 Let us look at the example now, a company plans to hire people to fill up job vacancies, on an average it takes about 6 months to adjust the labor shortfall, the desired level is 100 people, very simple system that I know how many people are required, I need to spend some time to hire them, hiring process takes time, this example it takes on an average it takes about 6 months, where to advertise and people will apply and then later we make offers and some may join, again if you still there is shortfall again you have to apply for multiple rounds, because you are not getting at the same type of people, you need a range of people with variety of talents, so this is a very simplistic system based on that. So, let us assume that the initial value is 0, there is nobody in the system yet, desired value is 100. Ready to build a SD model above system, ensure that model runs without error, units are consistent and system stops in dynamic equilibrium, let us take time as months, time unit as months, so simple reason is I have already written that on average it takes about 6 months to adjust the labor, so if you are going to use time unit of months anywhere then everywhere it should be time unit of months, so that makes our choice easy that is why it is taken as months and let us take the time step, simulation time step as 1. So, the dynamic equilibrium is a physical analogy imagine a kind of a ball sitting on top of a hill, so at that point it is in equilibrium, but any small perturbation to it it will start rolling down the hill, so it is at a point where system when you simulate it you find that there is no dynamics in the system, system is constant over time and then when you make a small perturbation in the system then system starts to change, like if you imagine a pendulum then dynamic equilibrium is pendulum is at rest, unless you apply external force it is not going to start moving. So, before you start simulating ensure system is at rest then we can start simulating then we will figure out whether are we at a kind of already at a equilibrium point where you will return to the same point afterwards or are you going to settle at a new equilibrium those things will come to you. Dynamic equilibrium is a point where system has there is no other perturbation system and all values are kind of constant. Therefore, all of you have installed winsome education version. First is let us click new model time step is already units for time is already will be month and time step is 1, so let us just leave it as it is. So, this is what we are trying to model, the labour is a stock here and net hiring rate is your inflow, we have an adjustment time coming in, labour shortfall which is nothing but the difference between desired labour force minus the labour. So, this is what we are going to model. I might use slightly different terms what comes from my head. So, we have labour, I am clicking outside and then it is not click and drag just click once outside and click once inside net hiring rate, desired labour, labour gap, adjustment time. So, once it is done then I am just going to connect them. The arrows can be straight lines, they need not be curves that has no value to the model other than aesthetic aspects. So, it can be just simple straight lines, you can make it just curves look slightly better looking that is all, it does not affect your model whatsoever. To connect it you have to connect the arrow, say click on labour, click on labour gap, it will draw a blue arrow, that is it. In the diagram I use we can put the plus and minus signs, to do that you can right click on the arrow and there is a option called as polarity here that you can say plus or minus whatever you want. So, that will appear next to the arrow. So, you right click it you can get the plus or minus. I am just clicking the arrow head and clicking the adjustment time it will be minus because we are dividing by adjustment time. Since, adjustment time increases net hiring rate will fall down and direction is opposite. Again plus minus are just for visual aspects. Now, click this equation f of x is what shows to me, you will have something called as equation and f of x, click that it will go black and white, it will go dark mode that is I think common terminology these days. So, once in dark mode you click, let us start with labour, you click labour. Let us start from the top name labour is fine type is level as it to a level or stock is same. So, nothing to change there units unit is person, initial value it asks as it is already integrating net hiring rate we do not need to touch it. So, we go to the initial value let us put initial value as 0, let us click ok. Let us go to desired labour, let us go to units again units will be the same person. So, equation it is a constant value, let us start with the equation as 0 ok. Let us put the desired labour values also 0. Now, let us go to labour gap what will be the units for labour gap. So, click the drop down already the other units that you have already type will come by default when some gives two units one is d m n l which means dimension less other is the time unit itself which is 1. So, then we have defined person. So, this also as we person difference of persons again person differences we want is desired labour minus labour. So, if you click the variable here the same will appear there ok, you click it once or you can type it up to you, but all the variables listed in this box where I am pointing with my arrow has to be used in the equation defined in this equations box. If not it