 Hello and welcome back to the NPTEL course on Supply Chain Digitization. I am Sushmita Narayan, a faculty in the operation and supply chain management area at IIM Mumbai. We will be continuing on the lecture on channel structures in the supply chain. In this particular lecture, we shall be continuing upon the example that we were discussing in the previous lecture. As we have already discussed in channel structures in the supply chain, we have understood that there can be possibilities for supply chain coordination through decentralized and centralized channels. So, we have been considering an example of decentralized and centralized decision making, considering a news vendor problem. And first we are trying to understand the deterministic setting of the news vendor problem. And then we will move to the probabilistic setting of the news vendor problem. So, in this session, I am going to continue upon the deterministic setting that we were discussing in the last session. And to conclude upon some of the ideas that we had brought forth. And then I shall introduce the probabilistic setting for the same news vendor problem. And we will also see how they are different from each other and what kind of challenges we may see. Again, when we talk about what kind of a decision making that we are trying to understand, we had already seen that there are a variety of decisions that can be taken place in a supply chain. And in this specific context, we are looking at the decision making related to how much to order. So, in the last example, we had considered 7 different scenarios which are looking at deterministic setting for demand. And we said that you know it is known for sure what the demand is going to be and 7 such scenarios could be considered for our analysis. And we had come to the conclusion that there are some cases in which one of the parties is going to be profitable and not the other. And in some cases, we found that both the parties are going to be profitable. And this leads to some very interesting ideas and insights when it comes to what kind of decisions would be taking place in the news vendor problem. Now, remember I said this is a deterministic setting which means the demand is known with certainty. And in this specific example that I have considered, we are looking at the news vendors profitability to be occurring when the order size placed by the news vendor is more than the demand for sure, but less than twice the demand which is going to be seen. So, we will examine this particular case a little bit more in detail in the next slide. So, if I were to consider this particular case that we are going to see, the same problem I am extending a bit more in order to understand the payoffs of both the news vendor as well as the supplier. And then we are going to see how this is going to be different or same and what are the impact of the decisions of the news vendor. Now, remember when we said that we are looking at the payoffs of the news vendors and the supplier and decisions, we need to remember what kind of order is there to the decision making. The first player who takes the decision is actually the news vendor. And the supplier has no other option, but to either accept what the news vendor orders or to reject it. This is the only decision that the supplier can actually take. So, over here we can see that the news vendor is actually determining for the entire supply chain what order gets placed. So, if we were to consider the decision making and the sequence of payoffs that we observe over here, when we consider the news vendors payoffs, what I have done over here is looked at all those 7 scenarios in which there was a market demand. These are the same market demands that we saw in the previous example. And these are all possible orders that the news vendor could actually place. So, when the demand is 0, we are considering that the news vendor can actually order 0, 1000 units, 2000 so on and so forth up to even 5 lakh units. And when the demand is 2000, the same possibilities exist for the news vendor. Now, remember when we looked at scenario 1, we said that when the market demand is going to be 0, the news vendor was actually ordering some amount. And we can also have a look at what that amount was. If you consider the previous example, when the demand was 0, the news vendor was ordering 2000. When the demand was 2000, there were 3 options that the news vendor actually looked at. So, let us go and see whether that would be the best decision. When the demand is 0, the best decision for the news vendor is to not order anything. You can observe that as the news vendor starts ordering more and more, there is actually no possibility of profit occurring for the news vendor. So, the very option of 2000 which the news vendor was actually placing is going to give him or her no profitability at all. So, this decision will actually not be taken. Now similarly, when the demand is 2000, we had seen in scenario 2, the news vendor was ordering 40000 units which is coming over here. And as you can observe over here, the news vendor's profitability is not positive over here. And the best decision for the news vendor is actually 20000 units. So, even this decision will not be taken. In fact, you can observe that even for larger amounts that is 3000, 4000, 5000, 10000, above 2000, in those cases also the profitability is actually reducing. So, the best profitability occurs at 2000. Now, why is this the case? Let us remember what happens when the news vendor places an order. When the news vendor places an order of 2000 units, then he is going to be matching the demand with the order size equally. Now, as a result of this, his profitability is going to be the highest. Now, when the demand is 2000 and the news vendor actually orders more, 3000 units, he is ordering in an excess of 1000 units. Now, when the news vendor