 Hello and welcome back to the NPTEL session on supply chain digitization. I am Professor Sushmita Narayan from IM Mumbai and in this session, we are going to be continuing our discussion on channel structures in the supply chain. In this particular session, we follow up on the previous lecture where we had considered decentralized and centralized decision making scenarios in a news vendor problem. We had looked at the deterministic setting and we had looked at what are the possible kinds of conflicts that can arise between the news vendor and the supplier and between the news vendor as well as the supply chain or between the supplier and the supply chain because of the decisions taken in a decentralized manner. Remember this was a deterministic setting and a deterministic setting implies that you are well aware of the nature of the value of the variable in advance. In other words, in the case that we had taken, we had assumed that the news vendor is well aware of what the demand is going to be like and accordingly takes a decision on how much the order size should be. However, this is not usually the case. It is not always fully known to us what the demand is going to look like and hence we look at the probabilistic setting of demand in today's session. And then we are going to look at some of the conflicts that arise over there. We see some similarities with what happens in the deterministic setting and then in the example of the probabilistic setting, we also explore the role of contracts with a simple contract and a popular contract that is usually understood in the case of supply chain coordination. And then towards the end of the session, we are going to look at the potential role of coordination in the platform economy for the supply chain given that these are the fundamental aspects of coordination that are going to happen in a typical supply chain. This is a very exhaustive topic in itself. However, I will try to keep it as simple as possible for the participants and viewers to understand. So, let us look at what was the example that we were seeing in the last lecture. So, in the last lecture we were looking at the supply chain coordination decisions with respect to how much to order and we had seen the centralized and decentralized decision making in the case of a deterministic setting. But what if our demand is not fully known? What else can be known about the demand attributes? Remember in the deterministic setting I had mentioned that one of the ways in which we can say that the demand is deterministic is if we actually know what the value is going to be like that is one way to look at deterministic settings. The other deterministic setting could be if we are able to figure out what is the relationship between the demand and other parameters or variables such as price, such as other indicators of demand, such as weather etcetera. Those are called deterministic settings in which we are able to connect the demand value with a known value. In the case of probabilistic setting we are looking at a specific diversion from these types of scenarios in which we are not very well aware of the relationship of demand with other parameters and we are also not very well aware about the nature of demand itself in terms of what exactly is the value. However, we do know some amount of information as what potential values the demand could be taking up. So, in this example that I am going to be demonstrating for decentralization versus centralization in the same example of the news vendor in the supplier. Instead of the actual demand what we do know over here is the demand's probability distribution. In other words we know what are the potential types of demand levels that we can observe and what is the probability associated with these demand levels. So, for example, it could look something like this. We have five scenarios which are possible. In the first scenario the demand could be 10,000 units for the newspapers, in the second scenario it is 20,000, in the third it is 30,000, in the fourth 40,000 and in the fifth 50,000. Now, I have represented these five scenarios with also probability estimates which means these probabilities indicate the chance with which we can observe such a market demand. There is a 20 percent chance that we are going to observe a market demand of 10,000 units in the market for newspapers or there is a 15 percent chance that we observe a market demand of 20,000 units or a 10 percent chance that we observe a demand of 30,000 units or a 25 percent chance of observing a demand of 40,000 units or a 30 percent chance of observing a demand of 50,000 units. Now, a small note over here. It is not necessary that our demand probability distribution should exactly look like this. It could be variants of this. In this particular case as you can see we have five scenarios which are discrete in nature which means scenario one and scenario two cannot occur simultaneously. Either scenario one occurs or two or three or four or five which means there are only five possibilities that exist in our current setting of market demand. So, the news vendor has to get at least this much amount of information a priori before taking decisions as to what should be the appropriate order size and what would be the outcomes such as profits etcetera for the players including the supplier the news vendor as well as the supply chain. So, if we were to consider other variants of this we could be having continuous probability distributions