 of stocks, stocks characterize state of system, it provides snapshot status of system and helps data to make, provides data to help make decisions. So, snapshot status means to make any decisions you need some information. For example, if you are flying a plane you need to know its altitude, you need to know the wind speed, you need to know the say outside and say temperatures, you need to know the, what is it, the actual ground speed and what is the speed at which you are flying, the altitude, the direction, the varying, we need various information. So, all the information that you need to make decisions that provides a state of system at any point in time, where is the aircraft, what all characterize is it. So, all those things become the stock because they provide data to make decisions. Whatever the data may be. So, if you are going to use it that becomes a stock. So, what is, if you are a production manager then you need to know information about what is the current inventory on hand, what is the expected demand forecast, what is the expected order that is in pipeline, where you ordered we are not yet received, what is the current cost of the raw materials, how much raw materials you need to make this current production, how many workers are there in the factory. We need to know all the information to make the correct production decision at that point in time. So, all those information can be classified as stocks, that is the characterized state of system. So, in any other course if you are saying that okay this is defined as state of system, that means you characterize the stock. Stocks provide system with inertia and memory, stocks only change through rates. What I mean by inertia and memory is that it accumulates past events. Like in the previous example, once the water level reaches the desired water level, it does not disappear. It just remains there forever until there is an outflow. If system does not have an outflow, it is not going to change. You can simulate it for how many ever time period you want the stock remains. So, that is what I mean by saying that it provides memory. And inertia and sense is not going to change until there is some change in the flow rates. If flow is always 0, the value of stock does not change. Only if flow changes, then that causes the stock to change. So, in real systems where it is held, for example, if you want to model the amount of ozone in the atmosphere, even if you stop the production of all say ozone producing equipment like shutdown CFCs and other stuff, refrigerant. But still the current ozone that is accumulated will continue to remain there. That stock does not disappear. Even the current rate of release of ozone or CFCs, ozone depleting CFCs you stop, the flow stops to 0, but your stock still continues to have that value. So, that is what is called as memory. The stock is something which characterizes the state of system. It has to change only if some external force is applied. That is not going to change. Stocks are source of delays. All delays involve stocks like if I want to, for example, like in courier, suppose sending any package through products or EPS or whatever courier, it does not reach instantaneously. You send it and after a time lag it reaches. So, until then the package does not disappear. It is there in the system somewhere. So, you can say packages in pipeline. As a stock so that the matter is concerned. So, whenever there is delays involved, that means that information or that order or that material has to be there somewhere. So, whenever there is delays involved, it means that stock is there somewhere and after say the package is delivered, then that package in pipeline gets reduced. So, we can use it to represent the difference between inputs and outputs. So, what is a delay? Delay means output lags behind the input. In a delay output lags behind the input. So, until then things has to be remain somewhere. So, that characterizes the stock. That is the simple definition of delay output. Stocks decouple rates of flow and create disequilibrium dynamics. It also absorbs the difference between inflows and outflows. Characterizes state of system. That is an important point. Stocks provide memory. Third we saw delays. What we mean is delays. Delay means output lags behind input. So, if I have say letters dispatched and then I have letters delivered. So, delivered will typically be whatever letters are dispatched some periods earlier or whatever letters dispatched today will be delivered say some L time periods later or say one week later. So, one week worth of letters has to be there in the pipeline. So, we can have a stock called as letters in pipeline. This becomes your stock because these other two becomes your delays. Or as soon as you put raw materials into the shop floor it does not become finished product. You take some, you spend some time in the shop floor after end of a week or end of a day or end of some month it becomes a finished product. So, raw materials after a delay becomes a finished product. So, until then until during the production process those are the kind of raw materials is available within the shop floor. So, delays involve stocks. It is not that everything whatever letter dispatch has to come as letters delivered it can be completely different things. Let us look at it as an example decouples rates of flow. So, let us see let us have a stock of say food grains. So, what will affect the stock of food grains? How will it increase? How will it decrease? So, let me just simply let us call it production, production rate. Let us call it consumption rate. Production rate consumption rate. As consumption rate changes the food grains change it reduces as production rate increases I get more food grains, the production rate comes down I get less food grains. But this is not a delay it is not that whatever I produce after some time I consume though it might happen. Production and consumption are controlled by completely different things. So, what do you think affects the production of food grains? As you can see completely different things can govern your flows and rates. But end result is what your interest in how much food grains we have. Just by mapping it out gives us some better sense because the rainfall follows some patterns and various other dynamics affects it. But eventually of course indirectly how much your will and inverse etcetera may be dependent on how much has been consumption rate in the past based on the different make some decisions or some feedback does occur. But this stock has helped distinguish between these two key things. So, link is their difference get accumulated here within this particular stock. So, to identify stocks you can use things like you know my difficulties when you look at a system how to identify stocks and flows. We can start using the units of measure. Stocks are quantities and associated rates are same units per time period that is quite simple. For example, if food grains are in tons then production also has to be measured in tons per time period say tons per year consumption also should be then tons per year. So, whatever the units of stock we have the same units should the flows also should have. You can remember because underlying you are having a differential equation right. So, the unit should match you can just subtracting which is has no unit mismatch cannot occur. Snapshot test this is like imagine you are freezing a scene that is you remove time from the picture and whatever is remaining you see those are the values of