will throw an error for example, if I just write it like this labour gap is decide labour and click ok. I will get an error saying following inputs are not used. So, it prompts you saying that there are two inputs you are not used one. So, you click ok and then put a minus sign put labour then we click ok. Let us move to adjustment time. Adjustment time time unit if you can see type is already constant it is not getting affected by anything else that automatically selected as a constant. The unit is month we are measuring time in months and problem statement told 6 months. So, I am just going to put a value of 6 into this ok. Last comes the net hiring rate percent per month. So, net hiring rate is labour gap divided by adjustment time. Net hiring rate is units is percent per month equation is labour gap divided by adjustment time. I am just going to save the model. So, let us again I will take a look at labour. Labour is units is percent initial value is 0 net hiring rate say is net hiring rate we just leave it. You go to decide labour units is percent equation 0 click ok labour gap units percent equation decide labour minus labour adjustment time units month equation 6 is just a constant 6 net hiring rate units is percent per month labour gap adjustment time. It is case sensitive and word sensitive somewhere you use use person somewhere else you use persons for it is just a string it will say it is wrong units do not match. It is just a piece of software it is not going to parse your English. So, once you have got this you can do model check model it should say model is ok. So, now, let us click simulate it will ask data set already exist you want to overwrite just say yes simulation is already done. Now, you can select any say let us select labour that is a line and if you click the graph on the left menu bar this one which is being highlighted right now 1 2 3 4th one from the bottom. So, you got a straight line there is no change in it. So, the system will always been dynamic equilibrium when what happens when decide state and current state is the same or when net flow is 0 when net flow is 0 then it has to be the same in this case. So, for example, if decide labour is 100 labour is also 100 then it is still been equilibrium no change will happen. So, this is what is called as dynamic equilibrium over time things are still in equilibrium nothing is changing. So, now we want to see what will happen when any of these cumulus changes. So, let us go open the equation click decide labour and make the decide labour 100. Click ok let us click play over a data set yes. Now, if we let us click labour I will start saying this nice goal seeking behaviour asymptotic growth has happened. So, over time the discrepancy has been adjusted over time until the labour force reached its goal of 100 percent. So, this is entire graph. So, let us see what happens is to visualize it better I am going to change the model settings to instead of final time as 100 let me keep it as say 30 final time step and just taking the final time step as 30 to get a better resolution graph. So, I am going to explain things. So, this is the value of the stock that you should be able to see even if x n goes 100 is fine, but so let us observe what happened at time 6. So, your adjustment time remember it was 6. So, all we are trying to see is what happened after one adjustment time went ahead. So, adjustment time 6 the gap full field is about say 65. So, out of 100 65 was full field. Now, let us see when time unit became 12 at time 12 the value is say about 88 I would say I do not know exact value, but I am just here saying probably it is 88 here at 6 it is about 65 or rather at time 6 about 65 percent was full field the gap was full field. Now, about time 12 total was at 88 which will be about 65 percent of the gap between 165. The previous time saved a 65 100 minus 65 about 35 about 65 percent of 35 that much person would have been full field at time 12. So, to every time unit at every interval of adjustment time about 60 percent of the discrepancy or 65 percent of discrepancy gets full field and asymptotically it will reach its desired goal that is how the scenario works in this model. Now, let us take a two different things the top represents the labour this net hiring rate how I open this graph was I click the labour I click labour and click this causes strip causes strip causes strip means it will plot the this one and plot all the inputs into this. So, that is what causes mean to understand what caused the dynamics of labour to change like this. There was only one input which was hiring rate net hiring rate and unlike your exponential growth systems in this the net hiring rate is going to keep falling down exponentially. Things starts at around 16.5 or something or may be 16.5 and gradually comes down to 0 which is expected because at equilibrium the system has to reach net hiring should be 0 because once you reach the goal you do not need to do any further hiring goals that are remaining constant. If you want to know the numbers you just click labour and click this table time down you will get time on access and get the actual values which it computes every time ok. There may be I can show you need trick. So, once you get this labour do not close this window do not close this window I am just resized it move it to the right. Now, you just click somewhere here click hiring rate and again click the same drop down. Then you will find that the hiring rate is also added as another column in the same sheet. So, you can