 I am Satish Therange, Assistant Professor of Civil Engineering, Walsh and Institute of Technology, Solapur. In today's session, we are going to see regarding the decision-making under uncertainty. At the end of the session, the learner will be able to identify the alternatives available for the solving of the problem and gather all the information relevant to the alternative and select the best course of action based upon the principle of the decision-making under uncertainty. Now let's see what is the decision-making under uncertainty. If the decision-maker doesn't know with certainty which state of nature will occur, then the decision-maker is said to be making a decision under uncertainty for respective course of actions or alternatives. The commonly used criteria for the decision-making under uncertainty are Waddle's criteria in that the particular first approach is that is the optimistic approach, that is the maximax and the second one is the conservative approach, that is the maximin. And there are the following principles or you can say criteria like Laplace principle, Hurgis principle and Savage principle. In today's session, just we focus on the Waddle's criteria and the Laplace criteria or you can say principle. Now before that, let's see what is the payoff table. The payoff table is nothing else, it's a table which shows you the sets of the decision alternatives. When this particular alternatives are compared with or tried to get the outcome with respect to the state of nature, here the payoff table usually in the payoff table, the rows are representing usually. There may be a different representation also but generally or you can say usually there is a presentation of the payoff table in the following ways. The rows are representing the particular alternatives or course of action and the columns are representing the particular state of nature or you can say future events and this state of natures are mutually exclusive and the collectively excessive. And the entire table shows the outcomes. Here the table which is showing you the alternatives, as I said the rows are showing the alternatives and these are the state of nature, the state of nature 1 and 2 for the alternative one for this with considering with the state of nature 1, the following outcome 1 is there. So similarly for all the alternative for the other state of nature, the following outcome is there. These are the area which is showing you the outcome. Now this is an example. Let us see the example in which Mr. Krishnan is having the 50 feet by 80 feet commercial site in the Gandhinagar and presently he is planning to pay, presently he is paying the tax of Rs. 25,000 per year. And he has three options either he has to, he is going with the plan of lodging facility or secondly for the lease out or for the other third option is doing nothing, there is no plan. And these are the following table which is showing you the, it is a profit table or you can say profit pay off table with the following available alternatives and the state of nature. These alternatives are under the control of the decision maker. Either the decision maker can go with the alternative first that is the lodging facility or the rent out facility or the no plan. So keeping in mind for the respective state of nature either there will be the high demand or there will be a normal demand or the low demand. If we go with the first option that is lodging facility if there is high demand he is getting the profit of 5 lakhs. This all terms are in the, outcomes are in the lakhs and similarly there is a normal demand there is a profit of 1 lakh and if there is a loss or you can say low demand there is a loss of 0.5 that is a 50,000. Similarly for the other also here these are the outcomes. Now keeping in mind we have to use this particular table, pay off table for the decision making. Now by the Waddell's criteria in that first approach that is the optimistic approach. This approach or you can say criteria help us to make a decision in the optimistic direction. Here the decision maker is optimistic about the future that is maxi max implies that maximization of the maximum profit means he is under impression that there is a particular state of nature that is of high demand and for the high demand what will be the value is just he will see that is for the lodging facility he has a particular 5 lakh profit if there is a rent out he has getting 3 lakh profit if there is no plan there is a loss of 25,000. So according to the maxi max principle first of all it is the optimistic approach show there may be 100% he is considering that there is a high demand then select the maximum values from all these values and select the maximum from there. So out of this all these alternatives lodging facility rent out space and no plan the maximum values are 5 3 and minus 0.5 2 5 sorry and out of that the maximum is a 5 means this indication that you should go with the lodging facility. So second there is a conservative approach in this approach the particular decision maker is of prismatic about the future means he is considering that there may be the low demand then according to that the first for the first native when there is a low demand the value is minus 0.5 when if there is rent out there is a and for the low demand that is a prismatic then there is a loss of minus 0.30 that is of 30,000 and similarly if there is a no plan there is a loss of 25,000 out of that he is interested to select the minimum one. So coming to the point here he will select the minimum payoff that is a 0.25. So here the particular wireless criteria in that the conservative approach is making the maximum from the minimum payoff. So here the minimum means we are trying to benefit means we are trying to minimize the loss. So the maximum is out of this is 0.25 that is a particular highest when the negative that is why if you go with the no plan there will be a loss of only 25,000. This is regarding the wireless criteria that is a second approach that is a conservative approach. Now let's see what value we will get by the Laplace principle. If this principle is been used here it is based upon the absence of the knowledge about the probability of occurrence of the various state for the various state of nature. So here generally the decision maker go with the particularly average of all this particular outcomes for the respective course of action. So for the first lodging facility we have to go with for the average 5 plus 1 plus minus 0.5 divided by 3 we get this value that is 1.84 lakh. Similar for all the other three alternatives these are the following outcomes for the rent out space it is it is 3.5 and minus 0.30 so 3 plus 0.5 plus minus in the bracket minus 0.30 divided by 3 this is why as we are taking the average so we are getting 1.067 and for the no plan it is having the minus 0.25 plus minus 0.25 plus minus 0.25 we are getting the final answer divided by 3 that is a minus 0.25 out of these three the particular maximum value is 1.84 which is related to the lodging facility. So when we compare with all these criteria just see from the first approach it is defining that you go with the lodging facility because it is having the maximum value and when it is when we are observing with the second approach that is conservative that is presemitic means there is a loss then it says that you should go with the minimum loss that is of 25000 that is represented by minus 0.25 so that is related to the no plan means this approach is helping you to go with the no plan where you will have the minimum loss. Now by Laplace principle again it is a particular table which is helping you to make a decision based upon the maximization of the profit here but here as the particular decision maker would not have 100% knowledge or regarding the probability of occurrence of the state of nature he will go with the averaging of that and he is getting the payoff of 1.84 for the lodging and for the rent out it is getting 1.067 and for the no plan it is minus 0.25 so out of these two the maximum was 1.84 that is again by Laplace principle also it says that you should go with the lodging facility means out of these three principles or the criteria two of them are saying that go with the lodging facility where they will have the maximum profit and if we will go with the conservative approach or second approach of Waddell's criteria it says that you go with the no plan so with the help of this information we can make a decision. Now select the correct answers for the following questions hope so you have selected the answer as shown here these are the references for today's session thank you.