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Module 1: Bondgraph Modelling & Decision Making

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SAC vs OAT Function

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So, today will try to see few more examples. So, in last class we discussed about this problemof whether to have a function in a SAC or OAT, depending on the weather condition and ifyou know the probability of this conditions how do you make a decision about having afunction in a particular venue. That was a decision making process, of course, it was not avery complex decision making process, a simple decision making process where we use theprobabilities as well as the non chances and use this to get a proper decision. We will seeanother example today, which is slightly more complex than this.
(Refer Slide Time: 01:05)
So, this is basically a company is trying to build a plant for a particular product and they haveto make a decision whether to go for a fully automated plant or go for a conventional plant.And if they go for a conventional plant then they have an option of upgrading this to aautomated plant at a later stage depending on the market demand for the product. So, here thecompany has to make the decision before really getting the actual product or really gettingsome real data about the sales. They need to depend on various factors like the probability ofsuccess of the product and for 10 year period what will be the changes in the sales or howmuch revenue they will be able to make. So, based on all this information they have to makea decision at this stage whether to go for a automated plant or a conventional plant.So, the problem statement is given here the company is trying to decide whether to build aconventional or automated plant to produce a new product with an expected life of 10 years.The decision must be based on the size of the market for the product. Simply look at themarket and then decide whether to go for an automated plant or for a conventional plant.And they have some values or some approximation or estimations based about the sales. So,the demand is expected to be any of the following 3 cases. So, they have identified 3 cases,the demand is going to change. The first one is, demand is very high during the first 2 yearsand if found unsatisfactory by the users then it will be very low thereafter. So, initially 2years they will be getting very good sales, but then depending on the product, if the product isnot satisfactory then the sales will go down. And the other possibility is that the demand will
be high over the next 10 years. So, they are expecting that the demand will be very high overthe next 10 years or the third possibility is that the demand will be low over next 10 years.So, this are the 3 possibilities and again we need to find out what is the probability of this 3events occurring and based on this and the revenue they need to find out what should be thedecision whether go for an automated plant or a conventional plant.And the investment for this 2 that is for the conventional or automated plant will be different.So, now, we have to have some estimation of the demands, the probability of variousdemands. We will identify what are these probabilities and then based on this we will try tomake a decision tree and then using the decision tree we can arrive at a particular decision.(Refer Slide Time: 03:45)
So, let me give all the values of the probabilities of various sales scenarios, that is, we have 3scenarios identified. We have this initially very high demand initially high demand and lowafter 2 years, that was one case; there we have this probability of 15 percent or we can put itin percentage 15 percent is the possibility of this situation. The other one is, it is initially low,the demand will be initially low and be high after that. So, this is our there is no possibility ofthis is not identified. So, that will be a 0 possibility for this one, then initially high. So,initially you have very high demand and this is sustained over the next 8 years. So, thispossibility is around 60 percent.Then, we have this initially low and it continues to be low and this is sustained. The lowdemand is continuing that is another possibility and this probability of this one is 25 percent.
