 So, today's class we look at how to model information delays in a system dynamics model. See, when we want to make decisions, it involves the use of information and this getting the information their entire feedback mechanism to get the information and based on that make the decision is front with lot of delays. The delays could be in the form of measurement or perception of variable, updating of beliefs such as future inflation rates or forecast such as expected order rate, there are some examples where information is being used. So, whenever decision maker has to make a decision, he uses some information about some perceived value or some reported value, right. That means he is going to use information based on the past, the information of the past is being used and it takes in time to gather all this information, process information and then finally, use it for making whatever decisions that we want. Sometimes we have formal process of processing the information like when you imagine say like a demand forecast, you may think of a process where you know the actual sales data is collected and based on that I am going to estimate what is the forecast at demand and then upcoming week or upcoming month or upcoming quarter and use it to make our decisions. But most often it may not even result in such a formal structure, the sales regional sales manager may just go with his gut feeling to figure out what is going to be the sales next month, right. But even then he has to update it or kind of you know even though he may not have formal process, he does have a process through which the sales manager is going to estimate what is going to be the expected sales next month. So, we are trying to capture that kind of a process in this kind of information delayed. But information delays cannot be modeled the same way as we did for material delays. So, when we did materials for example, if let us say when you post letters, it goes through a system, it is in the tracks and vans and planes etcetera before it reaches destination. Suppose, there is additional delay that happened, maybe trucks got cancelled, maybe there is a workers strike, then what happens, the letters will get piled up. It gets piled up at different points before the strike it gets resolved or maybe the you know the congestion gets relieved and then again the letters get delivered. So, in that sense when you think of systems such as the postage postural delivery system, the letters are conserved just because there is delay people do not just throw away the letters. However, after some delay it eventually gets delivered, but information delays are not like that. So, in information delay the material is not conserved that is the key thing. Information delay does not involve conserved flows that is whatever goes in does it necessarily make it out after a particular delay right, we keep updating it based on the current information and then so that is how the information delay or information processing works. So, let us take up a very just like we did with material delay, let us take up some simple cases of how to model information delay and look at higher order models. There are some parallels like similar to material delay, we have a first order information delay and higher order information delays. So, we will be looking at that in today's class. On a simplest form of information delay is called as exponential smoothing or first order exponential smoothing for adaptive forecasting or first order adaptive forecasting. Those of you who have done a course on say basic course on operation management or something must have come across this forecasting method called exponential smoothing there is nothing but updating their information about the forecast based on the present value of the actual sales or demand that structure is called as a first order exponential smoothing and that is one of the first basic models of information delay as we will there is a first belief or perceived value gradually adjusts itself to the actual value of the variable. Once the variable changes holds constant after some time it reaches that particular value. So, let us see what is the basic stock flow diagram of that is delay, first order exponential smoothing is what we are going to do, there is nothing but all I just cited change in perceived value which is nothing but x minus x bar by your adjustment. This is a first order information delay or first order exponential delay or first order adaptive smoothing there are various terminologies that is used to represent the same thing. Let us take up a simple example of a forecasting example. So, in this forecasting example let us map it similar to this let us say we are going to forecast the expected demand rate or expected order rate of a particular inventory stock item say sales change in expected sales rate let us define it as say actual sales rate let us call it as S, let this be S, S hat difference in sales lingo are similar to exponential smoothing forecasting we can call it as a smoothing constant say alpha. So, in this case we define the change in expected sales rate or dS hat by dt as simply as S minus S hat into alpha where alpha is your smoothing constant. So, if we take a time difference equation of the same which will be similar to your exponential smoothing forecasting. So, what this model is doing is I have a let us assume current sales rate and the expected sales rate is the same say let us say 100 units it is been selling consistently 100 units and I am forecasting also saying expected sales rate of next week is also 100 units. Now suddenly the sales rate jumped to 120 I may not immediately change my expected sales rate to 120 I may just say ok sales has increased 120 let me wait and watch what happens the following week and following week and so on only if the sales is consistently 120 for many weeks together then it is ok looks like sales has stabilized at 120 now. So, now I will move towards this 120 but I do not just remain ideal at 100 I keep adjusting towards the actual sales by small fraction alpha, alpha fraction of the difference I keep adjusting towards the new target. So, if the alpha is very small that means I am not giving too much weightage to the new value of sales I keep closer to the old value of sales if alpha is say 1 that means whatever the difference I am going to immediately react to the new value of sales if sales jump to 120 I want to immediately adjust for that and keep reacting. So, that is what this model is going to do initially S and S star say is equal at 100 now if S became 120 so 100 minus 120 there is 20 units. So, I have to adjust for 20 units my expected sales rate has increased towards the actual sales rate. So, this is the actual information that is happening this is what I expect it to do. So, I want it to become as close to the actual sales as possible.