or continuous distribution for demand with respect to probability and those are other variants in which also we can extend the same kind of thought process. For simplicity I am taking a very simple example of possible demand opportunities and then we will explore what could be the role of decentralization and centralization and the potential issues that could occur. So, the question that is going to now come into place is again what should be the order size that the news vendor places. Remember the scenario is the same or the setting is the same the news vendor has information about the market demand to some extent. In this case the extent to which the news vendor knows is it is probabilistic in nature and the news vendor is aware of the various levels of demand. The news vendor is then going to take a call before even the demand can occur as to what should be the amount of newspapers to be purchased from the supplier. The supplier has the option of supplying the newspapers to the news vendor if the supplier is profitable else the supplier can actually choose to be out of this entire business transaction. Again we also consider that the news vendor and the supplier are rational players who are going to be trying to maximize their profit outcomes when it comes to decision making. Given this is the scenario we know that the news vendor is actually driving the decisions within the supply chain. So, if you were to consider this particular setting we have these questions that we want to answer. What should be the news vendors preferred order size? What would be the resulting profit and what would be the regional suppliers profit as a result of this? And if there are any kinds of inconsistencies or potential areas of agreement that are going to be present between the two players. We had seen that there were some issues or some scenarios in which there was a possibility that both players were profitable and in some scenarios there was a possibility that only one of the player was profitable in specific scenarios in the deterministic setting. How do we make that judgment over here in order to decide what is the preferred order size? So, this is where we are going to now look at a specific decision making profile for the news vendor. Like I said we are assuming that the news vendor is a rational entity who is going to look at maximizing profit when making a decision. So, the decision is going to be related to that particular value of order size which maximizes profit. Now, how do you define profit over here? We can see that the scenarios are not deterministic in nature. So, there is only a probability associated with the scenario with each scenario. So, how can you determine what is profit in such cases? Because the profit of associated with 10,000 units might not occur, a profit associated with 50,000 units might not occur or there is a 30 percent chance that it occurs and similarly there is a 20 percent chance that there is a profit associated with 10,000 units. So, how to take a decision in such cases? In such cases when we look at the decision making profile of the news vendor in this specific context I have assumed that the news vendor is a rational decision maker who is risk neutral and a risk neutral rational decision maker would be effectively looking at not a specific case of market demand, but an expected value of potential payoffs that are going to occur. So, in such a case what we are going to look at when it comes to decision making for the news vendor is the expected value of payoffs associated with that specific decision. And how do we do this? We will work out this example in an Excel file or an Excel workbook file. So, you can see over here we are having a few cells and matrices which are presented in your Excel sheet. Let us go step by step while trying to understand this. What I have presented over here is the news vendor side of the outcomes decisions and issues. So, in this case in this particular set of cells I am going to be looking at what would be the potential sale of newspapers that could occur. And for that what I have done is I have considered the five scenarios of demand 10, 20, 30, 40 and 50,000 units respectively. And on this side I have looked at what could be the possible decisions taken by the news vendor. I have matched these decision values to the demand values that we have. However, this is not necessary it can be extended beyond 50,000 units below 10,000 units and somewhere in between also. But as we will eventually see these are not going to be very relevant to the decision making of the news vendor. So, let us evaluate step by step as to how we can find out what is going to be the potential sale of newspapers. So, we consider every combination of demand and potential decision which is the potential order size. Suppose the news vendor has placed an order of 10,000 newspapers from the supplier. So, 10,000 newspapers have been received by the news vendor right and in stock the news vendor is going to have 10,000 units. Now, if this is going to be the case now the market demand is being realized and let us say the market demand that gets realized is 10,000 units. So, how much will gets sold? As we can very clearly see 10,000 units are on hand the market demand turned out to be 10,000 units. So, assuming that the market demand is all directed towards the 10,000 units that we have all of the 10,000 units can get sold to the market. Now, let us see if the quantity on hand is 10,000 units, but