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Module 1: Bondgraph Modelling & Decision Making

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Decision Making in System Design

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Today we willdiscuss about the decision making process in system design. We need to make manydecisions about the various processes involved in the design. We need to make decision atvarious stages about the next level of the design, or we need to make we have to getsomething outsourced from other sources or we need to make manufactures some of theproducts, or will get it readymade products, or making some decisions about logical decisionsor some decisions on the logistics of the project. So, like that there are various decisions to bemade during the system design.We will try to see some of the methods which can be employed in order to make somedecisions, where we apply the principles as well as use the existing knowledge and thecurrent database available and based on this we make some decisions. Most of the timesdecisions are made under a lot of uncertainty, we may be knowing some of the facts and butwe may be having a lot of uncertainties, that may be lot of information lacking in the decisionmaking process, or due to lack of information the decision may not be full proof or there maybe some mistakes coming in the decisions. So, how do we actually reduce these problems andhow do we actually make a good decision based on the available data; so that is the questionunder the decision making under uncertainty or we are going to discuss today.We discussed about the Columbia disaster and then mentioned that mainly it was an issue ofdecision made by the top level management, to continue with the mission even when theywere aware of a small problem with the vehicle; the space vehicle which was launched for themission, while during takeoff itself had some problems and lot of finances was carried outand then the decision was made to continue with the mission.Let us have a relook at this decision and then see how this could have been avoided or whatare the possibilities or what are the decision tools we can use in such situations.
(Refer Slide Time: 02:35)
Let us have a relook at this Columbia disaster, as mentioned this was the 28th which wasoriginally scheduled for launch in January 2001, but the technical problems led to an numberof postponements about 18 and finally, the mission was set for 16 January 2003. So, therewere so many delays and so many problems. And finally, after 2 years of delay it was set for16 January 2003. So, some of the insulation tiles had come loose in the previous launches andmany engineers felt that the launch should be postponed till it was rectified.So, this was a non problem there were some problem with the tiles and during the previousmission some of the tiles had fallen and then many people felt that there should be a furtherpostponement of the mission because unless we rectify this problem it is not safe to have themission or to continue with the mission, but then there were so many delays and then themanagement was not in favor of one more delay. And therefore, they wanted to take a risk orthey wanted to analyze the risk involved in this and then take a decision.So, the top level management took the decision to go ahead, considering various reasons, butthen during the launch few tiles ripped off and possibly damaged the wings. So, againinitially there were some damages, but then during the take off few more tiles actually rippedoff from the surface and then actually they probably hit the wings of the vehicle.And then again management decided to go ahead and not to interrupt the mission. So, theyrealize that there is a problem some tiles have come out and it has actually hit the wings.They are conducted many trials many simulation studies on ground and tried to find out what
will be the impact of losing this tiles. And they actually took a decision based on to enhancesthey took a decision to continue with the mission saying that it may not affect theperformance of the vehicle. While the returning to the earth and while (Refer Time: 04:35)entering the atmosphere actually because of the high temperature over 1500 degrees andspeed exceeding mach 24, Columbia disintegrated while entering the atmosphere.So, that was what actually happened and the whole Columbia vehicle was lost and for theastronauts was killed in this accident. So, here you can see that there was a very criticaldecision making processing involved, and considering all the facts available with the teamthey took a decision. So, decision making is always a process where we look at the facts andfigures available at present and always assume that the probability of the incidents or theevents going to happen have some values for this probability and then take a decision.This may be correct or it may be wrong that actually depends on various other scenarios, butthe team has to take a decision, when there need to take a decision they have to rely on theexisting data and then take a decision. So, that is the decision making under lot ofuncertainties.(Refer Slide Time: 05:39)
So, in system design also we need to make lot of decision like this, it is not only during themission, but while decision taking is a continuous process in the engineering system designprocess, because at various stages we may have to take decision about the structure, strength
