ORM | OPERATIONS MANAGEMENT | UNIT-5 FULL PROBLEMATIC EXPLANATION | SEM-2 | MBA @shivanipallela⁩

[00:00:01]Hello everyone, welcome back to our channel. So in this video, let's cover Operation Research Unit Number Five, Game Theory as well as Simulation.

[00:00:11]Especially, Game Theory is very important. Okay, so from Game Theory, we will have a compulsory problematic question in the question paper, that will be from the last unit. So how do you ask questions in game theory?

[00:00:26]How many methods are there and what should you do? I will tell you everything in this video.

[00:00:30]Without skipping the video, you will understand this unit only if you do it with a book, pen, calculator and everything else. It is not just this unit, but any unit, it is understood only if you do it in operations research. If you simply listen to it, it will not make sense at all. So, until you say it, it's my responsibility, but practicing the thing is your responsibility. So, there are two, game theory and queuing theory, which also include simulation, so it's like a total of three topics. So see what I said here.

[00:01:02]What I already said in the Important Questions video is to learn the problem from game theory.

[00:01:08]Learn problematics from simulation as well.

[00:01:12]Learn the theory part from the queuing theory. Don't be problematic, don't ask.

[00:01:15]Most of the time he doesn't ask. Only game theory is 99.9% 100% the same. And since there is no simulation, I will also say simulation. Work is getting done. So the first thing is, in simple terms of game theory, we need to find the saddle point. Okay, the saddle point is always equal, which means that when there is a cadastral point on the x axis, there must be another side, which we understand when we do the problem.

[00:01:46]If the saddle points are not equal, we use a mixed strategy. In mixed strategy, we have three methods in total: Algebraic method, Graphical method, Simplex method. How to use the algebraic method and when to use it. That is, the algebraic method should be used only if there are two rows and two columns. Okay, using any one of these three methods is enough. How to use it: There are conditions. In algebra, there must be at least two rows and rows of columns. Graphical methods can be used to answer questions such as how many rows there should be, how many columns there should be, how many columns there should be, or how many rows there should be, but not how many columns there should be.

[00:02:34]We use the graphical method in questions such as how many rows there should be, but not how many columns there should be. No, it doesn't matter how many rows or columns there are. If you want, we can use the simplex method.

[00:02:59]You might ask, "What is the best way to learn one method rather than learning these three methods?" That method is the algebraic method, but doesn't it give two rows and two columns in every question?" So, what should we do when we don't have two rows and two columns in each row?

[00:03:08]Now, if you look at the graphical method and the simplex method, you won't understand that it is very difficult. So let 's use the algebraic method. Let 's use the algebraic method, that is, 2 rows, so the question doesn't always give two columns, so we have to convert it to two rows, two columns. How do we convert? We convert using the dominance rule. It can be called dominance rule or dominance theory. So with this dominance theory, we can convert two rows into two columns. How many rows does he give, how many columns does he not give, how many rows does he give, how many columns does he give, we convert it to two rows using dominance theory, so when they are given either two rows or two columns in a question, then we use graphical method. If he is okay in the question, if he is given two rows or two columns in the question and the saddle point is not equal, what do we do? We do something like this. But what I'm saying is that if a woman gives two roses or two columns, then the saddle point is not equal. What should we do? We should use the graphical method. For example, here we see that she gave three roses. She gave three columns. She gave two roses. There is no saddle point. If there is no saddle point, what should we do?

[00:04:46]Algebraic method.

[00:04:48]Apply the dominance rule. We tried not to do the algebraic method, but don't do that. Because there are two roses, the graphical method must be used. After using the graphical method, you should use the algebraic method. If you still don't get the saddle point, then you will understand if all this is problematic for you.

[00:05:04]So now let's take the problematic question. Okay, so I'll take a simple question to make you understand.

[00:05:10]So what is that question?

