 Dear participants, welcome to the course on supply chain digitization. It is jointly being taught by Professor Priyanka Burma, Professor Sushmita Narayana and Professor Devabrata Das from IIM Mumbai. So, now in this lecture, I will focus on analytics in supply chain management module, which is module 3 of this course. So, before I proceed for the lecture, so let us have a quick summary of module 3 that is analytics in supply chain management. So, first we talked about what is analytics, then we talked about big data and its characteristics that is 6 ways, volume, variety, velocity, variability, value and veracity. Then you also talked about type of analytics, descriptive, diagnostic, predictive and prescriptives. Then we kept various examples of analytics from supply chain management domain. Then we also talked about applications of AI and ML models in forecasting and demand analytics. Then we also talked about supply chain network design, supply chain network optimization and we did few hands-on examples and solved using Excel solver. Then in the last 3 lectures, we were focusing on intelligent decision tool development in supply chains and specifically we took a case study related to location of distribution centers. So, that was the summary. Now in today's class, I will take one more case study related to the intelligent decision tool development in supply chain. So, let us focus on the case study first and understand the scenario. Then we will talk about what model will be fitted over there and which part of the analytics will be used and how can I use that tool or technique to get a solution for the case study. So, the case study goes like this. The senior management of an automotive company is very keen on measuring the efficiency of its 9 manufacturing facilities. They want to focus on key input and output parameters to identify the areas of improvement. So, now if you look at the data. So, they collected 2 output parameters and 2 input parameters and they have 9 facilities to compare. So, the idea is they want to find out which facility is more efficient, which facility is less efficient and if one facility is not efficient then where can they improve? What is their improvement area? Should they focus on outputs? Should they focus on inputs or what? So, the basic idea is the management wants to identify. If a facility is not efficient then where they should focus? Should they focus on increasing the output or should they focus on reducing the inputs? So, with that objective in mind they have collected the output parameters and input parameters. So, the first output parameter is production yield that is measured in terms of percentage of defect free product. So, if you look into the data, the facility 1 is having 92 percent production yield. That means, 92 percentage of the products are defect free whereas, facility 2 has 88 percentage of defect free products, facility 3 has 92 percentage of defect free product and so on. Now, if you look into this column you will see that facility 7 is having 96 percent defect free products. So, as far as this output is concerned that is production yield percentage, facility 7 is doing best and facility 8 is doing worst. So, this 74 percentage production yield. The next parameter is OEE that is overall equipment effectiveness. So, it is a very comprehensive measure of equipment efficiency by considering availability, performance and quality. So, if you look into this data I can see facility 1 is having 80 percent OEE, facility 2 is having 78 percent OEE. Now, if you look into this column you will be able to see again facility 7 is having maximum OEE that is maximum overall equipment effectiveness that is 85 percent whereas, facility 8 is having lowest overall equipment effectiveness 68 percent only. So, these two are the outputs. So, management thought that production yield and overall equipment effectiveness could be the main two outputs which they should focus on as far as efficiency of facility is concerned. Similarly, they also need to talk about inputs. So, in this case they took cycle time as input. So, how do you measure cycle time is the time taken to complete one cycle of production. So, if you look into this data the cycle time is provided in terms of minute. So, facility 1 has 32 minutes of cycle time that means, it takes 32 minutes to complete one cycle of production whereas, facility 2 cycle time is 35 minutes that means, it takes 35 minutes to complete one cycle of production and so on. So, if you look into this column I can see facility 6 is having maximum cycle time that means, it takes maximum time to complete one cycle of production whereas, facility 4 and facility 9 is taking least time that is 30 minutes to complete one cycle of production. So, as far as cycle time is concerned facility 4 and facility 9 is doing better because