requirement, or the forces appearing or the decision to make a product or to outsource aparticular service. So, all those are decision to be a taken by the design engineers.So, in this decision making so we need to make a lot of important decisions and then most ofthe decisions are not made rational or explicit process. So, you can see that not always youcan have a rational or an explicit process for decision making. There are many other situationwhere you cannot have a rational decision to be made because the available data may not besufficient, or there will be lot of other factors which cannot be considered at that stage. So,many uncertainties are to be tackled while making decisions, and important point in decisionmaking is that decisions have to be made with the best information available at that time,realizing that the outcomes associated with the decision is remain uncertain when thedecision is made.So, that is one of the most important point, decisions have to be made with the bestinformation available at the time, realizing that the outcomes associated with the decisionremain uncertain when the decision is made. So, we have to rely on the information availableat that time and then the outcomes associated with the decision remain uncertain till when weare making the decisions. So, this is the one important point which we need to be aware ofthat you have to rely on that information as well as the outcome is uncertainLevel of detail needed to make a decision in the engineering of a system and the level ofdetail needed to ensure proper implementation of the system components and CI need to beunderstood clearly. So, in order to make a decision we need to understand all the level ofdetails we may have to understand the many factors involved in that particular decision. So,we need to look at the details of this system level and component level details and understoodthem clearly. So, that whatever the decisions we are making is based on those informationwhat is available at that time.So, here when we make the decision, we need to be aware of these facts that there are lot ofuncertainties and there are lot of information to be collected and there are lot of informationwhich is not available also. So, based on this we need to make a decision.
(Refer Slide Time: 08:12)
And in the main elements of the decision problem are the creative generation of alternatives.So, whenever we need to make a decision we need to look at all the alternatives possible. Weshould not rely on one or two alternatives we have to look at what are the all possibilitiesexisting, and then identification and quantification of multiple conflicting criteria and youwill be having a lot of conflicting criteria. So, we need to identify them and quantify them,we need to look at the criteria and as well as quantify the risks involved those particularevents as well as the probability of those events. So, the identification and quantificationbecomes important. Then assessment and analysis of uncertainty associated with what isknown and what is unknown about the decision situation.So, again as I mentioned there are many things known and there are many things unknown;so we need to look at these factors and unless the uncertainty associated with the known andunknown factors. We look at those known factors and unknown factors and identify theuncertainties involved and then make a decision. So, here will use many statistical techniquesas well as logical techniques to find out the uncertainties and then quantify them. So, that willget some kind of quantitative information to make a decision; so in the getting thealternatives. So, I mentioned about there are many alternatives to be considered.
(Refer Slide Time: 09:30)
So, in getting the alternatives there are two approaches, basically one is known as lateralthinking, the other one is a vertical thinking. I will explain these two methods, basically thelateral thinking starts with a basic problem or a single problem it begins with a singleproblem that is the lateral thinking.(Refer Slide Time: 09:52)
Begin with one problem, and then look for alternatives through various concept generation orideal generation techniques and then develop many alternatives over here. So, here wegenerate numerous possibilities. So, we start with the single problem and generate numerous
possibilities for a period of time. So, we will start with a single problem and we use manymethods like brain storming, discussions, discussion within the team or with the experts, orwe can use some other method like, different brain storming techniques like 6 3 5 method or(Refer Time: 11:06) logical solving problems logical problems solving methods.So, we can actually use many methods to get numerous possibilities. So, this is the lateralthinking process where, we generate many ideas or many alternatives for a particularproblem. So, when we have to make a decision, we look for all the alternatives, generate allthe alternatives and then try to select one among this possibilities based on some othermethods. That is you need to quantify those possibilities or the uncertainties and then selectone solution for that particular problem.(Refer Slide Time: 11:47)