Now, using these values we can actually identify few other scenarios and find out what willbe the probability of those events happening. So, chance that initial demand is very high. So,we have condition this is initially high and this is also initially high and this 2 are initiallylow. So, these are 2 conditions where we can have initially high demands.So, this probability will be 60 plus 15, 75 percent and then this initial demand high and itcontinues to be high. The probability is actually initially high and sustained is only 60percent. So, this will be 60 over 75 it will be 80 percent. So, if initially this high the chancesof it continuing will be around 80 percent. So, here now we have to look at the income fromthese plants.(Refer Slide Time: 06:18)
Suppose we have a plant, what is the possible income from these plants under differentsituations? So, if you have an automated plant and it is giving high yield I mean high outputsthen the revenue will be around 10,000,000 per year. So, that is the expected revenue. Theseare all estimates, so, we do not we are yet to start the industry. So, this are the estimatedrevenue and you have an automated plant, but the low yield; that means, lower sales then therevenue will be only 100,000 per annum. We need these values to calculate the expectedvalue of the different scenarios. And if you have a conventional plant; we have 2 optionsautomated and conventional, so we have a conventional plant and the high yield high demandor high yield then it will be 400,000 and if it is low, it will be 300,000 per annum. And if youwant to upgrade the conventional plant or if conventional plant upgraded to meet high
demand will be 600,000; that means, after 2 years if you change this to automated plant andthe this 400 will become a 600 with high demandAnd the same situation, low demand, we will upgrade it, but the demand is low then therevenue will be 50,000. So, these are the estimated revenues and the construction cost this isthe revenue and say construction cost, automated plant be 50,000,000, then this will beconventional be it 20,000,000 and if you want to automate after 2 years, that is conversion orupgrading of conventional plant again it will be another 20,000,000. So, these are the costinvolved in setting up the plant. So, if you have a automated plant, conventional plant orconversion of the conventional plant to in automated plant. So, these are the data available fordecision making.So, we have to make a decision whether to go for a automated plant or a conventional plantand the options are that you can if you start an automated plant you can get a various sales,you can have a continuously high demand for the product or we can have a high demand forinitially and then low demand. So, if you go for conventional plant then again you have ainitially high demand which is sustained and initially low demand it is sustained. So, theseare the probabilities of having these kind of sales and we can again identify the other chancethat initial demand is high is only 75 percent, but it continuous to be high will be 80 percent.So, these are the various possibilities of sales and these are the revenues expected from theseplants under various situations; that automated plant high yield, low yield; conventional planthigh demand, low demand. Similarly, conventional plant upgraded and these are the costrequired for establishing the plant or conversion of the conventional plant to automated plant.Now, based on this information we need to make a decision tree which will actually depict allthese values and then tell us what are the chances, what are the decision we can make andwhat will be that expected utility or the expected value of various decisions.
(Refer Slide Time: 11:34)
So, here as you know that in decision trees we have a decision node. The decision node isrepresented by a rectangle. So, this is the decision nodes and in this case we will be having 2decisions; this is decision one, whether to go for a automated plant or conventional plant,then the second decision will be if you have a conventional plant whether to automate it ornot, whether to update it or not, that will be the second decision. So, here in this decision wehave 2 options, 2 chances; that is, you have a chance node here and you have a chance nodehere.So, this is automated plant, build an automated plant is one with investment of 5,000,000 andthen you have this conventional plant with the investment of 2,000,000. Here, once you havethis we have 3 chances again, we have these 3 chances like various sales, you have initiallyhigh demand and then it is sustained or initially high demand which is reducing or lowdemand throughout.So, we can actually represent all this. Here we have one decision, one chance, this is anotherone and then you will be having this situation. So, this is basically high initial demand and itwill be getting then we have low thereafter and here the low average demand, this is the lowdemand and here the probability is given as 0.6. So, we can get here this initially highsustained is 0.6, so this is the high initial and sustained is 0.6 and this is low demand which is0.25 and this is 0.15, initially high and then reduces low after 2 years. So, it is initially high
