 We will continue looking at our supply chain model as we will be doing. So, you should recall this is the final complete retailer model that we developed in the previous class. So, if you have the model please open it. Now, set the customer orders to 10 plus step of 2 comma 10, run your model once to see whether it is all working. If you do not have it in this version just check if I mean version is available in Moodle you can download that also. The key changes are you should be able to have adjustment for inventory, desired deliveries, adjustment for intransit, desired intransit also being computed through supply delay and desired delivery as per little's law. Desire inventory is now based on inventory coverage and customer orders are fulfilled only if we have sufficient inventory. So, all those aspects should be captured within the model. You might have used a different customer order rate let us try this one. This represents 20 percent increase in the demand earlier we used some arbitrary numbers, but now we have to be little more specific. So, what you are looking at is order is 10 kgs suppose it is 20 percent increase in the end customer demand then what happens to order rates and delivery rates, inventories etcetera is what we can actually see 20 percent increase in one results in how many percentage increases in other. We have been looking at yesterday so all of you have got the model it is available right ok. Now, we will further improve the model and add next step. So, this model as you saw assumes that customer orders are not that are not immediately filled or lost forever right we have put customer orders is nothing but a minimum of inventory as well as the customer orders and found that. So, if you have order is higher than inventory then I do not deliver that and that order is lost. It may be true in many scenarios like a simple retail shops we saw as an examples, but in many other firms like say manufacturing firms or even distributorships they may not be able to deliver immediately. They usually maintain a backlog of unfulfilled orders and only when you receive when you have sufficient inventory then you go ahead and fill it. So, backlog accumulates a difference between orders and the shipments most manufacturers work like that. In fact, some of it we even do make to order kind of policy where they even start the production or procurement only after you make the order or even some retail shops like medical shops and other niche businesses where you may demand and they may procure it for you right. So, that aspect is called as backlogging and then fulfilling the order when inventory becomes available. So, that is one reason why we might have a backlog. Reason number one is if I am unable to fulfill the order immediately then that quantity the remaining quantity is kept as a backlog that is the difference between orders and the shipments. But backlog also arises whenever there is a delay between the receipt and the delivery of the order. Receipt when the retailer or whatever the player receives an order and the time he is going to ship the order whenever there is a delay it has to be accounted until that point in time as a backlog. Delays could be various reasons like administrative activities or need to configure the product as per customer specifications. For example, if you are going to buy a car because you may not be able to just walk in and drive away with a car you may have to go then you have to give your choice and under preferences then all your bank details and you may need to pay upfront some money, you may need to if you are buying on a loan then loan paper has to be processed. But until then that order is already in backlog. So, there may be some administrative delays involved but that order officially then goes into a backlog and once all these processing are done which includes administrative activities or need to configure product as per customer specifications or by delays in shipping to the customer site even it remains in the backlog until it actually reaches the customer. So, for all these reasons we may choose to model a backlog. So, the first task for today is to include this backlog in our previous model of a single player supply chain model. So, let us take the first case when the orders are we do not have sufficient inventory to fulfill the orders then the remaining quantity is backlogged and filled later. So, to illustrate that let us take these two scenarios the following scenario illustrates the behavior with the backlog suppose customer order is 10 units, you already have a current backlog of 15 units and current inventory is 40 units. That means we have sufficient inventory to satisfy both the customer order as well as the backlog. So, my sales rate becomes 25 units and new backlog is 0 since you already fulfilled this backlog the new backlog becomes 0 change in backlog can be captured as a minus of 10 units we will come to that or consider second scenario. So, here I have sufficient inventory to cover both order and backlog hence I am able to satisfy both of them so 10 plus 15 became 25. The second scenario customer order is 10 units current backlog is 20 but current inventory is only 5. So, in that scenario my sales rate is governed by the inventory of 5 units so among 20 plus 10. So, total to be shipped is 30 units but unfortunately we are able to ship only 5 units so new backlog become 25 units that is whatever is shipped out is only 5 units. So, difference between the customer order and sales rate is put as a added to the backlog. So, we are going to model this within our existing retailer model you save it as retailer backlog model as a separate model. So, to do this you are going to create a new stock called as backlog and backlog changes by the quantity of customer orders minus sales rate. So, this is the flow inside the stock the change in backlog will be governed by this equation. But you have to come up with the equation of how to determine the sales rate. So, let us take 10 minutes to model it. So, joining us now what you are trying to do is include a backlog in our existing retailer model that we used last class. So, you have the retailer only model the single player model with the adjustments for supply line, adjustments for inventory and also the maximum sales rate also incorporated the final model that we built this one. So, we are going to modify this model by including backlog. So, to do that you have to include a backlog and if it is a stock then some there has to be a flow the flow is also given the equations or flow is given. Now, how do we relate this backlog to my sales rate you can figure out the equations by looking at the two scenarios that is illustrated there. So, that is the purpose of scenario it shows how the it shows current backlog, new