 So, let us start with the very basic model, let us say retail sells a particular product in KGs. Let us assume demand is exogenous, how the retail likes to maintain a desired level of inventory. Inventory falls below the desired level, retail orders from factory, orders stop when stock reaches the desired level. It is a very basic model, a direct way that we have actually built similar models earlier is to model it as follows where the desired inventory is provided, inventory gap is calculated by the retailer who then desired what is the order rate depending on how long it takes to adjust the inventory and accordingly order is placed and then inventory increases, sales rate is exogenous to the inventory. So, this is a typical negative feedback system with a exogenous outflow is the model that we actually see here. So, let us open Vensim and start modeling this, you get the values, you can assume the following, adjustment time is 3 days, you can take the simulation run length is 100 and the simulation length as time step as 1 and time units as days, go ahead and build this model, the kind of behavior can above system exhibit. So, this is a starter negative feedback system, this is a simple goal adjustment behavior right. There is nothing, there is no table functions, there is no complexity, inventory gap is nothing but difference between desired inventory and inventory, desired order rate is inventory gap divided by time to adjust inventory which you might have guessed based on the variable names as well as the causal links and order rate can be just simply set as equal to desired order rate. So, kind of behavior can above system exhibit, it is a negative feedback system, simple goal seeking behavior. So, when you keep the sales rate as 0, so then the behavior you will see is there is nothing, it will be just a constant line because initial inventory is equal to the desired inventory both are 200 right, so you expect to see a constant line. So, this is what we call as dynamic equilibrium, system is dynamic equilibrium, now we can subject it to some changes in the exogenous variables for example, in this case it is sales rate and see what kind of dynamics we can exhibit, we know that this system will exhibit a goal seeking behavior. So, if suppose a sales rate increases to 20 units at time 5, then we expect the system to reach this new goal. What will be the steady state value of order rate? What will be the steady state value of inventory? You can do this without simulation, what should be steady state value of order rate? Order rate will be equal to 20 right, in equilibrium or steady state the sales rate should be equal to the order rate, so then order rate is 20. What will be steady state value of inventory? Will it remain at 200 or not? It will be less, how much less? The time to adjust inventory is 3 and order rate is 20, so it should be about 140 or why do not you simulate it in C? When this constant exogenous variable then the steady new steady state value will be the, will take an a value less than, less, the less amount is the product of the steady state sales rate and the time to adjust inventory. So, does it reach 140? Save this model as inventory 1.mdl file, so all of you hopefully got this model. So, let me just put sales rate is 0 plus step of 20 comma 5, run at order rate and sales rate, if you plot a graph after sometime the order rate approaches and as a goal seeking, typical goal seeking behavior it approaches the sales rate value to model inventory. Inventory falls down and stabilizes at a value of 140. We have already seen this when we were discussing negative feedback system in case of constant exogenous output your steady system reaches equilibrium, but at a value different from the desired value. An amount will be equal to the time to adjust inventory multiplied by steady state value of the sales rate in this particular case. We can expect a similar behavior even if we change the desired inventory, instead of changing the sales rate even a desired inventory from from 200 to say 220. We can expect similar behavior where your order rate will still exhibit a exponential chain or a goal seeking behavior as per this and it will quickly fall back down to 0. Now, let us go back to the slide and ask the next question. So, the behavior can exhibit is a goal seeking behavior. Now, to show this model and people are not happy because the actual inventory does not remain at the desired level in steady state. What we want to steady state was to be 200 kgs, but steady state value the simulation predicts that it has to be 140 kgs and that is going to be keep changing depending on how much we have the sales rate. So, more of sales rate falls down then again my steady state value is going to change. But how can we change the decision rule to ensure that it actually maintains the desired level in steady state? How can we do that? Some of the relation to the sales rate we know that every week the sales rate is removed, but I only add one-third of it to the order rate and one-third of the difference is added to the order rate. So, in first week if you already know the sales rate is it possible for us to give that user sales information sometimes reasonable to assume that we know the sales rate right. After the sales has occurred the sales rate is assumed to be known. So, what if we are able to use the sales rate in our