 Hello. Myself Satish Thalange, Assistant Professor, Department of Civil Engineering, Walton Institute of Technology, Solop. In today's session, we are going to see regarding the decision making under uncertainty. At the end of the session, the student will be or the learner will be able to identify the alternative available by collecting the overall information and select the best alternative on the basis of the various principles and the criteria. Now, coming to the point, what is the decision making under uncertainty? Particularly, if the person or the decision maker don't know what exactly the outcome is going to be there, that is, the certainty of the particular state of nature, then the particular human is said to be making a decision under the uncertainty. And the commonly used criteria or the principles for the decision making under uncertainty are as follows. The vital criteria, laplace criteria, Hurgis criteria, and the savage principle or it's also known as the minimax-regret approach. In the earlier sessions, we have seen regarding the vital criteria, laplace criteria, as well as, you can say, now, continuing to that, today, we are going to see regarding the Hurgis criteria and the savage principle or the minimax-regret approach. Now, coming to the particular pay-off table. What is the pay-off table? It's a particular table which is known as the profit table also. Now, the pay-off, as I said, it is very, the pay-off table is very helpful for making a decision by using various principles or you can say the criteria. Now, in today's session, we are going to see one of the examples and we are going to make a decision or you can say, select the alternative by using the Hurgis criteria and the savage principle. Yeah, the person, Mr. Krishna, is having a particular plot and he is interested to have the decision regarding the making or you can say, constructing the luxurious or deluxe or ordinary rooms and he can provide the facility of the lodging and next, he can lease the particular land for the parking or any traditional fare or any function or the third option is that no plan at all. So, by observing all these options, now, we have to make a decision but for supporting into that presently he is paying 25,000 a tax per year. Now, this is a table which is representing you the various alternatives and the state of nature means it's there may be the high demand or normal demand or low demand and these are the outcomes or you can say the pay-offs for the respective alternative for the respective state of nature. With the help of this table and using the various principles or you can say criteria, we are going to make a decision. Now, coming to the Hurgis criteria, it's the principle based on the decision maker view may fall somewhere between the extreme presumim or the particular extreme optimism. In the present example, the alpha, they are defining that 0.6 and of course, the 1 minus alpha will be 0.4. As these are the alternatives, lodging, facility, rent out space and no plan to find out the particular solution by using Hurgis criteria. The first step is what to identify the maximum value from each alternative. This is a column which is representing the maximum value from each respective column. So, lodging facility, the maximum benefit we are getting for the high demand that is 5 lakh. This is a maximum value which we have written here. Same for the rent out space, the maximum value is 3 lakh which we have mentioned here and for the no plan, it's a minus 0.25. Similarly, we have to find out the minimum pay off is minus 0.5, for the rent out the minimum pay off is minus 0.30 and for the no plan, it's a minus 0.25. Now, expected pay off is equal to maximum multiplied by alpha plus minimum multiplied by 1 minus alpha. By using this formula, we are going to get the pay off or expected pay off for each alternative. So, here the maximum is 5 multiplied by 0.6 plus minus 0.5 multiplied by 0.4, we are getting value 2.8. Similarly, for the rent out space as well as no plan, the values we are getting 1.68 and minus 0.25. Out of these two, we are going to select the maximum pay off, it's 2.8 which is the alternative related to the lodging facility. So, lodging facility will be best option according to the Hurig's criteria. Now, one more criteria that is a savage principle. The savage principle is nothing else, it's also called as a regrid criteria or you can say mini max principle. Here, this is the principle in which the particular decision maker convert the profit table into the loss table or you can say regrid table. How to convert the particular table from profit to the regrid table? Let's see. The regrid table is obtained by following method. You have to select the maximum or the best from the state of nature column. Here, the high demand, normal demand and the low demand are the three state of nature. Out of this, the maximum, when we see this table, the maximum outcome is 5 for the first state of nature that is high demand, for the normal demand it's 1 and for the low demand it's a particular minus 0.5, difference between each respective alternative with the help of the best outcome from the respective state of nature. So, 5 minus 5 is 0 and 5 minus particular 3 is 2 and 5 minus minus 0.25 is 5.25. Similarly, for the normal demand, we can get the regrid outcomes or you can say loss payoffs of the particular alternative with respect to the state of nature. Here, as I said, the one is the maximum best outcome from the second state of nature that is the normal demand. So, 1 minus 1 is a 0, 1 minus 0.5 is 0.5 and 1 minus 0.25 is a 1.25. Similarly, for the last low demand, same methodology we have to use and we are getting value as 0 minus 0.25 on minus 0.25. Now, coming to the next step, after getting the loss table, this is the regrid table. Earlier, we have mentioned the profit or you can say the profit table. Now, we are converted into the regrid table or you can say loss table. These are the values or you can say outcomes of the loss for each alternative for a respective state of nature. Now, we have to carry the stock that is the mini max principle. Means what? We have to select the maximum regrid from each respective alternative. For the first alternative, the maximum regrid is 0. For the second rent out space, the maximum particular regrid is 2 and for the no plan, the maximum regrid is 5.25. After that, this is the values 0, 2 and 5.25 are the maximum regrid. Means, these are the maximum loss for respective alternatives. For the lodging, it is a zero loss. For the rent out space, it is a 2 lakh loss and for the no plan, it is a 5.25. So, by getting the maximum regrid, we are interested to select. And I ask you from this maximum loss that is 0, 2 and 5.2, which alternative you are going to select, we are going to select the minimum value which is having minimum loss that is a zero, which is related to the lodging facility. Similarly, now we are getting lodging facility will be the best option according to the savage principle also. In this way, by Hurgis criteria also we are getting the lodging facility as I declared earlier and similarly by the savage principle also, we are getting the lodging facility. Let's select the correct answer for the questions, hope so you have selected these represented correct answers, these are the references for the today's session. Thank you.