 Hello everybody, welcome to the second live event SC0X and other people joining us. We have a special treat today. I'm Chris Kaplus and you've seen me in the videos, but I've got doctors Alex Rothkopf and Dr. Jared Gensel and they're going to talk about kind of a problem in practice. They're going to use some of the tools that you've been seeing in the first couple of weeks, first three weeks of the course and show how they use in practice. Also be joined by General Jeffrey Darko and talk about how the use of models can improve the way they respond to disasters here in the United States. I'll be running these things behind the scenes, running the Slido event, so there's a poll right now on Slido. You should all be comfortable how that works. Just type in sc0x-2 and you can enter in questions as well and I'll monitor those and we'll ask those as they come appropriate. So let me introduce Alex and Jared. Thanks Chris. Thank you very much Chris. Hello Global Supply Chainers and welcome to our second live event in SC0X. We are very happy that you have been already joining us. I have with me today my very beloved colleague Jared Gensel. He is the head of the Humanitarian Supply Chain Group here and we have done a project together and I thought that project is very good for our learners because it applies methods that we are using in our course. I'm very excited that you're with me today here. It's good to be here. Thank you very much for joining. Before we start we have a lot of program today for 60 minutes. I wanted to introduce you on how we want to do it. So we are going to do a motivation or Jared is actually doing that motivation. Afterwards we are going to introduce our model, do some math as we have seen in the course and then apply that model to an example to show you what we can actually do to set up disaster response networks and how we can model them and what kind of metrics we can come up with to look at them from a strategic perspective. So this is kind of our big picture and we are going to bring in a couple of practitioners that are going to talk about how you implement something like that and how we can make that use. So without further ado, do you want to take over Jared? I'll start talking about where this problem came from. I'm going to move up to the screen here and talk through things here at the screen. To motivate the problem here, again we have a lab here at MIT that focuses on humanitarian supply chains, meeting people's needs with supply chains. And so for example, we've done some work in the United States with FEMA. This is the Federal Emergency Management Agency. This is the lead organization for the federal government to respond to disasters. There's also state and local government officials that then provide resources and they work together as a whole government to meet people's needs after disasters. And actually we're in the midst of hurricane season right now. We've had a hurricane in Florida and Southern U.S. recently, Hurricane Michael, that has had a lot of destruction and they're actually actively responding right now to meet people's needs. We had hurricane Florence earlier this year. So the last two years, we've had very active hurricane seasons. So the kind of models we're using today will hopefully help prepare FEMA with its resources for the future. But as I mentioned, the federal agency is focused on helping people and our model focuses on the first days after a disaster and meeting people's needs with essential items. One of the essential items is water. So you can see in this warehouse here, there's racks. A rack has pallets here and all these pallets are full of bottled water that can be sent out to people in an emergency. But you can have a warehouse full of water but you have to move it there. So you need trucks, trucks to move these pallets of water to then be offloaded at the site and then finally hand it off in cases to be given to peoples in their homes. So this whole supply chain has to work together. All resources have to work together to meet people's needs. And one of the things we'll talk about today in feature is we've done some modeling in the past on how to think about where to put inventory to best meet needs in the first days of a disaster. But we're specifically adding some new features regarding trucking. The inventory is a critical part. This is a representation of the data from FEMA. We aren't using actual data from FEMA but it's very close to what their network looks like. They have a warehouse on the west coast. We put it in San Francisco. They have one in the south, in Texas, in Dallas, in the southeast, in Georgia, on the east coast near Washington, D.C., where the headquarters is, and then in the northeast in Philadelphia. So five locations that we're using that's close to the footprint they actually have of their warehouses. And the key question is where should we put inventory when we don't know where disasters are going to hit? Where should we put the inventory in anticipation of future disasters? So thinking about this, you've been learning some techniques and you're going to learn some more techniques in the course, we're going to, we put up a poll here. We're curious up front in making a decision of where to put inventory in anticipation of a disaster, which analytical approach is going to be best to fit this problem? And you could