it is taking minimum time to complete one cycle of production. Now, if you look into the last input parameters that is resource utilization it is again measured in terms of percentage that is uses of machinery equipment and labour in terms of percentage. So, if you see the data facility 1 is having 88 percentage resource utilization facility 2 94 percent and so on. So, you have 2 input parameter you have 2 output parameter you need to decide which facility is more efficient which facility is less efficient. If a facility is not efficient then where they should focus so that they can increase their efficiency. So, that is the overall problem and the case study. Now, by looking into this data take a pause and find out and some do some calculation and decide which facility is doing good which facility is not doing good which is efficient which is not efficient. So, look into this data and try to determine it ok. So, now before I talk about efficiency and specifically this case study we need to find out what is efficiency like how do I measure efficiency. So, we need to spend some time to determine efficiency measurement score and find out how to measure efficiency. So, in this case I have A B C D E let us say I have 5 facilities and I have 1 input parameter and 1 output parameter. So, in this case we are just explaining ok. So, before we proceed with the case study and finding out the efficiency of 9 facility we want to understand what is efficiency and how can I measure it. So, therefore, we are discussing this example. So, I have 5 facilities let us A B C D E and for each facility I have 1 input parameter and 1 output parameter. So, facility A is able to produce 1 unit of output with 2 units of input facility B is able to produce 4 units of output with 3 units of input and so on. Now, look into this data carefully and tell us or find out which factory or which facility is more efficient. So, since I have only 1 input and 1 output parameter I can plot this. So, if you look into the plot I have input in x axis and I have output in y axis. So, we have plotted these 5 data points. So, this is facility A. So, facility A it is taking 2 unit of input and is able to produce 1 unit of output. Facility B is taking 3 unit of inputs and it is able to produce 4 units of output whereas, facility D is taking 4 units of input and able to produce 3 units of output. Facility C is taking 5 units of input and is able to produce 5 units of output. Facility E it is taking 6 units of input and able to produce 8 units of output. Now, if I compare A, B, C, D, E these 5 facilities which one is more efficient. So, how do you calculate efficiency? So, efficiency is nothing but output by input. So, output O by input I. So, the output by input value for A would be 1 by 2 because 1 is output 2 is input. So, 1 by 2 that is 0.5. For facility B it is 4 by 3 that is 1.33. For facility C it is 5 by 5 that is 1. For facility D it is 3 by 4 that is 0.75. For facility E the output by input ratio is 1.33 that is 8 by 6. Now, this is output by input, but is it efficiency because for efficiency the maximum score could be 1. So, therefore, what we should do we can see here that facility B is taking the output by input ratio 1 by 3. For facility E is also output by input ratio is coming more than 1. So, therefore, it cannot be efficiency since I have a value which is more than 1. So, then how can I do efficiency? I need to divide this value by 1.33. So, I can divide 0.50 by 1.33, I will divide this by 1.33, I will divide this by 1.33, I will divide this by 1.33, I will also divide this by 1.33. So, if I do this division then you can see facility E the value becomes 1. Facility D the value becomes 0.563 which is nothing, but 0.75 by 1.33 and so on. Now, if you look into this data I have having maximum value as 1. So, these are my efficiency score. So, efficiency is not only output by input. So, if I just take output by input then I may end up getting a value which is more than 1. So, in this case you can see B and E for B and E output by input value is more than 1. So, therefore, it cannot be efficient it cannot be the efficiency because efficiency needs to be restricted by 1. So, we need to add a constraint such that efficiency less than equal to 1. So, the formula of efficiency or the measurement of efficiency is output by input provided this score is less than equal to 1. So, that is how efficiency is calculated. So, now I get the efficiency score of all of these 5 facilities and B is having maximum efficiency of 100 percent E is having maximum efficiency of 100 percent and the rest of them are non-efficient. So, this is how the efficiency is measured. Now, graphically how do I present efficiency? So, for that I have this actual value of A B C D E input and output. Now, since B and E are having maximum efficiency of 100 percent they