orders in an excess of 1000 units, remember the only amount which gets sold is the market demand. So, that excess of 1000 units have been purchased, but not sold. So, that loss is accounted due to the cost of purchase as a result of which the news vendor's profit actually falls from 20000 rupees to 10000 rupees. And as he starts ordering more and more, he is accumulating just a lot of newspapers with him or her and is not selling these newspapers. As a result, we are looking at the case where the news vendor is simply purchasing too many newspapers and is not selling them. So, there is a cost of purchasing in excess. Now similarly, if I were to consider what is going to happen over here, we can observe that when the order size is going to be lesser than 2000 units, then the news vendor can be profitable, but it is not the best case. Similarly, when the news vendor orders nothing, there is no profit, no loss. So, for the case of the news vendor, you can observe that the profitability is actually increasing right from this point onwards. It reaches a maximum over here and then it starts reducing further and further like this right. So, you can observe that this is not the best possible option and the best possible option is happening at 2000 units. The same case is observed in scenario 3 and 4. In scenario 3, we had considered that the news vendor is going to not match the demand or let us have a look once again in case we are confused. In scenario 2, we considered 40000 units and in scenario 3, we said he orders 1500 units. So, in scenario 3, we can observe 1500 units is somewhere between 1000 and 2000. So, over here, if we were to consider the profitability that the news vendor is going to make, it would be somewhere between 10000 and 20000 units. It would not be 20000 units or 20000 rupees. So, as a result, the news vendor will not take that decision right. So, this decision is not taken. In a similar way, this is the same payoffs that we are observing as compared to scenario 2. So, in the similar way, the best decision actually lies over here. So, even if you were to consider the demand as 2000 units, the news vendor will order only 2000 units. Even in scenario 3, that would be the better decision rather than ordering 1500 units. And finally, in this case, we actually saw that the news vendor is ordering 2000 units and this was the best decision taken by the news vendor. And as a result, we can see that when the news vendor is matching the demand with the order size, the profitability in that scenario is going to be highest for the news vendor. Now, in scenario 5, 6 and 7, we considered the case where the news vendor is going to be directly matching the demand in terms of the order size. So, you can observe this similar kind of scenario over here, where the demand is going to be 30000 units. If the news vendor orders nothing, there is no purchase which happens. So, no cost due to purchase and there is no sale which is happening. So, no revenue due to sale and also there is no cost due to sale. So, as a result of this, the news vendor is actually not having any cost associated or profit associated with ordering nothing. And as you go higher and higher in terms of the number of units ordered by the news vendor, you can see that the profitability starts increasing more and more and more. So, in fact, the news vendor has a choice of several positive payoffs available in order to choose. So, the news vendor could order 1000 or 2000 or 3000 or anything more in order to be profitable, just profitable. But the maximum profitability is again observed when the news vendor matches the demand. So, in the same way over here, we see that the profitability is increasing and then it reaches a maximum over here and then again it decreases. Now, the question comes as to whether the news vendor will order 5 lakh units when the demand is 30000 units. This will not happen because first of all in this case, 5 lakh units is going to give no profitability to the news vendor. And why is that? Because the news vendor will only be able to sell 30000 units. The remaining amount of units have only been purchased. So, out of 5 lakh units, only 30000 units get sold. So, there is a profitability of 20 rupees per unit, 30 rupees from the price that you get in the market and 10 rupees from the distribution cost which is going to be incurred resulting in 20 rupees per unit. But there is a remainder amount which is quite large that the news vendor has already purchased. As a result, it does not have any profitability associated with it. So, again the news vendor given a choice would only select 30000 units in order to achieve maximum profitability in scenario number 5. And in scenario number 6, if we were to consider following the same thread of thought, we will see that the profitability starts increasing and reaches a maximum at 40000 units. It reaches this maximum over here and then it reduces again. So, when the news vendor is matching the demand in terms of the orders being placed, the profitability is maximum and that is the order size that is placed by the news vendor to the supplier. Scenario 7 in the same case, you can see that the demand is going to the highest which is 5 lakh units. When the news vendor is going to reach 5 lakh units, we can see it is a maximum at least for order sizes from 0 to 5 lakh. You can go back and think whether you are going to have higher or lower profitability when the order size placed by the news vendor is more than 5 lakh units. So, this is an interesting thought that I will also leave it to you in order to think about what will happen when the order size placed by the news vendor is going to be more than 5 lakh units. And in this particular set of order sizes if the decision had to be taken, then the news vendor is definitely going to go with 5 lakh units as the best order size. Now, remember we