[00:05:15]He gives it like this. Question: In y1 x2 x3 y1, he says 2 6 -1 x2 8 9 12 7 13 6. He says, "Find out the game theory." He says, " Find out the game theory." This is the question. The question is asked like this. Now the first thing we need to do is check the saddle point. We need to check whether the saddle points are equal or not. If they are equal, there is no need to use the algebraic method, the graphical method, or dominance. Let's first look at how to find the saddle point in a row. First of all, we need to take care of the minimum. Okay, so this row is the minimum of these rows -1 This 2 6 -1 What is the minimum value of the least value in this 8 9 12 8 Here is 6 Do you understand that the minimum of the rows should be taken Here the maximum in time should be taken Here we are taking the minimum What should we take here Take the maximum Here is the time This is the maximum in time What is the maximum in time 8 Is there a maximum in time 13 Is there a maximum in time 12 Got it Now here is the minimum here What is the maximum number of these moods What is the highest number 8 Because here we have taken the minimum So here we have to take the maximum Here when we take the maximum What should we take here The minimum So what is the minimum What is the least number 8 13 12 8 So here is eight Here is eight So what happened to the saddle point When the saddle point is equal, do we need to do all this or not Simply we are game theory How to find out Value of game Value of game equals 8 We got 8 so how much should the value be 8 The strategy of the strategy of X player X player means here is this here is the plaintiff's horse here is here means A2 is here means here is the first second second second horse is in second A2 The strategy of Y player how much 8 is here means in the first first period so first 2nd saddle point means how many saddle points then 2nd means there is one in the second row there is one in the first period so the saddle point equals 2nd simple will you give 8 marks for this means the thing is that we in the long question he never gives saddle point means the means are not equal we here saddle point is equal so it seems so easy.

[00:08:49]I will now tell you what to do if the saddle point is not equal.

[00:08:52]First, what should we do if the saddle point is not equal?

[00:08:58]Which method should we use? Then let's do the graphical method. Okay. Now another question without saddle point.

[00:09:09]Game theory. Game without saddle point. Let's see how to do it if such a saddle point is not equal. First, he gave a question. In the question, he gave b1b2 a1 a2. B1.

[00:09:32]L 12. -8. Here is -6. 4.

[00:09:38]First, what should we do? We should take the minimum.

[00:09:41]How much is the minimum? Here is -8. -6. What is the maximum of these two? Everyone says minus. They say -8. Oh, maximum means -6.

[00:09:51]Then okay. What is the maximum of these two minuses? Don't say 8.

[00:10:00]Because there is a minus symbol. So, okay. Same here. Take the maximum.

[00:10:06]How much is the maximum? Here is 12. Four. The minimum of these two is 4. So, are these two matching? They are not matching. Where is the saddle point not equal to? The saddle point is not equal to. There is no saddle point. So what should we do? We should use a mixed strategy.

[00:10:27]How many methods do we have in mixed strategy? There are algebraic, simplex, and graphical. Okay, so what we're saying here is that we can use a graphical method.

[00:10:41]Before that, I will tell you how to use the algebraic method because only when you get the algebraic method, it will be easier to understand after you do the graphical method again. Now let's do the algebraic method as a mixed strategy.

[00:10:56]That's all we are learning how to do in algebraic method, that is, the first and foremost thing is to do algebraic method, there are two rows and two columns, so here there are two columns and two rows, so we are using algebraic method, so what should we do? This is the first one, which means the first value here, let's call it a1, let's call it a12, let's call it a22, which means the second row, second one, this is a2, this is the 2nd first period, first row, first row, second period, second row, first period, second row, second period. Do you understand that we have a1, a12, a21, a22, we have to make it fixed like this, now the formula is there, first let's do it for x1, okay, what is the formula for x1, that is, a22 - a21 divided by, okay, a22 -a21, wide by a1, up, a22 in the bracket a1+a2 minus a12pa1 This formula you should remember a2 now we need to substitute it just we need to substitute it that's it a2 means how much 4 so 4 a21 means how much -6 in the bracket -6 divided by a1 how much 12 a2 how much 4 minus a12 how much -8 plus that a21 -6 so here here is a plus here before here plus e - minus five so we are subtracting minus 6. Actually, there is a plus here, we put a plus. a21 how much is -6 soap e - right so that's why it means -6 now just substitute here is minus here is minus so minus minus getting solved okay then what happens minus e becomes minus plus so 4+6 is five next 12+ 4 how much is 16 - here is minus here is minus minus what is minus minus -8 -6 total -14 we have substituted like this so 4+6 how much is 10 divided by again here 16 -4 so here is minus here is minus minus e minus plus so 16+4 how much is sorry 16+4 14 so 10/ 16+ 14 how much is 30 so 10/ 30 we have to do.