pick, it could be a combination. There could be two or three that you could pick, but unconstrained optimization, constrained optimization, algorithms approximations. I think that's about where you're at in the course now. Is that right, Alex? Yeah. You're going to be learning about probabilities, hypothesis testing, regression, discriminant modeling and simulation. So there may be a best one or maybe a combination of things. So go ahead and vote now. We're going to reveal very soon what model we're using in this approach, but we're curious what your instincts are in terms of thinking about this. And I'll give you a little hint. We are combining a couple of things a little bit here on the list. So take the poll. I'm going to continue talking a little bit about the model and the inputs to the model, and then I'll give you a quick reveal on what we're using. So the inputs to the model, we're calling this various portfolios. We're looking at portfolios and seeing how they fit together. Portfolio of risks is the first thing. Where are their hazards? Where is there likely to be a disaster? Where is the population higher at risk for disaster? And then also the items, those critical essential items like water and food and medicine that they need, what kind of usage? How many bottles of water per day does a person need? How much food do they need? And so if you combine these two things, the risks of disasters or the item uses, we'll call this the need. We're characterizing the need after a disaster. To meet the needs, we have resources, and we have three different portfolios we're going to talk about in our modeling approach around this. The inventory we talked about in the warehouses, suppliers, FEMA can also go to procure from suppliers if they run out of stock, so they could buy water from a water supplier after that. And then between the inventory and their suppliers, they have to move it. And that's the big thing we're going to feature today is the carriers. Understanding how that carrier portfolio can help me need. So this is going to be our resources. And it's a basic model of how do we best align our resources, the combination of resources, to meet needs is what we're trying to do. These are the inputs, the key inputs to our model. So do we have our votes up here for the model? We have a few votes here. Looks like constrained optimization, linear programming, mixed integer linear programming is the winner with some algorithms and approximations and probabilities. Guess what? You are right on target. We have a stochastic linear program here that we're going to be using to model this, right? And it's going to be incorporating some probabilities and that's what makes it so stochastic. So it is a combination of two things that you were voting on up there. So that's exactly what we're looking to do. So we'll run a model and we'll talk about that in a moment here. Now what are the outputs? We can use this model to assess the system as it is now. What is the current capability of where the inventory is, the current supplier and carrier portfolios? How well does it perform against the risk portfolio that we have adopted? But we can also optimize and determine if we move things and aligned our resources differently, how would it change? And I think the key metrics that are interesting is looking at the combination of those, identifying metrics that a decision maker and FEMA could use to make decisions around resource allocation. So that's the high level model here. We have inputs, outputs in the model. We have a lot of math in the middle here and I'm going to invite Alex to come up. You've been learning this. We're going to show you how what you've been learning is applied in this particular situation. So I'll raise the background while you get going. Here's the clicker. Thank you very much, Jared. So let's see how we would model such a setting. This is pretty exciting. Don't get scared. This is our model. There's a lot of math. There's a lot of math going on. Most of what you're seeing here is something that you have seen in the course already. The only question is how do we introduce the stock toxicity to a linear program? That's what I want to cover in the next few minutes. So what we want to do is we want to serve multiple disasters which we don't know before about. So that's the stock toxicity that comes in. But let's start with what you know. What you know is a deterministic setting, right? So let me just quickly check this here. You know about having inventories or depots. I call them I. And you know about demand or need, I should say. So these are the disasters. And this is just one disaster I'm looking at now, J. And usually we set it up like that, right? So we want to deliver from our depots to our disasters. And this is exactly what I'm doing here, right? I'm transporting products Y from I to J. And instead of cost, I'm interested in time because it's a disaster response network. We're not so much into minimizing cost, but we want to serve people as quickly as possible. So we want to minimize time. This is our objective function. And the two constraints that I'm putting up here, obviously, they go more into that problem. But the two major constraints and those two you know about is I want to satisfy demand. So some of everything that goes into one disaster note needs to satisfy that demand. And I can