are most efficient they are most efficient they are falling on the efficient frontier. So, this line which is drawn here. So, this line which is drawn here is called efficient frontier it is passing through B and E B and E both are efficient both are having 100 percent efficiency score. So, this frontier is called efficiency frontier. So, now, let us focus on A the facility A which is not efficient you can see here it is only 37.5 percent efficiency. So, since it is not efficient the next question would be why it is not efficient and if I want to make it efficient where should I focus on increasing the output or should I focus on decreasing the input. So, now, if you see A is not efficient if I want to make A efficient A has to come here if A has to come here my output needs to be increased by this much volume this much quantity. So, my output needs to be increased by this much quantity or if I want to focus on input then my input needs to be reduced by this much quantity. So, that A comes here. So, either I should increase my output by this much quantity and come here or I should be able to reduce my input and come here then A would be on the frontier. Similarly, B is already on the frontier because B is efficient. So, therefore, it is already on the frontier I do not need to do anything now D is again not efficient if I see efficiency score of D is 56.3 percent. So, where should I focus should I focus on input should I focus on output. So, you can focus in either of this. So, if I focus on output then I need to increase the output of D by this much quantity by this much quantity. If I increase by this much quantity then D will come here. So, D will be on the frontier or I can reduce the inputs to D. So, if I reduce the input values of D by this much quantity then also I will be on the frontier. So, either I should increase the output of D and be able to come at this efficient frontier or I need to reduce input. So, that I can come to this frontier. Now, C is a very again not efficient if I see it is 75 percent efficiency. So, 25 percent still possible to improve. So, where should they improve you can either increase the output by this much quantity and come here on this frontier or I should be able to reduce my input and come here on the frontier. So, if I want to focus on increasing the output for C with the same amount of input that means with 5 units of input I should be able to produce this much output. So, that is how you can interpret and E is already on the efficient frontier. So, I do not need to do anything. So, now, if I summarize from here we can get the efficiency score. So, efficiency is output by input provided efficiency for each of this facilities is less than equal to 1. So, using this logic using this logic I can get this scores. So, A is not efficient B is efficient C is not efficient D is not efficient E is efficient. So, B and E are efficient. So, therefore, both of them are already on the frontier whereas, A D and C are not efficient. So, they are not on the frontier, but I can make them efficient by increasing the output or by decreasing the input. So, both is possible based on the resources you have you have to decide whether you should increase output or you should focus on reducing the inputs to get the same amount of output. Now, you got the idea of efficiency measurement. So, we want to now proceed with the case study. So, overall idea is clear now. So, I need this relationship efficiency is output by input and I have to make sure that efficiency less than equal to 1. Now, till now in this specific example we had only one input and one output, but the case study which we have we have two outputs and two inputs. So, the question is how can you measure efficiency? Since I have two outputs two inputs you can have multiple outputs multiple input you can have three outputs four inputs you can have five outputs six inputs and so on. So, in this case specifically I have two outputs two inputs then what should be my efficiency measurement formula. So, I can write it weighted sum of output divided by weighted sum of inputs. So, I need to multiply weights to these outputs and inputs then I will be able to get these values, but again as per the efficiency requirement efficiency should be less than equal to 1. So, now we have decided the weight. So, V 1 is the weight of output 1, V 2 is the weight of output 2. So, U 1 is the weight of input 1, U 2 is the weight of input 2. So, V 1 is the weight of output 1 that is production yield, V 2 is the weight of output 2 that is OEE, U 1 is the weight of input 1 that is cycle time, U 2 is the weight of input 2 that is resource utilization. So, now what would be my efficiency score? Weighted sum of outputs divided by weighted sum of inputs. So, let us focus on facility 1. If I focus on facility 1 what would be the efficiency? So, I