[00:14:10]So if we do 10th/ 30, it is 0.33, it is 0.33, now how much x1 we got, sorry, how much A1 we got, we got 0.33, we need to find A2, what is the formula for A2? 1 - x1 1 How much x1 we got 0.33, so if we subtract 1 number 0.33, it is 0.67, we got it. So now we got A1 value, we got A2 value, we got A1 value, we got A1 value, we got 0.33, A2 means A2 is 0.67, remember, do the same, and do the same, now what is the formula for y1?

[00:15:03]a22 - a21 divided by ok a1 plus a22 minus a12 ok caps a 2, so sorry, the formula is the same, here a12 is the same, ok ok a2 - a12 a11 plus how much is the same, just substitute the formula for a12 here. So how much a2 do we get? 4 a12 how much 12 okay sorry not 12 8 12 not 8 8 so -8 4 - in the bracket -8 now how much a1th1 will be very confusing you should keep in mind.

[00:16:04]So 12+ 4 - a12 a12 how much 12 simply substitute the formula -8+ 21 is -6 so -6 is five soap eps minus so -8 -6 so minus e minus plus so 4+8 is five so here is 16 16 is minus here is minus here so minus e minus plus so plus 14 so 8+ 4= 12 30 so if 12th/ 30 is 0.4 now to find y2 1-th1 so if 1-0.4 is y2 how much is 1-0.4 if 4 is 0.6 just we are substituting in a formula and converting so that's why I am doing it fast because the video length will be more so if you substitute in the formula y1 is 0.4 then y2 is 0.6 is true.

[00:17:21]Same thing, now we have to check the saddle point again. Sorry, saddle point is found in algebraic method like this x1 x2th1th2.

[00:17:33]That's it. The optimum strategy is the optimum strategy of a. How much x1 x1 is 0.33, x2 is 0.67. Same as B, the Emo came up with 0.4 Emo y1 0.6 6 Emo y2 So we have to convert like this That's it After converting like this, what else should we do? To do something else, you also have to use the B formula.

[00:18:13]How do we use the B formula, that is, v = B = a1 a22 - a12 a21 divided by a1 + a22 - a12 + a21 This is the formula. Substitute this formula into the formula. Simply, how much is a1th1? We have 12 12 How much is a2? 4 So 12* 4 minus a12 is -8 This is -6 How much is a11? 12p a2t 4 Here, minus a12 is -8 -6 So 12* 4 is how much is 12* 4? If we do 12* 4, we get 48 48 - * Minus plus, so 8* 6 is how much 48 48 - 48/ 12+ 4 How much is 16 -p Okay so 8+ 6 How much is 14 14 What is 8 14 So the phone suddenly stopped. So I explained the whole thing without looking. So, what's wrong? Just substitute it into the formula.

[00:20:06]Substitute into the formula and you get 48 - 48 0 16 - 4 14 2 So if you do 0/2, it is zero, so v = 0. Okay, so let 's use the algebraic method and find out what game theory is. Next, let's find out dominance theory. Okay, now let's make it simple and clear.

[00:20:33]Listen, in these three methods, we are learning the algebraic method.

[00:20:38]So, no matter what kind of question comes up, there are rules in the algebraic method. There should be only two rows and two columns. It doesn't work even if there are three rows and two columns. So, if you want to do all the row deductions, the best option is dominance theory. So, you should find the saddle point of game theories, learn dominance theory, and then learn algebraic theory. It's enough to learn the method. The graphical method will also come easily. You don't need any graphical method.

[00:21:10]It's just a one-minute problem. But now I'll tell you how to do dominance theory. Here he is writing a question for player A.

[00:21:19]You can also do it with me. Here player B is okay. So player A is one and two. Four. Four. He gave four columns. That is, how many columns and how many rows can you give? No problem. So here, here, 3240 34, that is, 34, 4240 0408. He gave you a question like this. You can find it using dominance theory. Or you can ask a direct question and find it using game theory.