only do that subject to my supply. So the Xi is the volume that I have in my depots. And I can only supply as much as I have. This is what you have been learning. That is what Chris has been doing with you in the last two weeks. So now we want to extend that for multiple disasters. So what I add is just one other disaster. Think of that as the two hurricanes that just hit the US. This is Hurricane Florence and I'm trying to dispatch the volume there. And this is the recent Hurricane Michael that just was here in the US a week ago. So again, I have the demand that I want to satisfy for Hurricane Michael. I have that supply constraint, my available inventory. And the only thing that really changes now is how I model my objective function. I still have what I serve for Hurricane Florence and I'm adding here the time I need to serve Hurricane Michael. And my objective function becomes a balancing act between those two. And the balancing is probabilities. So assume I'm thinking about that or I'm doing the assumption that both hurricanes are equally likely to happen. So 50% I would multiply the expected, the time to respond to Hurricane Florence with 0.5. And I'm adding the time to respond to Michael and multiply that with 50%. And I'm trying to minimize now the time it takes me, the expected time it takes me to serve both disasters. And now I can extend that to multiple disasters, right? Up to K disasters. And K will be later on about a 1,700 disaster that we have in our risk portfolio. And I'm going to talk about that later on. So this is everything you need to know to model this as a stochastic linear program. No, it's still the other way. Is hope erasing? No, I'm good. So what you're seeing here is now again that large portfolio, that large model that I was just showing you about. And now you exactly know what that first equation means, right? It is the probabilities that a disaster occurs. It is the transportation time it takes us to respond to the disasters. And it's the volume that we are shipping over all the disasters in our scenario. That's our objective function. You know about the demand constraint. We've covered that. And you know about the supply constraint. We've covered that too. Nothing changes. The only thing that really changes now is I add how I model carrier capacity because that's really what is of interest to us in this problem. You should think about that as adding additional nodes to the network. So let me return to my very simple depots with the disaster sites. And before I have just directly connected them, now what I'm doing here is I'm introducing, I'm calling them carrier nodes. They get the index R. What I'm doing is I'm shipping my volume through the carrier nodes. And this equation here is a balance equation to make sure that anything that goes into my node also leaves the node. So to make sure that my linear program actually works. And I'm imposing a capacity constraint on what I'm feeding into the nodes to model constraint carrier capacity. And this is another constraint that I'm just putting into my model. And in the end, we have our well-known non-negativity constraints. And here we are, a stochastic linear program for disaster response. So it looks intimidating, but when you break it down, it's what they've been learning all along. Exactly. The only change we really have is stochasticity. And that is pretty simple. We're just weighing. That's all. All right. So now since we have now covered our model, I'm wondering if there are any questions? There is. One question that you should answer is, how do you ensure that all the demand is met? All right. So I am ensuring how demand is met by setting up that constraint here. And essentially, my decision or my shipping variables, why, I'm summing up over all of them. And I'm feeding them, I'm making sure that I'm feeding exactly the volume in to the disaster sites that I need to have. But maybe I can add to that because maybe if you think about that, one thing that is perhaps not completely curious that I'm using dummy notes to ensure that I'm always meeting demand. So I may have larger disasters than I can serve with my inventory in that setting. So suppose I'm having a disaster with 60 million or more and I'm not having enough inventory, that problem will become infeasible. And what we are doing to solve that is we're introducing a dummy note. You can think of that like a large inventory with infinite inventory that I'm always using or drawing on when I'm out of real inventory, female inventory that I'm modeling. And that allows me to keep track on when we're out of stock. And I'm just tracking that to make sure that I can model these stock out situations. So it's like, here's what you're saying is you'd add a node over here. I, that's a dummy node, we'll call it D, doesn't actually have inventory, but it allows us to meet the demand. And all we have to do is count up how little, how, where we pulled on this to see what we're, where we fell short. Yeah. So it's a way of accounting for the inventory that we don't actually have in the nodes, but we can account for the fact that we didn't have it by supplying this, this pretend dummy stock, right? And for us, it's like a, a crotch to make sure that we can model situations where we have not enough inventory. Yeah. And if you, if you keep track of how much you use the dummy, this will