backlog, it shows the customer orders, it shows the what is the sales rate using which and your common sense you is be able to figure it out. So, if you see the above scenario the sales will be minimum of inventory and customer orders plus backlog, should minimum of that correct, should minimum of inventory and the sales rate should minimum of earlier you had sales rate minimum of inventory and customer order. So, it will be minimum of inventory comma customer orders plus backlog for it will logically work. So, just incorporate that then you can adjust it for invent what can I say units error basically this is what you want to do right sales rate is minimum of inventory and customer orders plus backlog. But if you do this there is units error mismatch that you fix it instead of inventory what did you use, you use max sales correct you change that inventory to max sales. That means instead of backlog what you need to do you figure it out instead of inventory we are using max sales you already modeled it right. So, this is the logical equation that we will have even if you do not care about units error still you must be able to finish this model based on these things written here then your model must be able to run then we can set the initial value of backlog to be 0 initially it should be 0 ok. So, zoomed in portion of the model is shown here along with the underlying equations there is stock inventory sales rate max sales minimum order time exactly the same as before and customer orders. New thing to be added is backlog change in backlog just as we described this change in backlog was given as customer orders minus sales rate. So, connected customer order and sales rate to it and then we write the equation for that. Now, sales rate is minimum of inventory backlog plus customer orders, but since I cannot directly add inventory I had to first convert it into max sales as per inventory and give it into the sales equation and backlog similarly as to be converted backlog to be cleared which is nothing, but backlog order minimum order processing time that units max then again if we did it into sales rate where sales rate equation minimum of max sales which is kind of equivalent to your inventory and backlog to be cleared is equivalent to your backlog. So, this is max sales and backlog to be cleared comes in only for units the award units error please incorporate this model then this is what I want you to do. Simulate the retail model with and without backlog and compare the results with backlog case show a graph without backlog case create the graph of customer order sales rate and order rate in a single screen and another one having inventory desired inventory and backlog in a single graph and observe the percentage change the input and relate to the percentage change with respect to the amplitude of the above variable or input change 20 percent. Step of 10 increase to 12 plus 2 units 20 percent increase in step input results in how much percentage increase in order quantity and including backlog should it remain the same or different. So, that is other aspects that we have to do in this course analysis is not enough if we just build the model and say here are the results I expect you to interpret it how much percentage increase is happening is there a difference between when we did not have backlog and sales lost plus as we had backlog and they are accounting for it is that change in amplitude what about the duration is there any fluctuation around the mean because of that has to be observed. I will give you a flavor of things what kind of scenarios you may end up doing. So, now let us move on to a two player supply chain consider two player supply chain the retail distributor model we already built the distributors customer order are from the retailers orders and retailers order rate is set by distributors sales rate we have made that that models available in model you can use it. Now, incorporate the backlog aspect in both the for retailer and distributor in this model we will make that as the base model and in that base model do these settings for both players the inventory coverage is 4 days time to adjust inventory is 3 days in transit 3 days minimum order passing delay is 1 day smoothing factor is 0.2, but also include a supply delay we had a supply delay is delay fixed instead of that replace it with a average 5 days delay of the third order material delay using the Wensum function delay n you do not need to incorporate for 3 stocks instead of delay fixed replace the functional delay n then some help will tell you what to do once you read it you will be able to figure out what what is to enter and then just start the model dynamic equilibrium. So, once you have this base model we will run couple of what if scenarios to understand the implication of different policy decisions within our two player supply chain. Since you already built the backlog model once you must be able to copy paste it or replicate it quickly in both the case both the locations. So, we have backlog at the retailer center also backlog at the distributor side also in a default model other than the supply delay everything should be the same numbers for 331.2 should be exactly the same all you have to do is incorporate the backlog and set order rate as 10 kg per day and time step as 0.125 or any number lower than that there is only things you have to incorporate this will take some time to make the backlog, but should not take you more than couple of minutes. So, one of the purposes of building simulation model is to conduct water analysis evaluate various scenarios or policies as you may call it or even to do sensitivity analysis at different terms you may use. So, once you have the base model we are going to use it to evaluate and understand what happens when some things change. So, we can build our intuition better about the performance of the system. And only way we will get it is if we actually simulate it to see and relate the variables. If something changes then may order fluctuation is becomes higher or lower eventually that is the intuition you want to build. This is a smoothing factor which I wrote as point two refers to that fraction adjusted in your expected sales rate for the same thing. To figure out what are the important ones you need just think about what we are modeling here. We are saying customer order exhaustion is fine, but what decision we are making ordering decision. So, you want to see whether how that order decision changes with respect to the actual end customer sales. And what are the things that is going to contribute your cost your inventory how much you are ordering, backlog those are things going to add to your cost. So, then those becomes more interesting variables we do not plot this is what we started.