The other one is known as the vertical thinking; in vertical thinking begin with one problemwith numerous data, with lot of information with numerous data. So, we start with oneproblem and with lot of data. So, we have lot of data available for that particular problem,and we need to narrow down to a single solution. So, we start with like this. So, this is thevertical thinking we have one problem, but lot of information or lot of alternatives availableand then we go for logical thinking over here, and then try to get a single solution or we canuse the mathematical modeling and processes techniques, and get a single solution.So, here it is more like a rational approach in this case, we are having one problem with lot ofinformation or lot of alternatives, lot of possibilities and then we go for the logical thinking
and mathematical modeling or processing to get in to a single solution. So, that is the verticalthinking or approach for getting the solution. So, we have can actually the decision makingproblems can be approached both the ways can go for a lateral thinking or for a verticalthinking both will actually give you a solution.But the approach will be different we start with the single problem and then try to generate lotof alternatives and then choose one solutions. In vertical method we actually start with oneproblem with of data and then we try to narrow down to a single solution based on thisinformation available. So, here we can use logical thinking methods as well as mathematicalprocesses to do this.So, these are the two approaches and another method the decision making by search process.So, search process is look at the alternatives available. So, we have some problem and youwant to take a decision about that for example, if a company finds that their products are notselling in the market or their profit is falling. So, what will be the decision where then it toreduce the price or increase the marketing strategy or what other things to be done. So, in thiscase we can actually go for a search process and try to find out the solution say actually itstarts with the problem.(Refer Slide Time: 14:39)
So, for example, if you take the profit the company has making lot of losses, actually thecompany can start thinking what could be the decision whether to reduce the price or toreduce the manufacturing cost or to increase the marketing. So, what is the decision to be
made in this case? So, the problem is basically why has the profit fallen, there is a problemthe company has to answer and then the other possibilities are here we actually start whetherthe cost has gone up, has the cost increased or the revenue of the sales decreased.This is the cost of production or manufacturing sales that is increased or the revenue hasfallen, revenue from the sales. And the company is making losses then this could be twopossibilities. So, they need to analyze what is the real issue here. And again can actually lookat the possibilities. So, this the numbers sold whether total sales has gone down, numbers soldthat the cost number of products being sold is reduced over the cost. The net price haschanged. And then we take a decision whether what(Refer Time: 16:30) should be thepossible option.So, the decision has to be taken based on this analysis this is a search process they will try tosearch for the solution over here to make a decision and here again you can have multipleoptions. So, whether the cost if the cost is change then whether it is the fixed cost or thevariable cost. So, here also there may be some issues, we can actually identify you can searchfurther if the fixed cost is changed we can search further or the variable cost is changed wecan look at what is actually making it whether the productivity has changed reduced. So, theproductivity of the plant or the people whether reduced or the changes in the cost changes inmaterial cost or other cost variable cost involved that has changed, and again based on thiswe need to make a decision. Whether what is the decision to be made if this is the situationwhat should be the decision and if this is the situation what is the decision.So, this is the basic search process. So, you search for the solution or the decision through aprocess of looking at various steps involved and search through this steps and then try to findout what is the actual problem and what is the solution we can achieve. So, that is one way ofmaking the decision. So, this is known as the search process of making decisions.
(Refer Slide Time: 18:27)
And then coming to the decision analysis, there are various axioms such you can see here thevarious axioms used in decision analysis, one of the most important axiom is the probability.As we know there are lot of uncertainties. So, we need to use the probability methods to findout or to quantify the decisions or quantify those situations. So, that is a common approach inengineering used for analysis. The other one is known as order rule order rule states that ourpreferences are well defined that any possible list of outcomes associated with thealternatives can be ordered from least preferred to most preferred on each objective in thefundamental objectives hierarchy.So, we assume that there is a particular order in which we can always put them and then takea decision based on that. So, it is actually it is not that we have everything as equal. So, wealways put that they can be arranged in a particular order. So, that we can choose from thisorder least preferred or the most preferred based on the objective hierarchy. The third one isthe substitution rule we are willing to substitute any combination of outcomes, if we areindifferent between them. So, if we have we are indifferent between two decisions then weare willing to take any one of this. So, that is the substitution rule. So, this are the threeaxioms we normally use in decision analysis the probability order rule and substitution rule.We need to learn little bit of probability fundamentals in order to understand how we use theprobability theory and the probability associated with various events in the decision makinganalysis. So, I will just give you a brief idea about what are the different probabilities we