start comparing the values. So, if you select multiple things and click the graph both the things will be displayed. You can do one by one or you can use shift. So, first if I do labour and net hiring let us see what happens I selected both. Now, I am going to click graph I get both the graphs simultaneously. So, very simple features but very useful all I have to do is whatever variables I want I use shift to select all of them and click that graph button. Then I get multiple graphs in one picture to show that I can see exactly how it changes, but be careful about the units because here it uses left y-axis and right y-axis left y-axis is used for stock right y-axis is used for persons per month. So, if you have more variables it will start to superimpose multiple y-axis one on top of each other ok. So, just be careful we can try that also. Let us see what it does let us do net hiring, labour, labour gap all three other two are constants I am not putting it. So, it is up to our intelligence to figure out which graph is mapped against what, but you get enough evidence. So, already shows here labour and bracket it says person that means, the unit of labour is person labour gap is person the same units are appearing in this graph here. So, if you do not write the units it will just show it as blank. So, you would not know what is happening same thing net hiring let us say person per month. So, it must be person per month we know it is blue. So, I will highlight it as you go here it highlight. So, there are these kind of subtle features which is makes it very useful and powerful. Now, let us we already done this simulates in a when initial labour is 0, simulates in a when initial labour is 200 let us try that. So, I am not changing anything yet with 100 itself I want to know what it is. So, when I click play it will ask you this question that, current data set already exist do you want to overwrite it? We just say no. So, here we can say labour 100. So, labour initial level was 100 let us click save. So, that data set is now stored as labour initial 100 desired labour stage 100, labour changes from 0 to 200, change labour to 200 initial value of labour 200, desired labour continues to be at 100 desired labour goes to 200. Then when I click simulate again it will ask overwrite this labour initial 100 you say no do not overwrite it save it as labour initial 200. Oh boy that should be labour initial 0 anyway labour initial 200 even if you did not get overwrite it will come back. Observe the graph. So, instead of approaching it from we are not change the bottom I mean we are not change the model desired labour is 100, current labour is 200 that means effectively we need to fire people. So, the net hiring rate here actually means I am removing from the system. But the same model works by just changing your inputs as you can see the labour is now falling to 100. It will be a mirror image of the graph that we got here we are adjusting the discrepancy every time unit above 60 percent of the discrepancy is getting adjusted. So, if you are not able to do both the graphs I will give the instructions again I will write it and put it in model you can check out those instructions basically before simulating for each setting you give the under what it should be stored here in the top you can see the name here you give it and store it. So, and automatically all those data set will be alive as long as simulation is up and running come in your when sim is open. So, all those graphs will just get super. We can also see how the net hiring works. So, here as you can see this was the people who are hired in the first case and the initial labour was 0. So, we had hired lot of people and then slowly reduce the number of new hires. In this case lot of people are laid off and then as over time less and less people are laid off when the initial value is 200. So, the system remained the same we just change the parameters and the model became even for letting people go the same model was used. When you change the adjustment time what do you think will happen? So, adjustment time from 6 became 2 how do you expect the shape to change, but adjustment time is lower we must reach the goal sooner or faster earlier right. So, we can try that and go to equation change adjustment time to say 2 run it over right and we are going to put no labour initial 282 let us save the labour graph it. I am going to remove one of it I just removed these two lines. So, I am just putting two graphs one when adjustment time was 6 which is the green one and the red one when adjustment time is 2. So, initial value of stock was 200 the goal is 100 both reaches the same goal except as to expect as adjustment time is longer it takes longer time or adjustment time is shorter it is has to reach the goal earlier it is the same dynamics that we can expect, but the shape of the system continues to be asymptotic. So, for adjustment time is 2 months instead of 6 months we just saw that. So, I have the graphs here also. So, when the initial level is 200 and adjustment time is 2 initial level is 0 adjustment time is 2 because it will be mirror image except that you are approaching a goal from either the top or the bottom as the case may be and as adjustment time becomes longer it is going to take even longer to reach your goal that is what this graphs are telling us, but as each adjustment time passes will be adjusting about 60 to 65 percent of the discrepancy. An exponential approach to goal happens state of system reaches goal at diminishing rate over time.