the demand turned out to be 20,000 units. So, in such a case we can observe that the demand actually turns out to be 20,000 units which is much more than what is on hand and this purchase has already been made by the news vendor. So, no further purchase is going to happen right now in this very particular moment. So, whatever is on hand only can get sold and not more than that and as that is going to be less than 20,000 units only 10,000 units gets sold and as you will observe across all the scenarios only 10,000 units is getting sold in each combination of demand and order size of 10,000 units and this is happening because the order size is less than the demand which is realized in the market. Now, let us say that the order size was actually 20,000 units which has been purchased by the news vendor. So, the news vendor now has on hand 20,000 units and now goes to sell in the market. The demand in the market turns out to be 10,000 units. If the demand turns out to be 10,000 units how much is going to get sold is the minimum of what is the demand in the market and what is on hand. On hand is 20,000 units but of that only 10,000 units are going to be sold because that is the demand there is no more demand than 10,000 units. So, we can observe that the sales that are going to occur are just 10,000 units and you will observe that this is going to be the scenario across all possible order sizes. As the news vendor is going to order more and more if the demand turns out to be only 10,000 units only 10,000 units gets sold and if the demand is going to be between 10,000 to 50,000 units but on hand is only 10,000 units only 10,000 gets sold. But let us say the demand is going to be 30,000 units the order size is going to be 30,000 units then what gets sold. In case of the demand being 10,000 only 10,000 gets sold in case of the demand being 20,000 20,000 units gets sold and as we will observe as we go further across the various scenarios at the max 30,000 is going to get sold. So, when we observe this a very interesting pattern is going to show up over here. We see that whenever the order size is going to be greater than the demand then it is the demand which is going to determine how much gets sold in the market. Whenever the demand is greater than the order size then it is the order size which is going to determine how much is going to get sold in the market. So, in the case of the order size being greater than the demand we have a case of excess stock being present with the news vendor which is unsold and in the case of demand exceeding the order sizes we have a case of a loss of sales or potential loss of sales that we are going to have as a result of not having enough stock. Now considering all of these issues we can observe that there would be certain opportunities which are more useful to us. From a deterministic setting we have seen in the last case that it is always preferable to have the news vendors demand and order size matching each other. But is this also the case that is going to happen in the probabilistic setting? For this we need to evaluate what would be the potential profits of the news vendor. So, in this particular case I have also plotted what could be the potential profits for the news vendor. So, let us take up this particular combination of sales. For a demand of 10,000 units given that we have already purchased 10,000 units as a news vendor what will be our profit? Remember we have from the previous example certain amount of information with respect to what is the price of the paper in the market at which it gets sold. What are the costs associated with distribution for the news vendor? At what price is it purchased from the supplier? What are the suppliers manufacturing and operating costs? In addition we also have fixed costs associated with the supplier which is 150,000 units. Now if we were to look at the profitability of the news vendor considering this particular combination of 10,000 units being the demand and 10,000 units being on hand. So, we can see that what gets sold is 10,000 units and what was purchased was 10,000 units. So, the margin which is going to be present on selling and distributing 10,000 units of newspaper in the market would be 30 minus the distribution cost of 10. So, 20 into 10,000 units minus the selling price which has been paid or the cost which has been paid to the supplier which is the wholesale selling price which is 10 units. So, that would effectively be 20 minus 10 into 10,000 units which comes out to be 1 lakh rupees. Now if it so happens that the demand is actually 20,000 units but 10,000 is what is on hand since the demand is going to be 20,000 units and on hand we have only 10,000 units we can sell only 10,000 units. So, the profit is going to be the same which is 1 lakh because only 10,000 units is going to get sold. Similarly, we are going to see that as we move to higher levels of demand if we had on hand 10,000 units we would be selling only 10,000 units. But if we had on hand 20,000 units and the demand turned out to be 10,000 units we can observe that in such a case we are in a no profit no loss scenario. And why is this occurring? We are going to incur a cost of 10 rupees per unit in purchasing 20,000 units that is 2 lakh rupees over there. At the same time we are going to be selling of these some units in the market. Will we sell 20,000 units? No, we will sell only 10,000 units and in selling these 10,000 units I am going to obtain a margin of 20 rupees per