stocks. So, these can be both physical or it can be informational or it can be tangible as well as intangible things both can occur in this when you freeze the scene. Like when time is up population is known not the birth rate. If you can generate you need to look at two different time points. So, what you can see is actually the population or if we stop the factories production you can see the amount of inventories at various points in time but not the production rate. That is what I mean by saying that when you freeze time what happens. Stocks can be physical quantity information or even memories and beliefs right. So, what is the expected orders per week? What is the expected price of onions? So, we have some mental beliefs which are accumulated that also will be calculated as a stock. What is the say employee morale? What is the inflation expected inflation? Those are again values that we have in kind of what can you say. This forms part of our memories and beliefs which also is a stock. As I told stocks uses memory. So, all memories can be modeled as a stock. So, is of time units must be consistent like in the agriculture example consumption can be in tons per day while the production is in tons per annum. Simulation won't work unit should match. Close can be positive or negative please remember that we are just dealing with a simple simulation. It has no extra logic built into that. It is just a variable names for it. So, just by looking at the variable you may have a sense of direction of positive this cannot go negative and things like that but for computer it is not going to do anything. So, you have to be careful in defining whether there is sense of direction positive or negative and accordingly you modeled the system. Contents of stock flow network is conserved. So, whatever leaves the stock, leaves the flow kind of goes into the stock. Whatever stock drain it goes into the next stock and so on. It doesn't just disappear from the network. So, we have to remember that. Inventory of stock drinks. How do you think stock or flow? It is stock. What could be its units? Bottle. Procurement of soft drinks. So, flow what could be its units? Bottle's per some time period. If you want to, the stock is buying it every say week. We can put the week. Bottle's per week. Assigning homeworks in a course. Flow or a stock? There is only two people here. Some half of you have to be correct. Let us look at the word is assigning homeworks in a course. So, it is flow that is units. Let us look at questions per week. Assigning homeworks comes as a rate. The number of homeworks due that will be a stock or number of uncompleted pending assignments. Number of pending homeworks will be a stock. Assignments are given that stock increases and as and when you complete it, that stock goes down. Room temperature? Units? Ok, degree Celsius fine. Employee morale? Units? You know it cannot be unitless. You have to come up with some unit. We just come up with the, let us keep it simple and call it say percentage. Oh it is it? Sorry. Salary? That is not the units. I do not think so. Not everything is governed by that. Yeah. You can assume morale is extremely high. We will say about 100 percent is the morale. And then meaning I am just making the scale between 0 to 100. Promotion of associate professor to professor. So, flow can be number of say employees per promotion does not happen every day, month. Maybe we will put it a year. So, we will look at reasonable time scale, number of employees, rupees to dollar exchange rate. So, it depends on how we have model. So, when someone says auxiliary information, they are modeling something else and you just want that information for now and that remains constant and does not change to the system then we can consider it like that, but there is no option I have only stock or flow. So, I have not given the context, but here it is like a stock at any point in time even if it is now you know exchange rate right now. Various things you know how the stocks are being traded keeps changing this rupees to dollar, the rupees per dollar. So, the units is again comes to the same as rupees per dollar, entire units for it. So, this is your base we can actually try to quantify. We are very cool and we are kind of very used to things which are physical, you know informational to some extent. Once you get into memories and beliefs, it starts becoming controversial or rather subject lot of discussions I may prefer percentage, you may prefer a scale between 0 to 10 or minus 10 to 10 it is fine. So, we just pick up some units and we consistent with that unit and how it affects your or your team 0 to 1 and make a measure and then come up with the employee morales. So, this is not all whatever doesn't have order doesn't need to be exchange rate. So, whatever the expected value whatever is that current value can continue to be a stock. Let me do another example or let me draw it differently. Give me a minute. Let us take another example. See customer demand and you say customer demand occurs is usually units per week sales units per week, but then demand when you ask a shop or when you find out we all know the values of the demand. What is the forecasted demand for the next or the expected order? So, the expected order expected order per week could very well be a stock and this could be the change in expected order. So, the units for this is say pieces per week and change in expected order could be pieces per week which is units of the stock per week. Similarly, the exchange rate whenever you go there is a more money exchanger where the value is written for you. That is today's rate is not going to change it every minute for you. The rate is already given maybe computerized systems still some more updates the sucker and that acts as a kind of a thumb rule for people, but at any point in time you are able to freeze it and get that one. So, in that sense you are modeling rupees per dollar exchange rate and rupees per dollar exchange rate how it changes every minute because then model as a change in the exchange rate as a flow like this similar to this change in exchange rate and this can be a change in the exchange rate actually and having done that maybe I can give some more example like with units for example, let us take it as product price and change in product price. So, product price is typically say rupees per unit and change in product price is rupees per unit per let us assume it fluctuates daily per a day. Some can change over time over year. So, these also others some of it are very intuitive for example, population then you know population is a number of people and birth rate is people per annum, death rate is also people per annum. So, population is quite straight forward. Inventory production inventory is say shock keeping unit let us say all others cases are bottles in their example bottles production rate is bottles per minute consumption rate also can be in bottles per minute. This change though the direction is only one. So, some of the modeling convention it says has to do with this one also. There is actually bidirectional arrow to model it. So, as a change it is positive it increases exchange rate, change becomes negative it decreases the exchange rate. So, whether you are adding a negative or subtracting a positive. So, it is better to just do not worry about double headed arrow just put one headed arrow showing the direction and so that is the direction which is getting added. So, the value becomes negative it kind of subtract and it is inspired.