low after 2 years that is 15 percent that is the probability 0.15 here. This is initially high, thenlow. These are the 3 chances here.We know the revenue what is going to be for this various situations, so we will write downthis revenue also here. The revenue is 10,000,000 for 10 years. So, the plant life is assumed tobe 10 years and so, 1,000,000, per annum we assume that the total revenue is 10,000,000.Now, here the revenue is 2.8 million for 8 years. So, this is 2.8, initially 1,000,000 per yearfor 2 years and so, it is 2 plus 0.8, so, 2.8 million for these first in 2 years initially very high.So, 2,000,000 and then it is very low it will be 0.8 million. So, 2.8 million is the revenue andthis is only 1,000,000 is the revenue. So, that is the output here. So, this automated plant withan investment of 5,000,000 and we have the 3 possibilities here, high initial demand and it iscontinued with an output of 10,000,000; initially high, but then it is reduced 2.8 million andlow demand 1,000,000. So, these are the 3 possibilities over there.Now, look at here this conventional plant, you have high initial demand and low initialdemand. So, if you have high initial demand for the first 2 year this is low. So, when youhave a high initial demand the first 2 years, we will actually go for this possibilities, 0.75 highinitial demands and then in that case will take a decision whether to go for an automated planor upgrade it or not. So, this again a decision node this is the decision 2.So, we have another decision to be made here and again you will be having all the 3possibilities. So, you automate the investment. So, this is chance node automate, is aninvestment of 2,000,000 or you can go for the yeah. So, this is the other one go for theconventional one, no change. This is no change. So, this decision node will take a decisionwhether to automate the plant or not. So, one option is automate with a 2,000,000 investmentother one is no change and again will be getting this is a initial high.So, after initial high you will be having 2 options; one is sustained, other one is low. So, thisis a sustained high demand continuous high demand probability is 0.8 here and this lowdemand, it is 0.2. This will be 5.6 million revenue and this will be 1.2 million and similarly,here also you will be having high and low again the possibility is 0.8 and 0.2 high and low,but here the revenue will be 4M and 3.2MSo that is about this decision and here again will be having the same situation be going as thisoutput. So, here you will be having 3,000,000 revenue and this is the low initial demand, theprobability is 0.25. So, these are the decision nodes; 2 decision node and this are the chance
nodes. As we can see here, we have the initial decision to be made, whether to go for anautomated plant or a conventional plant. For automated plant the investment is 5,000,000 andconventional is 2,000,000 and when we go for an automated plant. The possibilities of salesare here, 3 possibilities; high initial demand which is sustained, initially high, but it is lowthereafter after 2 years and low demand throughout the probabilities are 0.6, 0.15 and 0.25.Again the revenue is calculated as 10,000,000 for this situation 2.8 million for this and1,000,000 for this.So, there is the first situation when you have an automated plant. But, when you have aconventional plant if there is a very high demand for the first 2 years, the company can decidein such a way that they go for a conventional plant initially and depending on the demandthey will try to change it to a automated plant. So, here the conventional plant 2,000,000investment and the demand very high is 0.75 for the first 2 years, if that is the case thenactually they can decide whether to go for an automated plant or to upgrade it to anautomated plant or not. So, these are the 2 chances upgrade or not the upgrade is theinvestment is 2,000,000 and this year the investment is not there no change and again thehigh demand is continuing it will be getting 5.6 million. If it is not continuing it will begetting only 1.2 million. So, that is the revenue.So, in this case the no change then again if high demands 4,000,000 otherwise 3.2 million andif this not changed then it will be the revenue will be 3,000,000. So, these are the dataavailable to make a decision. Now, as we discussed previously we need to find out what willbe the expected value of this decisions. So, we have a automated plant decision orconventional plant decision, we need to look at what is the expected value of this decisions.We have the investment and we have these probabilities. Looking at this probability and theother revenue values we will find out what will be the expected value of these 2 decisionsfirst.So, as you know the expected value is basically the probability multiplied by the utility of theevent happening as well as the event not happening, add them together and you will begetting the expected value of the decision. To find out the expected value of the first decisionwe need to find out these expected value of this decision and expected value of this decision.
(Refer Slide Time: 21:08)
So, the expected value of the automated plant, if you go for an automated plant expectedvalue can be obtained as 10,000,000 into 0.6 that is the revenue for 10,000,000, 0.6 plus 2.8million into 0.15 plus 5.6 million multiplied by 0.25 minus 5,000,000.EV=10 M ×0.6+2.8 M ×0.15+5.6 M ×0.25−5 M=1670000So, this 5 is the investment and these are the revenues, these are all the revenues for the 3cases and its probability and that will be equal to. So, this will be the expected value of thefirst decision.Similarly, for the conventional plant the expected value will be 3.04 plus 0.8, because wehave 2 years revenue plus the other revenue. First 2 years will be having this revenue andthen other revenue. So, 3.4 plus 0.8 multiplied by 0.75 plus 3.25 minus 2,000,000.EV =(3.04+0.8)×0.75+3×0.25−2=1630000So, this will be the expected value of the conventional plant and it will be given as 1,630,000.So, these are the expected values of these 2 decisions, whether you go for an automated plantor a conventional plant. This actually tells you what is the expected value of these 2 decisionsand from there we can see that this has got a high expected value of the decision therefore,can go for the automated plant. That is the first decision whether to go for automated plant ora conventional plant.