have weights. So, I have weights if I write it here V 1, V 2, U 1, U 2. So, for facility 1 I need to multiply 92 into V 1 and 82 into V 1 and 82 into V 1 and 82 into V 2. So, if I add this then I will get weighted sum of output. I have to divide this value with weighted sum of input. So, 32 will be multiplied by U 1 plus 88 will be multiplied by U 2. So, that would be my efficiency in facility 1 because weighted sum of output divided by weighted sum of input. So, 92 into V 1 plus 80 V 2 divided by 32 U 1 plus 88 U 2. So, that is my efficiency and my objective is to maximize this efficiency that is my objective and to maximize the efficiency of facility 1. Now, as per the definition of efficiency and the formula I have to make sure that efficiency is less than equal to 1 for each of these facilities. So, although I am trying to maximize efficiency of facility 1, I have to make sure that other facilities efficiency is not becoming more than 1. So, for that I have to write constants. So, first constant is V 1 plus for facility 1 again 92 into V 1 plus 80 V 2 divided by 32 U 1 plus 88 U 2. So, that is efficiency of facility 1 that should be less than equal to 1. I have to also make sure that efficiency of facility 2 is also less than equal to 1. So, what would be the efficiency of facility 2? 88 V 1 plus 78 V 2 divided by 35 U 2 divided by 35 U 1 plus 94 U 2 that is nothing, but weighted sum of output divided by weighted sum of input for facility 2 it should be less than equal to 1. So, same way I need to calculate the efficiency of all my 9 facilities and make sure that all efficiency scores are less than equal to 1. So, although I am maximizing the efficiency of facility 1, I have to make sure that all other facilities efficiency score is less than equal to 1. Now, if I solve this optimization model, then I will get the value of V 1, I will get the value of V 2, I will get the value of U 1, I will get the value of U 2. So, V 1, V 2, U 1, U 2 are my decision variables, V 1, V 2 are weight of output 1 and output 2, U 1, U 2 are the weight of input 1 and input 2 respectively. So, I have these 4 decision variables, this is my objective function and these are my constants. So, if I solve this optimization model, I will be able to get the value of V 1, V 2, U 1, U 2 and if I plug in there, I will get the efficiency score of facility 1. So, that is how you can find out efficiency of facility 2, facility 3, facility 4, facility 5 and so on. So, in this case I am only focusing on facility 1, if I want to focus on facility 2, then my objective function will be changed, my objective function will be maximize efficiency of facility 2. If I want to focus on facility 3, my objective would be maximizing the efficiency of facility 3. If my focus is on facility 4, then my objective would be maximizing the efficiency of facility 4 and these constants will remain same. So, all these constants, these 9 constants will remain same, only change will be there in the objective function. The constants will not change, only objective function will be changed. So, let us see, if I want to focus on facility 5, if I want to focus on efficiency, facility 5, can you tell me, how your objective function would be, your objective function would be maximized. So, let us, I am writing it for facility 5, my objective would be maximized efficiency of facility 5. So, efficiency of facility 5 is 90 into v 1 plus 80 into v 2 divided by 34 into u 1 plus 90 into u 2. So, if I write it here, 90 into v 1 plus 90 into v 1 plus 82 into v 2 divided by 34 into u 1 plus 90 u 2. So, that is my objective function. The rest will be same. Similarly, if you want to focus on, let us say, facility 8, constants will remain same, constant is not going to change, objective function will change, how to be the new objective function, maximized. Facility 8, 74 into v 1 plus 68 into v 2 divided by 35 into u 1 plus 94 into u 2. So, weighted sum of out of the facility, output divided by weighted sum of input. So, that is how, your objective function will keep on changing depending upon what facility you are focusing on. So, I will have total 9 different objective function, I have to solve 9 times for each facility. However, the constants will remain same. So, then I will get the value of v 1, v 2, u 1, u 2 and if I plug in those values, I will get the efficiency score of each of the facilities. So, this model is called data development analysis. So, DEA. So, in the next lecture, we will see how to solve this model. Although, we have developed a model, but we have not got the solution yet. So, in the next lecture, we will solve this model, get the output of all the facilities and then see which one is most efficient, which one is least efficient and if a factor is not efficient, where they should focus on. So, see you in the next lecture. Thank you so much.