 So, we will continue to look at stocks and flows. So, introduce you to the two key concept of building a system dynamic model which is identifying your stocks and flows. Stock is represented as a rectangle and flows are represented by thick arrows with valves in it. Direction of arrows shows whether we are adding to the stock or removing from the stock and whatever we add we are calling it as inflows, whatever we remove we are calling as outflows. And it is important to note that the underlying equation to this graphical representation is nothing but a differential equation where the change in stock over time t is nothing but inflow minus outflow, this is also known as net flow at a particular point in time. If you want to actually see what is the say change in stock, so change in stock that is d of stock can simply be delta t times your inflow at time t minus your outflow at time t. And when we are actually saying trying to simulate it what we are, so this d t represents your time step or time yeah time step or time interval and we were measuring the change in stock during that particular time and that is amount of stock that is changed from its previous value that is amount added or subtracted from the stock. So, let us try to look at an example on looking at a description how to identify the stocks and flows and construct a diagram looking at stock and flows. Then in today's class we will say that if the inflows or outflows behaves in a particular fashion over time, let us try to graphically figure out how the stock changes over time. So, we get a feel of how the simulation itself is expected to work because many times what happens is when we start moving into equations, we kind of just blindly trust it and but before that we need to build intuition the best way to do it is graphically and trying to see what kind of behavior we can expect over time. So, that is the agenda for today's class, first part of the class, let us move on to the examples. Let us look at a scenario, we will do a few examples last class identify stocks and flows. So, today we will begin with an example of just mapping the stock flow diagram, the arithmetic representation of a model ok. So, the description using the same description you can model a causal loop diagram we have seen some examples of that last week, but we can go one step further and start to identify what are the stocks and flows within the same based on the same description. Let us take a very straight forward example where many things may be physical. So, let us start with that the manufacturing firm orders raw material from outside which it processes and produces finished products. The firm maintains inventory of finished goods from which it ships to customers. Customer order when received is not immediately fulfilled, there is a delay caused by order processing credit checks etcetera after which the order is fulfilled subject to availability ok. So, this is the very brief description. So, what all could be the stocks in this model in this scenario? I think the example is quite easy to remember all we have is a I mean company gets raw materials then it produces and makes finished products and when customer makes an order they keep it in backlog while they are doing all the various checks and then once it is done it is shipped. So, you identified three stocks raw material inventory finished goods inventory then let us have something called as customer order backlog to this is the example. So, these are three stocks we have on the description starts out saying that manufacturing firm orders raw materials from outside. So, we can or rather we need to have a flow which is coming into the raw materials right otherwise how is the stock going to change. So, we need to have a flow we cannot have anything else we have to have a flow. So, that will be the rate at which I am going to be procuring materials. So, I can call it as I am using RM for raw material procurement, procurement rate and raw materials I am going to use a raw material to make the finished products right. So, logically there must be some production process that is happening which converts these raw materials into finished products and based on and there has to be some conservation right based on the raw material use I produce finished products. So, I can have a single arrow like this hold as production again note all arrows need not start with a cloud, cloud means such like an infinite source whenever I order it keeps coming it is almost it is a kind of at least in this model looks exogenous, but production rate is going to remove material from the inventory and add them to this finished good inventory. So, it is going to remove so material in that way is conserved that was one of the states we told for stock it gets conserved and from the finished goods we are going to have something called as shipment rate. Just observe how I have given the variable names whenever there is a flow we just told flow or rate or flow rate just to ensure that we do not make mistakes in units we can always say RM procurement rate, production rate, shipment rate or you could have just use a word shipment or production, but then we get confusion units so it is always good to rate shipment rate. So, whenever you say rate it means units over time so it helps us doing that. It is also good to think in terms of some of the units so procurement since no other information is given just for example, we can take it as say pieces per week could be the units here. If this is the units here then the same units has to be here you cannot have any other units that is to be pieces per week and I am arbitrarily chosen the time units as week if you day then make it consistent using day then the raw material units is pieces inventory unit is also I am counting in pieces or if you measure in tons you use a tons if it is kilograms consistently whatever the units if it is in cases or if it is in some sort of stock keeping unit then you use the same units appropriately. The idea here is rates is there is a per unit time and others it just has pieces. So, this is the physical flow of the material that we have captured the second part of description dealt with the information flow. So, what we have is customer order there is backlog what we have is customer order rate. So, as more orders come in the backlog is going to increase. So, we can just call it as order rate and as we start fulfilling