 Hello everyone, welcome to this course on supply chain digitization. This course is offered by Indian Institute of Management, Mumbai and jointly taught by the three faculty members including myself, Professor Priyanka Verma and my colleagues Professor Sushmita Narayana and Professor Devavrata Das. We are going through this week on analytics in supply chain management and in the last two sessions if you remember we have focused mainly on network optimization. The two topics that we have covered in the last two weeks includes decisions related to locating of facility considering their coordinate system. For that purpose we have used gravity location models and also we have seen a decision to take in terms of the selection of the facility given that we have some options of selecting a facility where their fixed cost and their unit variable cost are given to us. So considering this fixed cost and variable cost how can we use a very simple tool like break even analysis to decide about facility selection. This we have seen through a simple case in our previous sessions. This is the third week for the session on network optimization and today we will be talking about capacitate facility location problem. But before that we will also try to understand the scenario that how a demand allocation model works. So to understand this model which is related to demand allocation and capacitive plant location model let us see a simple case and try to understand the different scenarios which are given for a network optimization model. Because there is a executive which is working in an Indian company and is making critical decisions with respect to the location of the facility and also about how the capacity of the facility should be allocated. So that the cost of supply chain turns out to be minimum. So here we have seen that in this scenario the decision is not only about selection of the facilities but also about how the market should be assigned to these facilities. So we can see that the decision includes about the facility location decisions and also about how the market should be assigned to these facilities which are already located. Now here we are trying to consider the customer service requirements and you can you can consider the customer service in terms of the response times also. So there are two telecommunication equipment manufacturers which are given to us. Their names are Maxiou and Baby and these are the two companies who are involved with manufacturing of the telecommunication equipments. If we talk about the company which is Maxiou, they are primarily operating in the northern and in the eastern regions of the India and the manufacturing facilities are assumed to be situated in Delhi, Gurugram and Kolkata. However, they are trying to serve the markets in cities like New Delhi, Kolkata and Lucknow. So you can see that they are primarily operating in the northern and the eastern regions of India. In parallel, there is another company which is termed as Wavy over here. They are focusing majorly in the southern and in the western region of the India. So they are trying to provide telecommunication equipment to the markets which are located in Chennai, Hyderabad and Mumbai that is why we have referred it as the southern and the western part of the country whereas their manufacturing plants are primarily located in Chennai and Mumbai. So these are two companies serving the country in two different ways and here we are trying to find out how the demand should be allocated for these two companies. Now in parallel to this, there are some more information given to us which is about the capacities of the plants. What are the market demands and also what is the variable cost which includes both production and transportation cost per 1000 units shipped. So here we have calculated these costs by considering both production and transportation cost over here and also the fixed cost is also considered. This is taken as fixed cost per month for each of these facilities. We already had a discussion about fixed cost in our previous sessions. So let us see the whole data which is given to us about this given scenario. As we know that we are talking about the supply chains of two companies. The first one is Maxue and the second one is Wavy communications. The supply cities are all clubbed together over here for both the two companies and parallely the markets are also clubbed over here for both the companies and the production and transportation cost per 1000 units are given to us. In parallel the monthly capacity for each supply city is also given and the monthly fixed cost is also considered over here. So if you also see we have been given with their monthly demands for each markets and it is trying to specify the whole data over here. So if we try to formulate this problem and try to provide a solution this is ensuring that how the supplies which are available from the different manufacturing facilities are transported to these markets to fulfill their demand but in a way that the total cost of transportation is minimized. So here if we analyze this data we can make a statement that the company Maxue has a total production capacity of 76000 units per month whereas the demand is coming as 34000 units per month. The company has got a capacity possible capacity of producing more than the demand which is a good scenario. It means that this company has got enough manufacturing capacity possible so that it can fulfill the demand easily. Similarly, if we talk about the another company which is Wavy Communication its production capacity possible is around 48000 units per month and demand is around 30000 units per month which again confirms that the available capacity is high enough to fulfill the demand of the overall markets for this particular company as well. Now here the company has to take a decision that how the products which are manufactured at their production facilities should be allocated to these demand points or the market points such that the cost of transportation is minimized. So we have seen this type of problem. Let us try to formulate this problem in a simple way and this problem formulation is referred as demand allocation problem and which we can solve it very easily with a demand allocation model. So let us try to formulate this problem as well. We have been given with the information about unit cost of production and transportation from i-th manufacturing facility to the j-th demand point. So the Cij is the per unit cost of production and transportation from i-th plant to j-th market. Similarly, we have also been given information about the demand of all the j-th market and the supply limits of all the production facilities. So if this is a scenario we have to take a decision that how much quantity of products should be transported from which plant or from which manufacturing plant to which demand point so that this total cost of transportation is minimized. So this is a very simple demand allocation problem as we can see. Suppose if we have to take a decision about the quantity to be moved from i-th plant to j-th market let it be Xij. So if this is our decision variable our objective is to