 So, in today's class we started looking at a basic inventory model and then slowly started to include the supply line aspect of it as shown in this stock flow diagram and we found that this is causing unnecessary oscillations within the system because the supply line information was not used in the decision making of computing the desired order rate. So, that is where we kind of exploring the model, today's class we will further expand on that and include different aspects in the decision making and move towards the supply chain models. Now, first step is let us figure out how to account for the supply line in the decision making. What I mean by supply line is the one that is shown in red after things are ordered after some supply delay things are getting delivered, so until then the quantity remains in transit. So, this is what physically is happening we are captured that in the physical aspect of it, but in decision making you can find that none of that information is actually feeding into this decision making of the desired order rate. So, one way to account for it, how do we consider supply line that is the pass and pending orders in transit when we make the new ordering decisions, any thoughts, how we can include the supply line decisions in a decision making, supply line information in a decision making. So, let us the only other structure that we are familiar with is a simple negative feedback kind of system where when we had only the inventory we had a desired inventory and then adjusted the desired inventory to assure us a good quantity getting delivered or appropriate quantity getting delivered. Let us see whether we can mimic the same decision here. Before that I hope all of you have the model in the previous one, you have all this model, if not you can download the latest version. So, let us see the dynamics before we proceed, so that we know what we are trying to correct. When we ran this model, we found that there is a dynamics in the order rate inventory fluctuates and the quantity in transit is opening of the grasp for each order rate fluctuates and reaches then the desired new order quantity of 20 units initially it was 0 units, system was in dynamic equilibrium. The quantity in transit fluctuates and finally settles out at 40 units and inventory after fluctuating comes to the desired value of 200 units. So, that is what we have, let us go back to our model, what are we going to do? We are going to adjust the in transit inventory in a similar manner as we have been adjusting the end inventory. So, let us define a desired in transit inventory and say that you know if the decide based on desired inventory level, we will go ahead and adjust the in transit inventory to meet that desired value and see whether that can help in minimizing our dynamics. We saw that the inventory was able to reach its desired value, but the in transit inventory it reached some value of 40, we do not know what it is, so we will let us try to figure out how we can do that. So, once you do that we will update the desired order rate to include this adjustment. So, let us I would like you to update your model as shown in this diagram here, few changes are after 10 minutes you will figure it out, for now we will we will assume some constant values. Let us see. So, we have the in transit there is no change in this model here, but let us observe what I did here, you save you save as a current model to save inventory SL.MDL meaning supply line is now considered, the inventory gap is removed it is now called adjustment for inventory. Try to update the equations for that adjustment for inventory, then we have the desired delivery delay, which is now the sum of adjustment for inventory in expected sales. All the thing in red represents the decision making to include the information about quantity in transit. So, quantity in transit and desired in transit quantity we are taking a difference of it in adjustment for in transit, then divided by time to adjust in transit and order rate is now equal to the adjustment for in transit plus what is the desired delivery that we want. So, you got the section updated in your model, then let us look at the underlying equation. I am just starting with the equations for the stocks, the equations for inventory quantity in transit, delivery rate is delay fix, this was in the previous model you do not need to update anything here, sales rate is nothing but the integral of change in sales and change in sales, nothing but sales rate minus expected sales rate multiplied by a fraction adjusted this from the model that we just saw, all these are exactly same as the previous model. Now, let us look at adjustment in inventory, so your adjustment in inventory to be the difference between a desired inventory minus your actual inventory divided by time to adjust in inventory. So, your adjustment for in transit will also have the same form, nothing but desired in transit minus in transit, if you say quantity in transit, but I think you will get it quantity in transit this is the stock in transit quantity divided by time to adjust in transit. So, these are two variables that we are having. Now, we started to define new variables, one is called as a desired delivery or to be desired delivery based on your stop flow diagram desired delivery will be equal to plus expected sales rate plus adjustment for inventory, the desired order rate is desired