normally encounter or what are the basics of probability analysis. So, of course this is notdetailed analysis on probability, but just to make you understand that some of the terms whatwe are using during the analysis are familiar to you. So, most of you may be aware of someof this fundamentals.(Refer Slide Time: 20:30)
So, normally when we say probability of any event A, event A occurring is given as P of A,and0≤P( A)≤1So, that is the probability of an event A happening and then we have another probabilitywhere the probability of event not happening. So, A ́ , so if the probability is will is nothappening then we put it as probability of A or the A ́ . So, this is the probability of Acompliment, that P(A) is not happening normallyP( A ́ )=1−P(A)that is P( A) is not happening the probability of A not happening, is 1 minus probability ofA. And always this will be P(A) plus probability of A compliment will be 1 because, we cansee this can be if we add this will be getting 1. So, a probability of a happening and nothappening total probability will be always 1P( A)+P( A ́ )=1
And then we have few other things like probability of A and B, probability of event A Boccurring both the events occurring, that is given as probability of A intersection B, which isgiven as probability of A multiplied by probability of B.P( A∩ B)=P( A)⋅ P(B)So, here if the two events are happening simultaneously or same time then we get probabilityof A intersection B is equal to probability of A multiplied by probability of B. Similarlyprobability of either of this A or B, either A or B happening is given as probability of A unionB. So, that is given as P of A compliment multiplied by P of B compliment, that is P of Aunion B either A or B happening is given by 1 minus P A minus P A multiplied by P BP( A ∪B)=1−P( A ́ )⋅P(B ́ )and if you can simplify you will be getting it as this is equal to P(A) plus P(B), it isprobability of A plus probability of B minus P(A) P(B). There is either of A or B happening.P( A ∪B)=P(A)+P(B)−P(A)⋅P(B)So, in many cases in decision making we will have to use the probabilities associated withvarious events and try to see what will be the total probability of
this events three eventshappening together or any one of this happening. So, those things we need to analyzequantitatively using the probability theory.And there is another term associated with this analysis.
(Refer Slide Time: 23:50)
So, this is known as expected value, expected value of an event, again we know that theremay be many events happening and we can actually identify the probability of this events, butthen what will be the outcome of this events some events will be having a preference andsome events will not be having that much preference. So, how do we actually calculate theexpected value of this events.That can actually be done by this term expected value is equal to probability of A, that is theevents happening A probability of the event happening multiplied by the utility of this eventA, plus probability of A not happening multiplied by the utility of A not happening.EV=P( A)×U ( A)+P( A ́ )×U ( A ́ )That is given as the expected value that is if we have an event A which has got a probabilityof P(A), and it has got a utility of U, then the expected value is given as P(A) multiplied byU(A) plus P(A) compliment multiplied by U(A) compliment that is it is not happening whatis the utility and if it is happening is a utility and you multiply the probability with the utilityand add them then you will be getting the expected value of that particular event. We canexplain this with an example for a lottery, if you consider the lottery there is an example, wehave many lotteries and there are lots of other involved in this kind of lotteries.So, if you want to find out the expected value of a lottery, we can actually use this principle,EV=P( A)×U ( A)+P( A ́ )×U ( A ́ )
now consider a lottery where you have a 6 digit lottery here to select from 49 digits and set arupees 1 for each lottery cost 1 rupee for you to buy and the expected amount will be assumethat it is 10 lakh.(Refer Slide Time: 26:00)
So, you can consider the lotteries 10 lakh rupees the outcome. So, you should pay 1 rupeesyou can get maximum of 10 lakhs, and this actually a 6 digit. So, if all the 6 digits arematching, there are actually 49 possibilities. So, you take 6 digits from and then we will get10 lakhs. So, what is the expected value of this lottery whenever we talk to a person aboutlottery he will always tell there is a 50 percent possibility, he can get or he cannot get thelottery? So, he always thinks the probabilities only. 5, but actually the expected value of thelottery is much low compared to the expectation or understanding.So, here you can see that probability of the win a. So, will given as.P(win)=149!6!43!