give you a sense of how many, how much resources you're short on a regular basis, on an expected basis across all of the disasters that we have. What's the expected amount of inventory that we don't have just to meet the needs? Alex, there's a question from Krishna. Yeah. Krishna, can you unmute and ask that online? Yeah. Can you hear me? Yeah. Hi, Chris. Hey, Alex. I was just wondering in the actual model that is implemented, how many disasters are factored in or how many different probabilities that are going into the objective function? Yeah. So we are going to talk about that just in 10, about 10 minutes. We're going to show you exactly how we feed in the risk portfolio and what kind of risk portfolio that is, but I can say it's about 1,700 different disasters that we're feeding into that. But I think more generally, and we've been using this model elsewhere, I'll talk about in a moment, but a nice thing about the math model is we put it into a, you know, a computer can handle thousands, tens of thousands, hundreds of thousands. As long as we have the data, we have the structure here that allows us to keep adding up to K, right? So it scales very well. And in fact, what we've been doing with this model is kind of approximating the way the insurance industry thinks about setting up policies. They run thousands of disaster scenarios and determine what's the right coverage for a region that might be affected by disasters by running thousands of potential scenarios. So we actually like the fact that this can scale up because we can incorporate that really robust test across lots of different scenarios. Two things I wanted to mention. One thing is we're talking about probabilities here and this is kind of a step. We're going to take probabilities in the next week. So in week seven where Chris will be talking about probability distributions and how to implement and how to think about probabilities and the rest of the course essentially will all the time think about what happens if we don't know exactly what is going to happen. That's one thing. The other thing is we had a lot of talk about which tools to use to run such a problem. And of course, in a course setting, we always need to scale down our problems to make them handle in a course setting. Such a large setting, you need to have the right tools to solve them. And this is actually implemented in Python with a groovy pie, which is a specific solver that deals with all kinds of linear programming problems to attribute or to make sure that we can solve this problem on such a large scale. So with Excel that would be more problematic. It would tax Excel, but the thing is the modeling structure is the same. It's just you implement it in a different software to scale up. So it's an IT. It's an IT question and a question of what kind of tool you want to use. I see a question up here at the top. Can I can I jump in here? It's a good question that Harry asked about in disaster response, which is the most important aspect to consider cost effectiveness, short delivery time or high fill rates. And I'll say this model, we're focused on time, because as I mentioned, this is the initial days of a disaster and we have the initial inventory in our warehouses. How fast can we get it out? So for the initial days, time is really important. That's why we decided on that as being the objective function. Although we do capture cost and we can measure cost. And in fact, we can look for different budgets. How fast can we be so we can do a trade off of cost and time with our model to do what we call Pareto optimization. But we also in our lab done some research in the past to come up with a multi-criteria objective function. I could post some information about that to the learners if they're curious. How do you come up with an objective function that considers all the things you may want to incorporate when thinking about disaster response? It's a good question because that objective function really drives what the solution is going to be. That's a key thing in doing your linear programming and picking the right objective function is really critical. That's a really key question. Chris, is there anything that we need to address regarding the model that learners have posted? Time frame is the model covering and we'll supply restock after a certain time after an event happens. That's an important one too. We are assuming you caught something that's very clever there. Remember he mentioned the first disaster being Florence, the second one being Michael. We assume that the warehouse gets restocked before the next disaster. We're looking at disasters being what we call independent. It could be that you could have multiple disasters happen in a time window that wouldn't allow us to replenish our stock. It depends on how fast you can replenish the warehouse to get ready for the next disaster. Again, all we're doing is replenishing to meet the first few days of demand. If our suppliers are set up and they can respond and fill our warehouse within a couple of weeks, we should be ready for the next disaster in a couple of weeks. If we have disasters that hit very close to one another, this model wouldn't necessarily capture that. To look at that, we'd have to look at some other kind of modeling that would look at that contingency of demand across a period of time where there's overlapping