orders that orders rate is going to go down so order fulfillment rate the rate at which orders are fulfilled just a side note let us call it CLD note if the same thing I want to represent as a causal loop the top part how I will write it is like this RM procurement rate then let us call it raw material inventory and let us call it production rate. I am just going to give one example you can extrapolate it for others so here as raw material increases my raw material inventory is going to increase correct so direction is the same. So, I get an arrow like this whereas, production rate increases my raw material inventory is going to fall down because I am going to consuming the inventory. So, the direction of arrow will be like this. So, when you see descriptions like this so this negative arrow I mean the arrow with a negative causal direction this is denoted by an outgoing arrow here ok. So, you can see this image in contrast with this you get similar thing here like order rate customer order backlog order fulfillment rate exactly similar linkages right. If you want to add a finished good inventory this production rate will have a plus sign to finish good inventory and then it will have a like if you want to have a finished goods inventory shipments. So, this is exact causal link of this one, but this when we start moving to causal stock flow diagram it captures some more information that is the flow of material is conserved here automatically. But here it looks like production rate is I can have a different equation for inventory and this and it can affect both in a different ways right that is not very intuitive here. So, when you do it here you are grounding it a little more into what actually happened let us go now back to the stock flow diagram. So, I am just trying to illustrate how the CLDs can be translated into stock flow. Now, this model is not finished one way to check that is how we are getting the order rate just to make our life little more interesting. So, order rate suppose we measure it as orders per week. So, then this has to be orders this also has to be orders per week. This flow is now conserved this is also orders per week this orders is also orders per week that is unit of measure I have, but now I have to link these two I have shipment rate and I have an order fulfillment rate where the units do not match. So, I cannot just say that order fulfillment rate equals shipment rate and model the equation what else what do we need? Average size of an order or average number of pieces per order this is just a simple variable I need based on which I can link these two ok. So, I can have another variable called as average pieces per order. So, now what all should I link intuitively what we expect to do without going into the equations it is simple. See every week imagine what do I do I look at the backlog ok this is the backlog I have then what is the average number of pieces that it demands ok this is the total pieces I need then I look at the inventory do you have enough piece and based on that I decide how much I should ship correct. So, to decide on the order fulfillment rate I need information about say the customer order, average pieces as well as current inventory. If inventory is more my fulfillment rate will be higher say I can have a plus these are anyway some constants. So, now I got an order fulfillment rate and based on whatever the order fulfillment rate the same rate I will do the shipment. So, I can write an equation simply setting shipment rate equal to order fulfillment rate or something. There are two arrows here one is shipment as well as average pieces. So, this arrow here represents that customer order backlog information is used in computing order fulfillment rate. So, this thick arrow only indicates that backlog uses this information of customer order fulfillment. This thick arrow only represents this line ok I have not drawn it only represents a line between order fulfillment to customer backlog. So, if you want an other line I have to draw it explicitly, but to start with it is ok once it is going to equations you will automatically start doing it our system will prompt you that you connect the arrow for you. For now all you have to understand is we have defined two stocks and flows there is one auxiliary variable which actually connects these two information. So, this arrow here looks quite messy at least initial model it need not be so messy even if you are connected at one place it is fine we are not looking at accuracy of the model yet as long as there is an extra variable here. So, units of it will be say pieces per order let us say units. So, that we can do all multiplication addition whatever it is we want to do figure out the calculations ok. So, in this if you want since you are practicing I can tell you this is an important link this is an important link and this is an important link. If you have captured these three arrows in your model that is efficient the other two is are optional if you have figured it out it is good it is not you will get it by practice do not worry about it. So, this arrow indicates that I am using this information here so, it is important this arrow indicates that this and this are connected so, it is important and this is an extra information I use to connect these two. So, that information also somehow used in this calculation so, that is all it says so, after that we can at least those three arrows are minimum required to have a decent model. Again as I mentioned cloud clouds indicate an infinite sink or infinite source that marks the boundary of your model whatever happens to that afterwards we do not care about it like it is already shipped that is all I worry about as long as it is left my premises I do not care when it reach the customer yet. If it is required then we capture it if not that marks the boundary of your model no there is extra delay that is described in the described here customer order when received not immediately fulfilled if we directly connected that means, immediately fulfilled that is what I am saying as soon as an order comes it is not immediately fulfilled that is how the description says there is a delay caused by order processing credit checks etcetera so, there is some delay in there. So, to capture the delay we are modeling a stop so, while they end up doing that so, after sometime only the order is ready for shipment so, may be one week later.