So, this is the possibilities. So, you have 49 factorial divided by 6 factorial multiplied by 6 43factorial because of 6 digits and then remains 43 totally we have 49, and this is given asalmost like, 1 over 13983000
P(win)=149!6!43!=11,39,83,000
1 over 1398000 is the probability of A win. So, we can see that the probability is so small forgetting a lottery, it is not 0. 5 as pursued by those who are actually going behind lotteries.Now if you look at the expected value the expected value is that you have a probability of thismultiplied by the utility of winning, the utility of winning is around 1000000. So, that is theutility and utility of not winning is rupees 1, you are losing 1 rupee, but this is probability ofnot winning this 1. So, now, if you take the utility value we will see that the utility value is7.15 multiply 10 to the power of minus 8 multiplied by 1000000 plus the probability of nothappening that is 1 minus this value.EV=(7.15×10−8
)×10,000,00+1×1
So, this will be almost 1 we just write as 1 multiplied by 1. So, this is the expected value ofthis particular lottery we can see this would be very small or the expected value of this lotterywill be too small for you to find to at any particular benefit from this.If you multiply this you will see that the value is very small. So, the expected value of anylottery is very small, compared to what actually we are thinking that it will be providing. So,based on this kind of principle, we can actually find out the expected value and this kind ofanalysis will be very useful in analyzing the expected value of various functions or various
options.
(Refer Slide Time: 28:59)
So, that is how we use this one for analyzing the decision making process and quantifying thevarious options available for the decision makers; in to do this decision making we normallyuse various kinds of tools. So, one of the tools is influence diagram and the other one is thedecision tree. We will discuss about the decision tree first and then I will take an example andthen shoe how decision tree can be used for making some decision using the principle ofprobability and expected value.(Refer Slide Time: 29:33)
In decision making what we do is, we let us discuss about the decision tree first, in decisiontree we use three kinds of nodes. So, first one is known as a decision nodes, so basically it isa diagrammatic representation of the decision process that is why it is known as decision tree.So, we have a decision node which is represented by a rectangle or a square that is thedecision node.Then we have the chance node is represented by a circle and then we have the terminator orthe final decision, where that particular tree branch comes to an end that is known as theterminator. So, this are the three nodes used in the decision trees. So, here it we have adecision node suppose we have to make decisions various decision thought this may bedecision one decision two or the probability of decision.So, you have to make a decision this or this, when you want to buy the product or one tomanufacture the product. So, that those are the decision you want to make. So, this actuallyshows a decision node and then we have many choices. So, when you come to one particularstage will have the choices of various options you can go for a low cost product or you can ata high cost product or a medium cost product when you want to buy the products. So, wehave many choices over there. So, the choices are shown by this choice node and theterminator the final decision is shown as like this, these are the nodes by which we canactually develop the decision tree. So, decision tree will start with decision nodes and theremay be more than one node in particular in a tree; so here behind decision nodes choicenodes and terminators. I will show you an example how to create a decision tree for aparticular event.
(Refer Slide Time: 31:32)
So, let us take an example where we want to conduct a function in an institute like IIT wewant to have a function which actually preferred to be conducted in a open air theatre thatactually the utility of that event is very high.But then there is a possibility of rain. So, if you have a function in the air open air theatre andif it rains then the whole thing will be failure and the expected utility will be 0 for that one,but then if you have the function in the auditorium then actually the utility of that function isreducing because it is perfect to have it in the open air theatre, but because of the rain weneed to move it to the indoor stadium or the indoor facilities. So, how do we make a decisionand how do we calculate the expected utility of these two and then make a decision what willbe the probability of rain and what will be the utility of these events and based on that weneed to make a decisions.
(Refer Slide Time: 32:48)
So, this kind of decision process can be represented using a decision tree. We will see how touse the decision tree to represent this kind of decision making process. So, we can see herethe nodes the decision node shows the this is the decision nodes and we have two decisionswhether to have it in open air theatre or the indoor facility, student activity center or indoorfacility and there are two chances, here the chances are basically there could be a rain or norain.So, chances are rain or dry weather. So, this are the two chances similarly here also when wehave it in here actually we have a both chances of rain or a dry weather now based on thishow do we actually make a decision; so if you take the decision here and what is the utility ofthis functions or this particular branch. So, this is one branch where the function is O A Tother one is in the indoor stadium. So, if it rains basically when you have this function in O Achoice, and similarly here if itis in indoor and if it rains we will actually feel this perfect to have it there, and if it is sac and