[00:22:07]First, what should we do? We should check the saddle point.

[00:22:12]How do we check the saddle point? 3. 240 3434 4240408.

[00:22:23]First, we should take the minimum of these four. How much is the minimum of the minimum of the minimum of the zero?

[00:22:30]How much is the minimum of the 3? There is 3. Any 3 is the common. 4. 2 is zero. So, zero again.

[00:22:37]Here, zero is what? We think the maximum is 3 saddle points, so if I do it fast, we should take the maximum here from now on. In this period, the maximum is 4, the maximum is 4, the minimum is 8, so will a saddle point be equal? ​​No saddle point, a saddle point is not equal. So if we want to use the algebraic method, we need two rows and two columns, but here we have four rows and four columns.

[00:23:08]How do we do it? How do we do it from two rows to two columns? That is, dominance theory. How do we learn dominance theory? Write the same question again 3 2 4 0 3 43 4 2 4 0 408 After writing the question like this, we need to do the first row deduction of R1, then we need to do the period deduction.

[00:23:37]First, we need to do the dominance row deduction, period deduction, first row deduction. So, ROS means these, right? RO1 RO2 RO3 RO4 means R1 R2 R3 R4, first row deduction. Row deduction means comparing the first row with all the others. Here I will simply give you a rough work: compare R1 with R2. R1 should be compared with R3. R1 should also be compared with R4. First let's look at R1 R2, that is, the row is 3, the row is 3, the row is equal, the row is equal, so the row is equal, the row is R1 R3, the row is R1, the row is 3, the row is R3, the row is 4. Which of the two is the highest? Where is the fourth highest? Located in R3. Which one is the least? R1 is there, so R1 is the lowest in R3, so one should be added. If we compare the numbers here, the highest is 4, where is it in R3? How much is R1? There is 3, the lowest is one, the same is R1, R4, there is zero, yes, there is 3, zero, zero, or the lowest is zero, where is there four, so R4 should be added. Next, look at the second one. Where is the list?

[00:25:06]So here, one is equal to 2. So, equal to 2. One is not equal to 1. So, one is not equal to 1. If you do n't understand, repeat it again. You will understand. Where is the list? 4. There is 3. What does 3 mean? Let's put one here. 4. There is equal to 1. Zero is equal to 1. Zero is equal to 1. So, equal to 1.

[00:25:35]Next, the last one is zero. Where is the 1.

[00:25:46]So, put 1. So, we are adding the list. The list is 2.

[00:25:52]Sorry, zero is zero. Zero is equal to 1. We are also putting equal here.

[00:25:57]Zero is 8. Where is less? R1 is less? So, R1 is not equal here. Do you understand? So now after putting R1 or 2 or 1 times, there is a time, okay here is the last one, there is the last one, there is the last one, there is the last one, there is the last one, there is the maximum, where are they, that is, here is here, here is here, that is, row one or two times are repeated, so row deduction is done, row deduction means nothing but we are deducting this row, we are canceling it, now what is left, these are left, row deduction is done, right? Now time deduction means the same, now this row is canceled, so we have to add the remaining, that is, what are the remaining 3 4 3f, next next 4240, next 0408, now let's do the time deduction.

[00:27:08]We call this C1. Okay, we'll deduct a period, we'll think C2, we'll think C3, we'll think C4. So compare C1 with C2, compare C1 with C3, compare C1 with C4. So, what is the time like this?

[00:27:25]Sorry, what is the time like this?

[00:27:28]Let's see if c1 has 3, c2 has 4, where is the highest, where is the highest, where is c2, that is, where is the highest, we should put one there. Earlier, in row deduction, we put the least there, but in time deduction, we should put the highest there. Now, if we compare c1 with c3, it is equal. If we compare C1 with C4, we are putting C4 here because it has a larger pitcher. Do you understand? Same as 4 is 2 is the highest 7 is c1 is 4 is 4 is equal to 4 is zero is the highest where is c1 is so we are putting here zero is 4 is where is the highest c2 is the highest zero is zero is equal to zero is 8 is where is the highest four is the highest now look where are the highest repeated c2 is two c4 is also two that means here we can cancel c2 also means second period can be cancelled fourth period can be cancelled no problem here I want to cancel second period okay my choice that means c2 also can be cancelled c4 also means two are equal so whichever number we get we can cancel that number now what are we left with 334 4400 008 now period So, once again, we have to compare R1 with R2 and R3 with R1/R2.