But, in case, the company decides to go for the conventional plant then again the decisions tobe taken whether to go for the upgrading or not, that also again to be calculated. So, we needto see what is the choice here whether upgrading or not upgrading and how do we take adecision at this point. Here, again we have to take a decision whether to upgrade the plant ornot. This is done by looking at the high average demand the possibility of 0.8 and this is 0.2and here we have this again 0.8 and 0.2. We can actually get the expected value here is,expecting value of decision whether to automate or not that is upgrading. So, this isupgrading, expected value will be given as 3.84 that would be 3.84 plus 0.8, it will be 3.92minus the 2 investment 2,000,000. So, it will be 1,920,0003.84+0.8=3.92−2 M=19200003.92M −2M=1920000that will be the expected value of the first decision to automate it after 2 years.And if it is not upgrading, no upgrading then the expected value is 3,040,000. So, this will bethe value of the of course, you will have 1 million, 3.04 million. So, therefore, you can seethat this expected value is very high in this case. So, here the expected value is only 1.92 hereit is 3.04. So, if the company decide to go for a conventional plant initially and then whetherto go for a automate upgrading or not it shows that not upgrading then it is the expected valueof the conventional plant itself will be very high compared to the expected value of theupgraded plant.So, therefore, the company can decide not to upgrade even after 2 years because thatexpected value of non upgraded plant will be much higher than the upgraded plant. So, usingthis expected values basically we look at the various probabilities of sales and then we willfind out the revenue its estimated revenue and we will calculate the expected value of variousoptions and based on this expected values we can take a decision whether to go for aparticular type of plant or not.So, that is the alternate of using decision trees and this is how we make a decision based onthe available data. All this data whatever we assume here they are all estimated values theyare not the real values. So, based on the estimated values we can find out what will be theexpected value of this particular decision and based on the proper decision can be arrived at.
This is how we use the decision trees to make a decision in a system design. So, that wasabout the decision trees.(Refer Slide Time: 26:44)
Another tool we normally use for decision making is influence diagram. So, this influencediagram also basically give similar information or it can be used for same purpose of makingdecisions, but they actually give you better information, basically the dependability of thedecision on what is the kind of dependency existing and what kind of relationships are there,how it is related to a particular decision or how much it can influence the decision. So, that isshown in the influence diagram.Next, we can see here it is a graph-theoretic representation of a decision. So, it is a more of agraphical representation and there are 4 nodes; a decision node, a chance node, a value nodeand a deterministic nodes. So, these are the 4 nodes normally used in influence diagrams andthere are directed arcs between the nodes. So, this directed arcs basically shows the kind ofrelationship, which one is depending on the other one; that is shown using the directed arcs.And then a marginal or conditional probability distribution defined at each chance node,value node and deterministic node. So, we can actually defined some kind of probability forthis nodes and that can actually be incorporated in to the influence diagram which will tellyou how much dependency is there between different nodes.Here, the decision nodes are square boxes, chance nodes as oval and value nodes as squarewith rounded corners. So, this is how we actually represent the influence diagram using these
nodes. I will take few simple examples and explain how do we use the influence diagram torepresent the dependency of various decisions and how the inter relationship and how thedirected arcs actually represent the relationship in a influence diagram.(Refer Slide Time: 28:44)
So, as I mentioned it has got a node square box as a node a decision node. So, this is thedecision node and you can actually have discrete number of events attached to the decisionnode. You can have any decision discrete, number of decisions coming out of the decisionnodes or discrete number of states. We can say decision node can have discrete number ofstates.Then we have the chance nodes, it is represented using a oval. This is the chance nodes andagain this will be a random discrete random variable can actually find out what are thenumber of chances are existing. And then we have these value nodes. They are represented asround tangles with rounded corners or you can actually represent it as a diamonds also. Theseare the value nodes. Then we have the arc which actually determines the dependency. So, arcis nothing, but the arc which actually represents the dependency between these nodes. So,these are the basic construction elements for influence diagram. So, these are the influencediagram elements.Just take a very simple example to show, how do we use the influence diagram to represent aparticular decision making scenario. So, of course, this will not give you a decision directly,but we can actually represent the inter relationship between various nodes and choices and