minimize this total cost of transportation this becomes Cij into Xij and summation over i and summation over j. This will give us the total cost of transportation from i-th plant to j-th market. Now if we talk about the constraints which are available over here, if you have observed there are primarily two type of constraint. One is the demand satisfaction constraint and the second one is the capacity constraint. So this was our supply chain let us look into this once again to understand our constraints. So if this is the set of plants which are existing and which are indicated by the index i and j is the index j which is indicating the set of markets. So we have a simple supply chain for a set of plants and a set of markets and we now have to write constraints related to the supply and demand. We can say that suppose this is my plant i-th plant this plant can supply to any of these markets so if Xij is the quantity which is moving out of manufacturing plant i. So this is supplying to all the possible demand points that is all the j demand points are there this becomes the total quantity which is moving out of the plant i and this cannot exceed the possible capacity or the available capacity of plant i. So obviously this has to be less than equals to Si and this is only for one plant as we have to write this constraint for all the plants possible we will include for all i symbol as well. This is my supply constraint in a similar way we can write about the demand constraint as well. So suppose that we are trying to see that which plants can fulfill the requirement of this j-th market over here. So this market can get the supply from plant 1, plant 2, plant 3, plant 4 and so on. It means that if Xij is a quantity which is being shipped to the market j this can be shipped from all the possible supply points or possible production facilities such that the total demand available at the market point j is satisfied. So this becomes equals to dj again this constraint is only for one market so this has to be solved for all j and thus this becomes my demand constraint as well. So as you can see it is a very very simple demand allocation problem which is based on supply restriction constraint and also based on the total demand to be fulfilled and my objective is obviously to minimize this total cost of production and transportation as Xij is the quantity moved between i-th plant to j-th market this is a non-negative value as this is representing the quantities to be moved. So this is my overall the demand allocation problem. Now once we know the formulation of our problem we will use this formulation to solve it separately for both the companies and the solutions we have shared with you in the excel solution which is which is attached with this session you can refer to the sheet and follow the formulation which is mentioned over here to see the solution that we have obtained for the demand allocation model for both the companies. So when we solve this problem by allocating demand to manufacturing facilities where the objective is to minimize the total cost of facilities in transportation inventory here when we solve this problem in excel and for solving it remember that we will be using the solver tool which we have already introduced in previous sessions as well. So the solution is just reproduced over here for your reference we will check the excel also once again but let us see this solution that we have got as you can see for both the companies for max ui as well as for wavy we have now got the quantities which requires to be moved from their respective manufacturing plants to the corresponding markets and considering that the capacities how much they have got utilized and in parallel whether the demand is completely fulfilled or not this information can also be seen from this table. So let us check this once again with the excel that we have got so as shared with you we are providing you the excel solution of the demand allocation problem as well you can see in this excel all this cost are mentioned over here which we have discussed in our previous example followed by the capacities of the manufacturing plants also the demands are mentioned which you can see here in green in color and the fixed cost is also given for the facilities. So when we solve this problem remember we have solved it twice once for the company max ui and the second time for the wavy company and this demand allocation problem is solved twice separately for the two companies because right now we are trying to find a demand allocation for the two companies in a in an individual manner and the solutions are shown over here if you can see the excel sheets the yellow part is showing you the solution for the company max ui and the orange part is trying to show you the solution for the company wavy the green color of objective cost is actually the production transportation cost and here we have also considered shown you the fixed cost that is the plant which are playing a key role for fulfilling the requirements of these demand corresponding to that the fixed cost are also calculated and is shown over here for a reference. So you can follow this sheet and you can follow the formulation that we have discussed just now and correlating it you can see the solution that we have presented over here and now let us try to analyze this solution in detail. So if you observe the company max ui they are not they are not utilizing their Kolkata facility and they are producing very low quantity from Kolkata facility reason being they have got a high cost of production and shipping even though the facility cost that is the fixed cost is incurred over here. So similarly when we analyze for the total cost for both the company we can see that max ui is incurring around 1 crore 74 lakh 50,000 rupees with a monthly fixed cost of around 1 crore 46 lakh whereas the total monthly cost is coming around 3 crore 20 lakh 50,000 rupees. Parallel the wavy is also incurring a monthly variable cost of around 1 crore 57 lakh 20,000 rupees where the fixed cost is coming around 90,000 26 lakh with a total monthly cost of 2 crore 53 lakh 20,000 rupees. So we can see that the total monthly fixed cost and the total variable cost are calculated separately for these two companies. Now do we have a better solution for this scenario and what happens if we or what are the ways by which this cost can be reduced further. How the max ui companies using their production facilities to fulfill the requirement of the markets. Similarly how wavy is utilizing their production facilities to fulfill their corresponding market demands. So on observing this pattern let us try to find a better solution for this problem. So here we are trying to introduce the well known problem called as capacity plant location model where the decision is all about finding out the optimum location of the facilities such that the total cost of transportation along with the fixed cost of selection of the facility gets minimized. So here the management has taken a decision that let us try to merge these two companies max ui and wavy and form a new company called as max ui and then try to redesign the whole supply