[00:29:06]So now if we compare R1 with R2, where is the least? R1 is the least, that's why we put one in the list.

[00:29:15]Let's put the pitcher with the least one, shall we? Where is the least in R1 R3? The least is in R3. That's why we're wearing it here. Again R2 sorry R1 R2 34 is the lowest where is it 3 is it means R1 is the pitcher again where is it R3 is the pitcher where is it in R2 is the lowest in R2 so we are putting it here again this will put R1 color like this like this after putting it where we have the highest R1 is the lowest two R3 is the pitcher two [clearing throat] means you can cancel R3. The row is the same, you can cancel that third row, no problem. Now I'm canceling the third row.

[00:30:07]How many are left now? 34 44 40. Now it's time again because we got two rows but there are only three columns.

[00:30:16]Now suppose we cut one period. That's enough. So this is C1, this is C2, this is C3, C1 should be done with C2, and C1 with C3. So c1 means period one is equal to period two. Okay, period one is equal to period two.

[00:30:35]Malala is the highest in period 3, so c3 is the highest, so we are putting a pitcher in c3.

[00:30:41]Malala is the highest here. We are also cutting the time like this.

[00:30:48]What happened here is c1 is the pot, c3 is the pot. Okay, so in this, whatever time you have, whatever pot you have, c3 is the pot. That means now you have your choice, that is, you can cut c1st time one or you can cut it even if it is the third time.

[00:31:08]You can delete a period in both of them according to your opinion because there is one here, there is one here, that is, C1 C3, you can cut the period if you like. I am cutting the period C1, what will happen if I cut it? Now it is 3/40. Sotoo Rose Two Columns have arrived. Now look at the saddle point.

[00:31:30]How do we see the saddle point? First minimum, minimum, 3, zero. Okay, here is the maximum, 3, maximum, how much is 4?

[00:31:42]Here too, four is obtained. The point is not equal. Now use the algebraic method. What is the algebraic method? 2, this means that there should be rows of columns. There are rows of columns. So 3, 4, 0, this Got it, what else is better? According to my suggestion, it is enough if you learn dominance theory and learn algebraic method. Got it and the last thing is graphical method.

[00:32:32]When do we use this graphical method? When he gives the question, whether it is two rows or two columns, when he gives two rows or two columns, we use graphical method.

[00:32:46]For example, I will give one example. He gave two columns.

[00:32:55]The number of rows given is not a saddle point.

[00:32:59]Then what do we do?

[00:33:01]Before dominance theory, we should do graphical method. Okay.

[00:33:05]Even after doing graphical method, if there is no saddle point, we should do algebraic method. So, let's do it now. How to do this graphical method? I have already written the answer for you and I will show you how to practice it here.

[00:33:19]In the graphical method, how did he give the question, look here, he gave the rose, he gave the four columns, we looked at the saddle point, the first minimum is minus one, there is one here, there is saddle point not equal, then what do we have to do, we should do the first graphical method, do not do the dominance rule algebraic method, do the graphical method because if you give two roses, you should also do the first graphical method, so on the graph paper, half side is a line, half side is a line, p1 +2 +3 +4, put the numbers there according to the highest values, here y is called, minus s is also here, plus here, minus here, after putting it like this, what is the first, 1st is 1 +2, 1 means here, p2 means here, so here, draw a line here, again 4th is 4 means here, plus s means here, here 4th -2p4 -2 means herep4 means here this line comes here like this next -3 -5 -3p5 Here all of them are pointed out and what do you call it? Draw the lines with the scale.

[00:34:42]After drawing the lines with the scale, now wherever the points intersect you will see the two lines intersecting like this. Draw a point out where it intersects here and here it intersects too. What intersected what intersected so look here this intersected point this is 4, 1 4, 1 intersected.