model? So, let us see whether it can maintain the desired level of inventory. Let us introduce a new variable expected sales rate. Let us just make it expected sales rate equal to sales rate and let us make desired order rate equal to expected sales rate plus whatever the equation you wrote inside your desired order rate. So, let us just do both these. Introduce a new variable expected sales rate, connect sales rate expected sales rate and decide order rate now has an additional input called expected sales rate plus your inventory cap divided by time to adjust inventory. Let me model it along with you guys. Variable expected sales rate arrow sales rate is expected. Expected sales rate desired order rate equal to desired order rate will be this. Inventory cap by time to adjust inventory plus expected sales rate. Got it? Right forward. Let me simulate. I am not going to overwrite. Let us look at the order rate and sales rate graph. Order rate and sales rate are exactly the same. I just overlapped the previous simulation run along with this one to get the exact same behavior for the order rate and sales rate. So, that means, addition of the sales rate actually did not affect my order rate. Is that so change in dynamics? Actually this is the order rate and sales rate. Now, it closely resembles the order rate. We will get a step graph here. Right immediately changed to that. Just ignore a previous statement. Previously, we got these graphs. For step change in sales rate, we got exponential smoothing behavior right here. But when we changed it to include the order rate, it immediately reacted and the order rate value became equal to sales rate almost instantaneously because of which my inventory is a straight line in this case as compared to the previous case where it dropped down and became came to 140. So, desired inventory is now equal to your. So, inventory is equal to desired inventory because we are at the sales information with us which we accounted for in a decision making. See that if this is a sales rate, then we accounted for that in order rate anticipating the sales is going to happen which immediately started offsetting the sales and the order started offsetting the sales and we meant to continue to remain constant. So, save this as a separate model. Now, let us understand what we did in the model. We just included the sales rate and immediately tried to adjust our order rate. But in reality, that is difficult to happen. Only at the end of the week, you know what is the week, what is the sales in the previous week? At the end of the week or end of the day, say your units are day. It is end of the day, you know what the sales happened in the previous day and based on that information, you want to order for the next day that is tomorrow. So, there is some sort of information lag which is involved before you can use the sales rate in your ordering pattern. So, let us try to capture that information delay now explicitly. The retailer does not instantaneously use the sales rate information to make decisions that is the demand. Instead, the retailer smooths the sales rate and uses long term average to make the ordering decisions. Just because sales rate immediately changes, he may not react to the change because we do not know the short term or long term changes. So, as soon as sales rate changes, he adjusts this expected sales rate slowly over time before he uses it in a decision making. To model that, we should now improve on our model here. So, this is where you should notice the information that, notice the modeling aspect where if we use as a variable versus if we are going to smooth it, what is going to happen? That is what we are going to find out. To do first order exponential smoothing, let us do it explicitly. So, let us model the expected sales rate as a stock and do a first order exponential smoothing based on that. So, we will update the model and observe dynamics assuming a smoothing factor of 0.2. So, what you are going to do is we are going to introduce a, instead of this causal link, there is going to be an information delay here, but we are going to model it explicitly. We are not going to use a smooth function or anything. We are going to model it explicitly. To do that, just stay with me here. I am going to delete this, select the variable, introduce expected sales rate as a stock, change in expected sales rate, smoothing factor, what is this? So, smoothing factor, let us start with 0.2, today is unit change in expected sales rate, the sales rate minus expected sales rate multiplied by the smoothing factor because I am just adjusting it based on the current value of the stock. So, sales rate increases, my expected stock also need to increase. So, that is why we are doing sales minus the expected sales rate multiplied by the smoothing factor of 0.2. So, unit of this is kg per day, expected sales rate. So, initially sales is 0. So, we can have expected sales initial value is 0. The units of that will be kg per day, but desired order rate continues to remain the same as expected sales rate plus whatever the adjustment in inventory. So, that equation does not change, but you just have to open it and repeat it again. So, what we have modeled here is a classical exponential smoothing forecasting method. So, in any other operations management rated course, if you are studying about exponential smoothing, that