said that the news vendor is the primary entity which takes the decision and why is that so, the news vendor is the one who is distributing to the market. So, the news vendor is the one who is also going to take a decision as to how much to order. This is not necessarily always the case, it can also be possible that the supplier takes decisions on behalf of the news vendor and then places that much of a batch size in order to be manufactured or printed out in this case it is newspapers. But in this particular case we are assuming that it is the news vendor who has knowledge of the market demand and the supplier only has knowledge of what is the order size which is being placed to the supplier by the news vendor. So, what we can only do right now is to see what is the impact of the news vendors decisions on the payoffs of the supplier. So, let us look at the suppliers payoffs. So, this is what it looks like the payoff matrix for the supplier given the news vendor is placing some orders as you can observe over here when the market demand is 0 the news vendor best option is to not order anything and in such a case if that is the case even the supplier is not going to have to manufacture or produce anything. And since if the decision is to print we said that there would be a fixed cost associated with it let us say that the supplier decided not to operate when there is no demand then there is going to be no profit or no loss scenario even for the supplier. But let us say the supplier decided to operate whether there was demand or not then this would have been minus 150,000 because that would be the fixed cost of the supplier. Right now here I am considering that the supplier is only going to decide on operating if there is any demand from the news vendor. But if that is not the case the payoffs for the supplier would have been minus 150,000. So, both alternatives are possible as you can observe here when the news vendor places an order of 0 which is the best decision taken by the news vendor when the market demand is 0 then the suppliers payoffs are also 0 or like I said it could be minus 150,000 if the supplier is operating irrespective of the demand. Now is this the best opportunity for the supplier? As you can observe here no for the supplier when the market demand is 0 the best profitability occurs as we increase the order size. Now why is that the case? We have already seen that there is a break even amount for the supplier in order to be operating which is 30,000 units. Right? So, this is the break even and at this particular order size the supplier is in a no loss no profit scenario for sure that is the fixed cost of 150,000 rupees is going to be balanced by the revenues associated with supplying 30,000 units to the news vendor. And as you can observe here anything more than 30,000 units the supplier actually makes higher profits which is in this case 50,000 when the order size is 40,000 when the order size is 5 lakhs the profit made by the supplier is 2,35,000. So, in fact in the case of the first scenario the supplier would actually prefer if there is a positive lot size which is going to be more than 30,000 units but that is not happening. The supplier would not be making anything or if the supplier chooses to operate and not make anything the supplier would be having a fixed cost of 150,000. Now let us say if this was not the scenario but the scenario was scenario 2 or 3 or 4 when it is scenario 2 we have seen that the best decision taken by the news vendor is actually 2000 units. Right? This is the best decision taken by the news vendor when the scenario is 2, 3 or 4. In that case we can observe that the profitability of the news vendor is at its highest 20,000 rupees but let us see what is the impact on the profits of the supplier. For the supplier we can observe that when the best decision taken by the news vendor is 2000 units for the order size the profitability is minus 1,40,000 in scenario 2, in scenario 3 and scenario 4. Remember I am only considering the best decision taken by the news vendor but if for some reason the news vendor is not going ahead with 2000 units which is actually the best decision for scenario 2 and goes ahead with 40,000 units which is the other decision that we had seen earlier then the supplier is actually profitable. Right? But does this scenario happen? No, we have seen in the previous slide also. The scenario is possible but it will not happen if the news vendor is the decision maker as to how much should be ordered and if we were to consider that the news vendor is a rational player who will look for higher profitability to make a decision then in that case it is not possible that the news vendor will even place an order size of 40,000 units. So, this does not happen 50,000 rupees profit for the supplier is actually a dream it will not happen. Similarly in scenario 3 the news vendor places an order of 2000 as the best option which will lead to a loss of 140,000 rupees for the supplier. What would be the best alternative in this case to be anywhere above 30,000 units would have been the best possible scenario for the supplier but it does not happen. Again let us say that the news vendor was ordering 1500 units instead of 2000. The profitability that can be expected for the supplier would be somewhere between the order sizes of 1000 and 2000 units which is somewhere between minus 145,000 to minus 140000. Will this happen? No, because considering the news vendor is a rational player who chooses the best choice if given the opportunity the news vendor would be ordering 2000 units. Now the same thing happens in scenario 4 where the news vendors best choice and the news vendors choice that we had seen are both the same which is 2000 units in which case again you can see the profitability for the supplier is 1,40,000 units. Now if you can see this we can see that for any