the decision making process, how actually they are related and what kind of influence aparticular event makes on the decision.Let us take a very simple example of a vacation planning. So someone is planning to have avacation, basically a short duration vacation. They are planning to go to a out station,basically a place where the tourist location, but there are so many factors which actuallyaffects this decision. So, here we can represent the decision node as vacation planning andthen there is a value node which is represented by a round tangle. So, the value node is what,is actually the outcome of that particular decision. So, we have to plan a vacation and thevalue is basically what actually we achieve through that particular decisions.So, here basically the satisfaction of going for a nice vacation is the value. So, that is thevalue here, but then we will consider one scenario or the one chance, but that the weathercondition which actually U turns the vacation planning. That is one chance. This is theweather condition. The weather condition can actually influence the satisfaction and yourvacation planning. That is why we can actually show in the influence diagram weathercondition and then weather condition actually can be obtained from and there possibilities areyou can actually have the weather prediction data. So, weather prediction may be availablewhich can actually used for decision making. That is the weather prediction.So, these are the 2 chance nodes and this is the value node, this is the decision nodes. Now,we can see that there are 2 functional arcs. So, actually one is this, the satisfaction and this isthe satisfaction. So, the vacation planning can actually the satisfaction it is a functional arc tosatisfaction because this actually leads to satisfaction and this weather condition also actuallyinfluences the value here, the satisfaction that is why you have to functional arcs here. That isthe functional arcs of course, we can actually add to these the probability distribution then itbecomes easy for the decision maker to find out to make a decision, but we are not going tothe that part we are just showing how to represent that decision making process using ainfluence diagram.So, here and then we have an information arc here. So, this is in information arc, you can seethat this weather information is used for the vacation planning that is why there is aninformation arc which actually influences the decision of vacation. Depending on the weatherprediction the vacation planning will be done and then lead to the satisfaction depending onthe actual weather condition. So, this is the predicted information, but the satisfaction actually
depends on the weather condition. It has now relation to the weather prediction and similarly,vacation planning has nothing to do with the weather condition because we do not know theweather condition. So, there is no influence on the weather condition on the vacationplanning.So, this actually shows that what actually is going to influence the vacation planning. It is notthe weather condition which is going to influence; it is going the weather prediction which isgoing to influence the vacation planning. So, that is why we are having an information arcover here and the satisfaction or the value of the vacation basically depends on the weathercondition. It has nothing to do with the predicted weather and what is the weather conditionthat actually decides the satisfaction level of the person who actually plans for the vacation.So, this kind of simple diagrams can be used to find out the dependency of these decisions.As you can see the vacation planning has nothing to do with the actual weather condition,that is why there is no arcs over here, which shows that there is no relationship between theactual weather condition and the vacation planning. So, that was a simple example.(Refer Slide Time: 35:15)
I can show you another example, where company wants to make a decision on buy or build.So, we actually developed a decision tree for this particular case. In the last class wediscussed how do we actually decide a or make a decision tree for this buy build decision.Whether the company wants to buy a particular product or they want to make the productthemselves. That is a decision they need to make, which can be actually be represented using
the decision tree and then decision tree can actually have all the values, the probabilities aswell as the cost and other factors. In decision tree of course, we can actually add thoseparameters also, but for the time being will be just showing, how do we actually make thedecision tree for this particular situation.So, here the decision node is basically buy versus build. So, that is the decision node here andthere are 2 factors which actually affect, the value is basically the value it gives to thecompany. So, that is the value node here, what actually the value it brings to the company isthe output or the value node here something like satisfaction and the 2 factors or the 2chances are that it may actually lead to build cost and the build schedule. So, build cost andbuild schedule these are the 2 chances; build cost and build schedule.So, these are the 2 chance nodes and then we can represent this as actually influences this andthis actually leads to the value. These are the 2 chance nodes, this is the decision node andthis is the value node. So, what I actually determines the value is basically the build cost orthe build schedule and the decision has not direct influence on the value here, becausedepending on the build cost or build schedule if the depending on the probability of thisincreasing or decreasing that actually leads to the value of that particular decision.Now, if you actually add the probability of the cost increasing or the probability of scheduledelay accordingly we can actually calculate the value and then make a decision based on thatwhich one actually gives you the highest value so that, decision