 Lange, Assistant Professor, Department of Civil Engineering, Walsh & Institute of Technology, Sulappu. In today's session, we are going to see regarding the decision-making under-risk. At the end of the session, the particular learner will be identified the alternatives available and gather all the information related to the alternatives and select the best course of action based upon the application of the principles or, you can say, criteria of the decision-making under-risk. Now, let us see what is the decision-making under-risk. A decision-making under-risk is nothing else. Here, the decision-maker has the additional information about the occurrence of the state of nature and he has collected the past data or he has the contents regarding the information related to the particular course of actions for the respective state of nature. And your decision-maker knows either the direct available probability of occurrence of the different state of nature or the frequency data for the different state of nature, which is helping us to convert the particular frequency data into the probability and use for the particular criteria for the decision-making and either he will subject it to the probability on the basis of the experience. Here, coming to the next point, the criteria for the decision-making under-risk. There are following two criteria which have been shown in this particular slide that is expected monetary value criteria and second is expected opportunity loss. Here, the first is nothing else. It is the criteria which is helping to make a decision for the particular payoff table that is of a profit payoff table. Here, it is helped to find out the particular expected monetary value by multiplying the payoff values for the each course of action one at a time with the probability of the corresponding state of nature. And finally, with help of that, we are going to select the maximum expected monetary value for the each out of the each course of action and expected opportunity loss principle you can say or citations you can say or criteria. The first you have to obtain the regret or the loss table with the help of the profit table or you can say profit payoff table for the each state of nature with the respective course of actions. And after finding the regret table or obtaining the regret table or loss table, you have to find out the particular expected opportunity loss value for the each course of action by multiplying the payoff with respect to each course of action one at a time with the probability of the corresponding state of nature. Once we come to know the expected opportunity loss values for the each course of action with respect to the state of natures, we try to select the minimum expected opportunity loss value and we define the particular course of action as a particular useful for the decision maker. Let us see with the example. The vendor here there is an example that the vendor buys the newspaper and he sells in the market. According to his he has he purchased the particular newspaper for 3 rupees and sell it for the 4 rupees per piece and if the particular paper unsold then he has to sell that particular paper for the particular as a scrap. Designing informations are available regarding the past 200 days and the below shows the frequency table representing the demand of the newspaper over past 200 days. Here this is a table which is showing you the number of newspaper demand 204, 206, 208 these are the demands and these demands are for how many days? There is a 40 days in where there is demand of 200 papers. There is 100 days where there is a demand of 240 and there is a particular 40 days again there is a demand of 206 and here there is a 20 days where there is a demand of 208 papers. And the probability for each newspaper demand is shown as in table. Now let us make a decision using the above criteria. Now the first a solution of the example by expected monetary value. This is an area which is showing you the information regarding the cost of the newspaper selling price of a newspaper that is 4 rupees means he is purchasing at 3 and selling at 4 rupees and the profit gain will be 1 rupee that is 4 minus 3. And if it is not been sold so it goes for the scrap and pays rupees of 0.5 as a regret value. So, the loss of the vendor on the unsold paper that is a per paper is 2 rupees 50 paisa. Now with the help of this all information we have to go for the construction of the pay off table. Here this is a particular course of action a1, a2, a3 and a4 means he may go for the course of action or the purchasing of 200 papers or 204, 206 and 208 and this state of nature is not under control of the particular person. So the state of there may be according to the 200 days pass data there is a demand of 204 or 206 and 208 again means these are the state of nature and the probability of occurrence is 0.2, 0.5, 0.2 and 0.1. And this is a pay off table which is obtained with the help of this all the data availability. I will explain one of the pay off table if he take if we make a decision that he will purchase 200 papers and 200 papers are sold then there is a 1 rupee profit means 200 into 1 that is a 200. And similarly we have to find out the values for all the other pay off for the each course of action and the each state of nature. Now after getting the pay off table that is a profit table now let's multiply or let's start to calculate the expected monetary value for the each course of action. Yes, this course of actions are control of the decision maker. This state of nature is not under the control of state of or you can say decision maker. So if I make a action of or if I go for the course of action A1 then this we have to find out the expected monetary value how to obtain this are the particular outcomes of the each particular course of action. So this is a particular formulae for the or you can say the particular calculations which are showing you that the how to find out the expected monetary value 200 multiplied by 0.2 plus 200 multiplied by 0.5 plus 200 multiplied by 0.2 and 200 multiplied by 0.1. This is a first equation or you can say calculation which is showing you that there is a expected monetary value of 200 for the course of action A1 for the each state of by considering each state of nature state of nature 1, 2, 3 and 4. And for the similarly we have to calculate the course of actions for a second A2 the expected monetary value. So the expected monetary for the course of action A2 is 201.2 rupee. So similarly for the course of action A3 and A4 we have to carry out same procedure and we are getting the value as 198.3 for the course action of A3 and 194 for the A4. Now according to the particular rule as it is a payoff table that is a profit payoff table maximum profit we are getting for the course of action A2. So select the maximum expected monetary value corresponding to the course of action hence under this criteria or can say principle the optimum course of action is A2. So we have to go for the purchase of 204 newspapers where we will get the maximum benefit. Now coming to the next that is a solution by example with the expected opportunity loss value. Here the opportunity loss value is nothing else here we have to find out the loss table or you can say regret table. So the payoff table can be transferred into the loss table by subtracting the particular highest profit value from the selected state of nature to all the other respective values from the selected state of nature means what is the meaning of that here we have to go for the selection where in this particular first state of nature the maximum value is 200. This 200 has to be subtracted with each respective values of that particular respective state of nature only 200 minus 200, 200 minus 190, 200 minus 185, 200 minus 180 as shown here we are getting the value 0, 10, 15 and 20. Similarly when we go with the state of nature 2 the maximum is 204 out of these two there is maximum 204. So we have to go with the ease respect 204 minus 200 means we will get the regret values for the state of nature of second and similarly for the state of nature of third and fourth. Now this is the overall obtained regret table. Now as we have done the same procedure we have to calculate for the finding the values of expected operational loss value for the ease course of action as we have done for the earlier step that is expected monetary value. So here 0 into 0.2 plus 4 into 0.5 plus 6 into 0.2 and 0 into 0.1. This is a particular calculation and we are getting the solution as 3.2. Just for the second course of action we are getting 2.4 and for the third it is 5.5 and for the last it is 10. Out of this all you have to select the minimum value because this is expected opportunity loss value. These are the loss values. So with the help of both the criteria when we observe this by the broader criteria here also it is defining that go with the course of action 8 only in the expected monetary value and in the expected opportunity loss value or you can say criteria or principle where it is also defining that you go over with the course of action a correct answer for this particular MCQs. Hope so you have selected this particular answers. These are the references for today's session. Thank you.