is exactly what it does, where the smoothing factor is nothing but you are probably calling it as smoothing constant, it is the same thing. You got this, let us simulate, let us look at the order and sales rate. Let us observe what is happening to the order rate. Sales rate immediately increases by a step, order rate actually increases beyond that and then saturates the value of 20. The inventory does initially fall down to represent the actual thing that has happened. So, suddenly on day 5 when inventory or sales increased by 20, your inventory will fall down. So, that is actually captured on day 5, it is increased by 20. So, that inventory has to fall down by 20 and it takes some time to adjust. But after it is adjusted, over time it is able to recover and reach back the same desired value of inventory of 200. So, even though we introduce a new information delay, that only delayed as reaching the desired value of inventory. It did not reach any other new value of desired inventory, it reached the same 200 value of desired inventory. But after some delay, it is attributed to the information delay that occurs for us to account for the change in the new steady state value of sales is being captured in this model. However, to achieve that, the interesting part is your order rate, here you can see all the three order rates in this graph. The green color or the blue color represents the first order exponential and the first model that we wrote, goal seeking one. In second one, if the instantaneous sales rate was available, then immediately I could react, but not a very realistic model. But once you added information delay, we can start to see, it is not really goal seeking behavior, we are starting to see the initial aspects of a oscillations within the model, whether it is just a one single oscillation. So, this point here, we can refer it as amplitude, there is a maximum in which the order is ever going to go, then followed with your phases. So, order increases beyond your sales rate and then gradually falls down to achieve the desired value. Let us observe how the expected order rate, expected sales rate, sorry changes, previously expected sales rate was changed instantaneously because you use instantaneous information, but now it will gradually approach because it is a first order delay and it is a goal seeking behavior. Any questions on this? It is clear? Fine. Now, let us make the model a little more realistic. Assume smoothing factor is one. So, what is smoothing factor one present? See initially say expected sales is zero, sales rate became say 20. So, 20 minus 0 is 20. So, if I give smoothing factor one that means, entire 20 units is added in the immediate period. So, expected sales rate will be equal to the sales rate immediately. Let us not use it instantaneously. Let us see what happens in that scenario. So, when say smoothing factor is close to zero or let us say around 0.2 and stuff, then we give higher weightage to the, we give lower weightage to the recent sales information. So, it takes longer to achieve steady state, but when value is closer to one, we give more weightage to the current sales information. So, let us see what happens. So, I just made it one. Let us simulate. Now, let me call it 3B. Let us see what happens to the sales rate graph first. The sales rate does almost immediately become 20 in this case versus previous case where it took long time to be 20. Now, I have one more graph called inventory 2. So, this represents the previous case when there is no stock to directly connected expected sales rate to sales rate. So, compared to that, there is still a one period lag within the system. That means, as soon as he started looking at the information delay, the minimum of one period lag is already introduced into the system. So, that you have to be careful of. That means, at the end of today you got the sales information and in tomorrow's order you are saying out today sales was 20 units. So, tomorrow let me order 20 units. So, that is what you are doing. In the previous case what you told us today sales is 20 units. Let me order 20 units today for using today itself. So, that is our unrealistic part there where we knew sales in the end of the day. So, we are using it to adjust the inventory for the day 2 that is the next day. So, there is a one period delay. Let us see what will happen to your order rate with a lot of lines. This one here with a sharp peak that is the inventory value is the smoothing factor is 1. It still overshoots and then has exponential decay or goal seeking behavior to reach your steady state value. So, higher the smoothing factor, faster it is you are going to reach your goal. Let us look at inventory. You can observe inventory as a sharp fall after immediately starts to rectify much earlier. So, smoothing factor is lower then you are quickly reacting to recent changes. Whether it is desired or not depends on the scenario, but in this particular case it results in reaching a desired level of inventory much earlier. So, all we did was introduce with our physical flow of material and information delay within the system which itself allowed it to overshoot its goal and then again it fell back to reach it. So, that is like kind of the origins for the oscillations that is occurring whereas, information delay within physical system that is going to lead to some oscillations.