unit considering the revenue side which is the retail price of 30 rupees and the distribution cost of 10. So, that comes out to be 20 into 10,000 which is going to be 2 lakh. So, 2 lakh is the overall that I am earning through selling and distribution and 2 lakhs is the cost that I incur in purchasing 20,000 units from the supplier. So, there is no profit no loss. And as you can observe as we order larger amounts we are going to go into a loss scenario and what does this imply? It implies that we are having a lot of stock on hand which is not getting sold, but which has been purchased. And similarly as the order size increases for this level of demand it would not be prudent to order very large order sizes. So, for a demand level of 10,000 units we would prefer to order 10,000 units, but this would be a deterministic scenario as we have seen in the last example as well. Now, let us look at what happens in this entire table. So, we can observe in this entire table that when we order 10,000 units we are profitable across all scenarios with revenue with a net profit of 1001 lakh rupees in every scenario. When we have ordered 20,000 units from the supplier as a news vendor, we are profitable in almost all the scenarios and in the scenarios where we are profitable we are earning 2 lakh rupees and this occurs as the demand also increases, but when the demand is low we are in a no profit no loss scenario. When we order 30,000 units then we can observe that we are profitable when the demand increases just like before and in fact, this profitability is going to be 3 lakh rupees for demand that is 30,000 and above. And in case the demand is less than that then in one case we are profitable with 1 lakh rupees earning and in one case we are incurring 1 lakh rupees loss. We can observe that this is occurring even in the case of 40000 units and 50000 units. Now, these are all the potential payoffs in other words we have all possibilities available with us for every combination of demand and order size. Now, if I had to make a decision remember we have assumed that the news vendor is a risk neutral rational decision player. So, a risk neutral rational decision player is going to evaluate the expected values of payoffs in order to decide which is the best order size. In this particular case if we were to look at the expected value of payoffs, we can see and let me calculate it separately for you. We can see over here looking at just the first case if the order size is 10,000 units the expected value of profit for the news vendor can be obtained by understanding what is the possibility of each of these cases occurring. Since there are five scenarios let us look at what are the probabilities associated with these five scenarios. We know that there is a 20% chance that the demand is 10,000 units. So, in other words we can also say that if we had ordered 10,000 units there is a 20% chance that we earn 1 lakh rupees, there is a 15% chance that we earn 1 lakh rupees, a 10% chance of earning 1 lakh, a 25% chance of earning 1 lakh and a 30% chance of earning 1 lakh. So, the expected value of payoffs associated with ordering 10,000 units for my supplier would be 20% into 1 lakh plus 15% into 1 lakh so on and so forth. In other words if you can see the excel formula that I have used here I have done the sum product of the probabilities and the potential payoffs associated with 10,000 units. Now, in the same way I can extend these two other possible order sizes which is 20,000 units for example right. So, in this case we can observe that again the expected value of payoff if I order 20,000 units there is a 20% chance that I earn nothing and lose nothing, a 15% chance that I earn 2 lakhs, a 10% chance of earning 2 lakhs, a 25% chance of earning 2 lakhs and a 30% chance of earning 2 lakhs. Considering the expected value of my payoffs I am going to end up with 1 lakh 60,000 rupees as the expected value of payoffs if my order size is going to be 20,000 units. If I had a choice only between 10,000 units and 20,000 units as a rational decision maker the news vendor would select ordering 20,000 units but that is not the case the news vendor can also order more than 20,000 units and evaluate those possibilities and those are the possibilities which are 30, 40 and 50,000 units respectively. So, in those cases if we were to again find out the expected value of payoffs we can see that the highest expected value of payoff is associated with the order size of 40,000 units placed by the news vendor to the supplier and this results in a expected value of profit being 2 lakh rupees for the news vendor which is the highest across all these possible scenarios that we have. Now, if this is the case in the deterministic setting we had seen that the news vendor was actually ordering 30,000 units as the best potential opportunity when the demand was 30,000 units but that is not the case over here it is not necessary that the demand should actually match the order size there is no such particular case that we are observing here. What we do observe here is there will be a balance between the cost associated with excess stock and the potential loss of sale due to less stock present with us. Now, in the next lecture we are going to continue our analysis and evaluate as to what is the impact of these decisions on the supplier as well as the entire supply chain what are the potential conflicts and how can we resolve the same. So, thank you and we will meet in the next session.