[00:35:12]Next, when we look at this line, we see that 1 and 2 also intersect here.

[00:35:21]So you understand, these two points intersect. These two points intersect, right? So if we say 1,2 4, 1, how should we write it? 1 4 2 1. If we write 1 4 2 1 like this, we get points. Now look at the saddle point. We need to look at the minimum.

[00:35:41]Here is the maximum. Here is the maximum. We need to look at the minimum. Here is the saddle point.

[00:35:53]Now we need to use the algebraic method. Do you understand that there is no graph? The points given by him are okay.

[00:36:04]Point out the points given by him on the graph and see where they intersect. Which two points intersect? These two points intersect. So we took these two values. We have 1/1 of these two values. So, if algebra says that the saddle point is equal here, the answer will be here. If the saddle point is not equal here, then the algebraic method should be used. Got it, so this is in the fifth unit, so let me tell you once again quickly. In the fifth unit, you should look at game theory, especially in game theory, look at algebraic method, look at saddle point, look at dominance theory, look at graphical method.

[00:36:48]After watching these four, what is simulation? I said, there is no simulation. Just watch the simulation.

[00:36:58]He gave the inter-arrival time.

[00:37:02]In the first four-six question, he gave the probability.

[00:37:05]Okay, he also gave random numbers. Just let us take cumulative probability.

[00:37:09]What does cumulative mean? First, put the first.

[00:37:11]0.20+0.25 0.45 0.45+0.35 0.80 0.80+0.10.90 90. Do the cumulative like this. Do you understand?

[00:37:24]After doing the cumulative, here is 20. There is 19 before 20, so 0 to 19 before 45, 44 before 45, 20 to 44 again, 44 after 45, 80 before 79, 45 to 79, 80 to 89, 90 to 97, okay, here is 98, so from 97 to 98, here is 99, okay, let's do this, whatever random numbers he gives me, whatever he gives in this random numbers question, put them here, after putting them, check the inter-arrival time, now the first thing is 12. Where is this 12 in this random number? Here is the number 0. Out of 19, 12 is the number. Where is this? What is the arrival time?

[00:38:16]That's why we put it here.

[00:38:18]What is here? 81 is here. 81 is yellow. Here is the number.

[00:38:22]What is its arrival time? 3 is there. Sorry, 81 is here. What is its arrival time?

[00:38:30]4 is there? That's why here are 36. 36th card is the number. 82th card is the number. 21st card is the number.

[00:38:37]74th card is the number. So, look at the arrival times and put the interval arrival time. If you add the total, you get 16. After converting like this, we need to substitute it into the formula. How do we do it?

[00:38:49]One hour divided by inter-arrival time. How many minutes is one hour? 16 minutes. How much inter-arrival time did we get?

[00:38:56]16 came. So 16th/ 16 how much is 3.75 75 Got it So that 3.75 75 Simulation Especially in case studies there is a chance of asking such things so learn it long but it won't come. If it comes then you are lucky because that is the problem.

[00:39:18]First after we put the cumulative, we put random numbers and find the arrival time and substitute it into the formula. That's it, this is the simulation. So in the fifth unit, we learned game theory simulation, we learned graphical method, we learned dominance theory, we learned all of that.

[00:39:36]Got it So now what is your task i.e. how is it asked in game theory by looking at the previous year question papers and what kind of questions are asked and how to do the problematic. If you watch this video and practice my questions and practice the problematic, it will be as simple as it is. Is this chapter okay? So this is all about the video. I hope that you have got clarity. If you have any other doubts, then comment in the comment section and let me know whether my explanation is understandable or not. That is, tell me whether you understand what I am saying or not.

[00:40:08]Because I am explaining in the video, tell me whether I am explaining fast or slow.

[00:40:15]So I will improve that. Now if I explain fast, you may not understand. If you tell me, I will try to say it a little slower from the next video. Okay, so this is all about the video. If you like this video, then like, share, comment and subscribe to our channel and share with all your friends and groups. Okay, so I want our channel to reach 50k subscribers. All the very best for your examination and yes, the preparation is good. See you all in the next video. Boy, boy, everyone.