disasters. Since we have covered our model, I thought it would be valuable to think about or to showcase the history of this modeling. We have done similar projects to structure disaster response networks. I wanted to invite Jared to talk about that a little bit, how we came up. We came to modeling this here for the US and what we did before. I'll tell a little bit of history about this. Should I sit here? I'll sit here. We developed this concept a few years ago. A colleague is a PhD student at MIT who was finishing. I had been working with the United Nations. Our lab had worked with international disaster response and the United Nations, specifically the World Food Program, which takes the lead on logistics following disasters. Identify this could be an issue. Where do we put preposition stockpiles globally to respond to global disasters? We developed this model a few years ago and started using it with the United Nations. They have these United Nations humanitarian response depots located in five locations around the world. They actually put a stock report online every night of all of the different non-profit, non-government organizations that stock their inventory in those warehouses. They provide a daily update. We've been grabbing that daily update and running our model every night to just track what those resources and those warehouses are doing to meet people's needs. How prepared are we for global disasters? We then, with that initial model, global model, the UN asked us to do some studies in the Philippines, in a very tiny island in the Pacific Vanuatu to see at a more regional scale how prepared we are. This approach of using the stochastic linear program to assess preparedness with stock has been used globally. While we were doing this, we actually had a student at MIT, a master's student who worked in our lab. Her name is Lauren Finnegan. She adopted this model to look at the U.S. and look at the U.S. disaster responses. So I want to invite her. She's actually on the camera today, on video from Washington, D.C. Lauren, would you like to talk about your experience as a student? Sure. All right. Can you hear me? Yeah. Hi, Lauren. Okay. Yep. Hi, everyone. It's great to be here. Thank you, Jared. So I currently work for FEMA, but as Jared mentioned, I was a student in CTL, and I did use linear programming to complete the research for my thesis, which I believe they're going to present a little bit later. And what was really neat was that I did all that work at MIT, and then I was actually able to use what I learned when I joined FEMA to support decision-making at FEMA. So some of the decisions that I was able to use this work for were setting stock levels for certain commodities and also citing new warehouses for FEMA. So that was really exciting and a great opportunity to use what I had learned at MIT and the linear programming that you're learning now to inform real decisions at an emergency management organization. So that was great. And so feel free to ask any questions. Yeah. Well, so Lauren, you actually, we used the code. We put it on an MIT server for your thesis, right? And you used that to solve the problem on your thesis. And then we allowed you to extend your account. You actually ran the code while at FEMA on an MIT server to help do this analysis, right? Yes. Yep. So this is an academia. We're helping support, you know, with our academic models some real decision-making. And the result of what happened as a result of that modeling effort? Well, so for one of the modeling efforts, we were able to suggest stock levels for one of the major commodities that FEMA stocks housing. And the second was to inform the siting of a new warehouse. So we were looking at, FEMA wanted to set up a new warehouse in the Northeast. And they had a couple of sites in mind. And I was able to use the model to compare the benefits in terms of, like Jared mentioned, time or cost to serve demand based on different locations for the warehouses. So that was... So in that case, you can look at new locations and see what that location could add to the network as well. So great. Thanks for sharing that. And actually out of that work, Lauren was talking with me. We identified that we had used our model internationally with the UN, and we had transportation modeled as international transportation over the ocean and air. And it wasn't as finely calibrated toward domestic truck transportation like we have in the US. So that was one of the things we identified as an opportunity to improve. And then we received a grant through the Department of Transportation, the University Transportation Center grant to do some research where we were able to take the model and improve it. And Alex has actually been doing the lead on that research to incorporate this domestic transport capacity in a better way. So can you share more about what that's been? Yeah. So how that's been able to inform things? Yeah. So the idea now I would say is we just walk through one of the examples and show how we set up the portfolios and see what kind of metrics we can do. Let's see how it works. Let's see how it works. So research in action, if you will. So let me move on with my slide deck here and get rid of my eye. Sorry about that. So Jared has been talking about the different inputs. We have that risk portfolio, we have the inventory portfolio, and