this? So these are all the things which you really need to take care of during implementation phase. At this point, I would expect you all people to think of some industrial environment, wherein you can think of applying this particular methodology. Just think like in a situation and in that situation, how can you apply this particular methodology of operations research? Let us take one small example so that you can understand how can it be applied in a given situation. So we'll consider a very common example of a two wheeler manufacturing company. And let us presume like there are three models only for the sake of some mathematical discussions, otherwise there could be more than three also. So two wheeler manufacturing company having three models of two wheelers. And now here the mathematics begins. We are denoting these models with the symbols X1, X2 and X3. Three vehicles, these three models, we are denoting by symbol X1, X2, X3. Next part will be objective function that is something that we want to achieve. What do we aim at? It could be either profit maximization type of a thing or it could be cost minimization type of aim or the objective we can have in these types of problems. Now here we may think of profit maximization, say for example, next is again the constraints. Mind the constraints, as I said, these are the basic limitations or the restrictions looking to the different resources available in running the business. And from those restrictions we have to again convert that data into mathematical form and then all together this objective function and the constraints all together will represent say a particular model. Now in this case, some mathematical relationships I have given here so that you can understand how we can really construct a model. Again same two-wheeler manufacturing company with three models X1, X2, X3 and objective function. How would you probably get this mathematical relationship? See here in this relationship what it is put up here is maximized Z is equal to three X1 plus five X2 plus seven X3. Say for example, this three with the X1 is the profit that we get per unit of X1 vehicle model. Then maybe it's 3,000 or 300 that is scaled down maybe. So it's three into X1 we can consider as a profit coming out from model X1 of the vehicle two-wheeler. Same X2 model is giving us five into X2 as the profit and similarly seven into X3 is the profit coming out from third model of the vehicle X3. While we add these all three together we get the total profit from all the models. So we let say denote it with Z as a symbol and as being a profit we aim at maximizing. So this maximized Z is equal to three X1 plus five X2 plus seven X3 becomes our objective function in mathematical form this conversion of real life data into mathematical form. Similarly here regarding constraints this first line four X1 plus three X2 plus X3 less than equal to 10 could be some raw material some constraint kind of a thing some resource constraint kind of thing maybe man hours, machine hours kind of thing wherein you cannot go beyond 10 units of this particular maybe raw material and this consumption is to the left side of this inequality and that total consumption has to be less than or equal to 10. Similarly this second constraint X1 plus X2 plus three X3 greater than equal to seven that may represent some other resource some other maybe material could be man hours, machine hours time aspects which normally we put up in man hours and machine hours. So any kind of such resources or maybe in money form also you can have it. So any space wise whatever. So these restrictions are put up in mathematical form. So that is what are the data we get from all the resources that we need to convert in mathematical form like this and that we call as the constraints. And the last line if you see here X1 X2 X3 greater than equal to zero there is a non negativity. This means if we do not manufacture anything in that case the vehicles produced will be zero they can never be negative. So mathematically that is indicated with this particular relationship and that is called as non negativity constraint that's also very important. So these are in all we have this conversion of real life situation into a mathematical form. This is a methodology we have discussed. And again these are the three books one by Taha, Sharma and Gupta. Otherwise as you know lots of books are available and resources are available on the net also. Thank you.