delivery plus adjustment for in transit, an order rate is equal to desired order rate for now, you have got this. The sales rate we assumed it is 0 initially and then there is a step increase of 20 at time 5 that is what you assume for sales rate, the sales rate we took it as 0 plus step of 20 at time 5. So, only equations you may need to fill up are these, the stocks these are only new things that has come up all others are you will get it from the previous model itself only the last five you have to check. Desired inventory we had set it at 200, desired inventory was 200 units, what do you want to keep it desired in transit as initially there is no orders. So, let us keep the desired in transit as 0, there is no orders right initially. So, let us keep the initial in transit as 0 or as a desired in transit as 0 as well as initial quantity of in transit also as 0 which is the default on any way I think and just check it. Just check if the initial value of in transit is 0, the quantity in transit let us go back let me find out what it is. I think I just said for time to adjust for inventory what was the value we took 3, then use 3. Time to adjust in transit also let us keep it 3 days, let me see what I have let us keep it 3 days. There is time to adjust in transit as 3 days, time to adjust inventory is also 3 days, supply delay will be 2 days if I am right. Now, this is important structure you have to understand, we now split the desired order into 2 parts, earlier we called this desired delivery as a desired order rate that is the sum of adjustment for inventory and the expected sales as equal to order rate, but now we are splitting into desired delivery, why is that? See here, if you recall the first model that you ever built where we assume supply is infinite and instantaneous as soon as I want it I will get it right. So, that is not actually the order rate that actually what we wanted was things should be physically delivered to us and just by using this adjustment for inventory and the expected sales we can very well control the inventory to the desired levels that we actually want correct. So, this sum of these term here will help us manage the inventory stock here. Now, but in the final order what we want to do is account for this in transit quantities that is already in transit or quantity already in transit. So, that is why we want to give a distinction between them which is why we call it calls a desired delivery a desired order rate. So, let them simulate it, earlier recall we had a dynamics in order rate let us see what we get here now we do not get that big of a we do not get any oscillation we get an overshoot and then slow decay to the desired level that we want there is an overshoot, but then there is a slow decay to level we want there is no oscillations as we saw earlier. You can compare the order rate I hope all of you know how to do multiple things in a graph you just click order rate click shift and then click sales rate. So, both the variables are selected so that you can superimpose both of them like this this is the actual sales rate and this is what the retailer has ended up ordering upstream you can imagine say order to some distributor this is how much is the quantity that we are going to order. Let us compare inventory and desired inventory select both ok earlier model inventory model is in equilibrium that is good, but what we see here is desired inventory remains constant 200, but your actual inventory because of adding the supply updating a model suddenly my actual inventory is saturating at not saturating reaching steady state at 160 units 160 units in a previous model when we did not account for it we found inventory reaching 200 units, but right now it is only reaching 160 units let us see what happens quantity in transit and desired quantity in transit. I hope you have put desired quantity in transit as 0 so we should get a value of 0 only in transit minus 1 oh no ok I will put the units that is why the problem this is kg see if you keep the both these units same first let me show the problem first let me show the problem and then I will come back then it is simulated I wanted to do this observe the graph carefully what it has done is desired quantity current and then there is open empty bracket here quantity in transit current and there is a bracket kg. So this quantity in transit uses units of kg and kg is plotted in the secondary axis secondary y axis this one is coming here on the left side. So if you want both the graphs to show the same scale then unit should match the when some by default of units are different it will plot it in different axis as much as it can select three different variables it will do something the first is fix the units this is kg how you do now you again simulate click quantity click in transit I will get a single nice graph ok some of these are just unplanned learning points yeah so in transit increases from 0 initially it is fine we are able to meet the desired as well as the desired value same as in transit value but after some time the actual value increases to 40 while the desired will remains at 0 because we set it at 0. So we just observe the results system reach equilibrium yes it reaches equilibrium what are the equilibrium values of the stocks we found that the in transit stock is reaches 40 and the inventory reaches 160 both are different from their desired values.