chain model the complete supply chain network and try to analyze the benefits because of this new merger. So here the management has a belief that if the two networks are merged appropriately the new company that is max ui will be able to fulfill these market demands in lesser cost. So now we can see that max ui has got five factories from where it can try to serve six markets. So this is the scenario once we merge these two companies together and considering these five factories the management is trying to understand that how these five factories should be used and how the supplies available from these plants should be utilized so that the total cost gets minimized. In parallel the management is also trying to understand that whether there is any possibility of shutting down any plant so that the supply chain cost can be minimized. So here again the similar problem is solved and the model we have already discussed in the previous in the previous problem. Here in this demand allocation model just one variable will get attached that is with respect to your objective function the total cost will be having two parts. The first part is about the unit cost of production and transportation cost and the second part will be about the fixed cost associated with the location of the variable. If the location variable is termed as yi where yi is equals to 0 or 1 indicating whether that ith plant is being selected in your final network yes or no. If it is a yes the value of yi will take the value as 1 if the if it is no the value of yi becomes 0 and suppose if f i is my fixed cost then the objective function will just get modified as z is equals to c i j into x i j summation over i comma j plus f i into y i summation over i which is the term coming because of the fixed cost to be incurred. In addition to this objective cost the other two constraints remain same which is about your demand satisfaction constraint as well as your supply limit constraints. So your demand and capacity constraints will also get attached with this objective function and your new network design model also called as capacitive plant location problem is now formulated. So we can solve this problem in a similar way in excel as well by using the solver function and again we have given you the solution sheet along with all the instructions over here. So let us see this part. So this is the excel sheet you can see from here at the template is shown over here. The excel sheet has got all the data entered in the similar format. You can see the data about the production and transportation cost is mentioned here. The capacities, the demand and the fixed cost are mentioned here. The variables x i j are all assumed to be 0 at the beginning and is mentioned in this table and this y variable y i is indicated over here. Initially all are taken as 0 means we are not sure which supply facility is currently allocated that is why they are taken as 0. This is your capacity constraint which is mentioned over here which ensures that the total supply from a given plant cannot exceed its capacity and these are your demand constraint which ensures that at any demand point the complete demand should be met by the supplies from the different plants and this cell will calculate your total cost of transportation and fixed cost. So the formulas that we will be using it to populate this excel sheet are also shown over here. You can use it and try to calculate all these values how once you have entered all these formulas and your basic sheets are ready you can go to data tab in your data tab we have the solver function available it is add in which you can install and by using the solver you can set your objective which is your total cost because we want to do the minimization select this minimization over here by changing variable cells indicates your decision variables cells. So highlight your decision variable cells over here as we have got majorly two type of constraint one is the capacity constraint and another one is the demand constraint. So these two are shown over here for your capacity constraints and these are shown here for your demand constraints and because the binary variable is all about selection of the facility. So this is also indicated over here for adding the constraint please follow this button called as add once you click it you need to enter the left hand side of the equation with the inequality sign and the right hand side of the equation. So in this way you can keep adding your constraints we have just shown you over here that what how does the final constraints will look like but it is you can follow this step for adding a constraint over here. Because all these variables are non-negative we will check this part which ensures that all variables follow this non-negative rule and as this model is a simple in a programming model which can be solved through simplex LP. So once you have done this go for solve the if its solution is optimal you will get a message that the solution found is optimal and you can also see that all these values of decision variables and the cost will get updated and here it is also about your plan decisions plans location decision is has got updated and you can see that only now with this new supply chain network you have to install your facility at Chennai at Gurugram and at Kolkata and with this new setup now you can operate your supply chain with just three plants instead of five plants that is one major saving as you can see from here and also your capacity constraints are shown over here your demand constraints are shown over here the total cost is coming around 52,000 to 72 rupees 1000 rupees and let us try to compare the two solutions in the previous solution we have tried to solve this demand allocation problem for both the companies separately in the later part of the problem we have merged the two companies formed a new company and we have tried to design the supply chain network for the bigger company as you can see that when we did the merger the max fee is able to close the plants in Delhi and Mumbai so now it can operate only with just three plants that is one major saving and the total cost is coming around 5 crore 22 lakh 72,000 rupees whereas this if you compare it with the individual cost of max fee and maybe we can simply say that the merger has helped us in saving our cost to about 5 million rupees per month compared to the situation when we were operating the supply chain individually for max fee and maybe so here we have tried to design our supply chain network in two ways first is we treated these companies individually and tried to solve this problem as demand allocation problem in the later part we have merged these two companies and formed a new company and for this new one we have tried to design the whole supply chain network we have now seen that how the merger of the two companies has resulted us into the savings of the total cost and this can be solved as the optimization model and in simple tool which is available with our excel we can try to get the solution as well so with this we will close today's session and thank you for going through this session let us meet soon in the next week.