of the order sizes from 0 to 20,000 units the news vendor places any order and for the supplier there would be no profit. So, why will the supplier even supply? The question would be will the supplier supply? The supplier will choose to not supply to the news vendor if the supplier is also a rational player who thinks about profitability. If only cost is being incurred and if that is my criterion for decision making, higher profitability leads to a better opportunity for me and that is the decision making reference for me then the supplier is not going to choose to even engage with the news vendor if the news vendor provides any order size from 0 to 30,000 units. So, that means we can observe that for these scenarios which is from scenario 1, 2, 3 to 4 the supplier is not interested in engaging with the news vendor. So, none of these scenarios as you can see here none of these scenarios would be of interest to the supplier, supplier would not perform over here. Now it becomes interesting only when we start looking at scenarios 5, 6 and 7. We can see in scenario 5 the best decision taken by the news vendor is 30,000 units leading to 3 lakhs of profitability which is the highest for scenario 5 and for that it leads to the profitability for supplier which is 0 that is no loss, no revenue kind of scenario and the question is will the supplier want to engage with the news vendor in such a case there is a good possibility that the supplier will not engage. They have to look at whether they can make profit out of this venture. So, there is a good chance that even in scenario 5 the supplier does not want to engage with the news vendor. Now it is in scenarios 6 and 7 as you can observe here the news vendor is actually going to place an order of 40,000 units when the demand is 40,000 units and for that the profit which is earned by the supplier is actually 50,000 rupees which is higher than 0. So, the supplier is profitable. So, we have seen in the previous slide that in the centralized decision for to be profitable the news vendor has to match the demand. For both players to be profitable the news vendor has to match the demand and if that is the case we can see that the scenario 6 is something which is quite of used to the supplier, but is this the best scenario for the supplier is the question. No, the best scenario for the supplier if the choices are only between 0 to 5 lakhs the best choice for the supplier is actually the order size of 5 lakhs and the best choice for the supplier similarly when in scenario 7 would be the order size of 5 lakhs or more. So, what can we observe here one of the main findings or one of the main ideas that we observe over here is as the news vendor starts ordering more and more the supplier starts becoming more and more profitable and the supplier would choose to have larger order sizes, but for the news vendor it is not the case. For the news vendor there is an optimum value of order size which is somewhere in between 0 and 5 lakhs which occurs in each case and it is occurring in such a manner that the news vendor is not interested in placing either a higher order size or a lower order size. So, as a result of this the news vendor is going to determine what will be the order size placed for the supplier and the supplier may choose to not engage with the news vendor or in some cases the supplier may feel that they are profitable, but they wish they could be more profitable. So, in such a case we see that beyond the break even point the decisions taken by the news vendor are actually good for the supplier, but the supplier is not feeling that that is the best decision. If we were to consider further the scenario for the entire supply chain we will see here what is the impact of these decisions on the supply chain spayoffs. When we consider the supply chain spayoffs so, this is let me write here this is the supply chain. When we consider the total supply chain spayoffs which is simply nothing, but I am adding for each cell over here the suppliers for profits or payoffs and the news vendors spayoffs in order to calculate what is the supply chain spayoffs. When we consider this particular case let us see what is the impact when the news vendor orders nothing then the total supply chain is going to earn nothing or lose nothing as well. And when the news vendor is placing 2000 units the total supply chain is actually going to make the best revenue of minus 1,20,000 rupees, but it is a loss. So, not a very good idea over there. Similarly, when the scenario shifts from 2000 units to 30,000, 40,000 and 5 lakh then we can observe that when the news vendor is ordering 30,000 units the best profitability for the supply chain also occurs at 30,000 units. In scenario 6 the best profitability for the supply chain occurs at 40,000 units which is also the best order size for the news vendor. And in scenario 7 the best order size is 5 lakh units for the news vendor and it also happens to be the best order size for the supply chain. So, what can we conclude over here some interesting observations we can make that the news vendor's best decision in each scenario is also the best decision for the entire supply chain especially when the demand is higher. It is not the best decision when the demand is less than 13,000 units, but the news vendors decision is not always the best decision for the supplier. So, this is how we observe that decentralized decision making may be good for the player may be good for the entire supply chain, but it is not always the best case scenario for the other player who is the supplier in this case. So, with this we shall conclude on our discussion on the deterministic setting. We shall next discuss the probabilistic setting and we shall try to understand whether similar situation is going to occur in that case as well. So, thank you very much and see you in the next lecture.