we have the carrier portfolio. And for these three portfolios, we need to come up with data to feed into our model to solve the problem there. And I'm first going to cover a little bit on where we get that information from and how it actually looks like to give you a feeling of data collection and what kind of data goes in. So the first thing is the risk portfolio. So the risks that we want our assets to handle. And getting such a data set is not as easy as you would think about because it's not largely publicly available. You need to find some way to approximate it. But we are lucky because we want to model FEMA's need or whenever FEMA is asked to support in a disaster. And actually what they do is they have this very cool data source called Open FEMA where they publish when they have been called into action and help respond to a disaster. We can use that data. And what we are doing is we are extracting the information on when they responded to a disaster in each county. And they have been collecting that data for, I don't know, 75 years or something. I'm going to reduce that data to 1990 to mid-2018 and assume that about 26% of the population of each county is actually our total affected population that I need to serve in case of a disaster. And to give you some idea of how that risk portfolio actually looks like, I have this nice heat map which tracks how many people are affected in the continental United States. And I'm focusing on the continental United States because we only want to model what we are responding to with trucks. So anything like Alaska or Hawaii or Puerto Rico is not in my data set right now. So my heat map works like that. Any disaster that happened between 1990 and 2018 that FEMA got called in, I'm counting. And green reflects that one to six counts have been happening and the red line is a lot of disasters like about 50. And what you can see here is we have a disaster belt around the west coast. We have a disaster belt around the south coast and into the middle of the United States, they call it actually tornado alley. And we have a disaster area right here around Boston, which is probably snowstorms. This is the geographical distribution of the disaster network that FEMA needs to take care of. And you can see that it spreads out through the United States, but you have also spots that you don't need as often to feed to and you need to come up with a portfolio of assets that actually works against that. So the next one is showing how the distribution works in terms of number of people affected. And we are going to discuss how to look at a histogram and how to look at a stochastic system and get these data. But I'm just highlighting here the number of disasters, which is 1,700 in our set that we are working against and the spread that we need to, that we have as need or total affected population. So the smallest disaster in our data set is around 200 people, very small. And the largest one is around 64 million. And FEMA is supposed to set up a inventory network to meet this large spread, which we can see here too, number of disasters, total affected population. All right, so this is our risk portfolio that we are going to bring in. Second one is the inventory portfolio. And let me get rid of my slides here. And we have just, we have prepared an inventory portfolio for you that is not actually FEMA's inventory on water, but just to showcase of how our model works. We have our five locations from the west to the east, and it's heavily skewed towards the east. So we have a lot of inventory sitting in the northeast and in the east, so Washington and Philadelphia, of about 21 million bottles of water. And we have very little inventory in the south and in the west, just to showcase how such an inventory portfolio could look like. The trucks are meant to give you an indication of how many truck loads that corresponds to. So 1 million units is about 60 trucks. And truck loads of pallets of water, right? Oh yeah, truck loads of pallets of water. So the key question for you or for us is where should we position that inventory? Is actually that distribution of inventory that I've just shown you here, is that good? Would you say we don't need to move it? Or should we move it? Should we actually move more to the northeast than the east? Should we go to the southeast, to the south, or to the west? So I'm looking for your intuition on where you should position that inventory. And while you're voting, I'm giving you some additional insight into how we set up the carrier portfolio. So for each depot, we have a carrier portfolio in place. And I'm just picking out southeast, Georgia, where I'm assuming that I have 80 trucks available. These 80 trucks are becoming available within 14 hours per truck. So this is the time it takes the carrier to bring in the truck and load it up so that it's ready to be sent out at a variable cost on average $2.7 per mile. And I'm setting these carriers up in each location to reflect a carrier portfolio of FEMA. I could dig deeper into that because it may matter how we contract our carriers. I'm just highlighting that quickly that in my example here, I have four tiers of carriers. One is the what I call initial driver that are prepared trailers sitting in the lot. And we are just bringing in the tractor to send them out. It takes us about four hours here, and we have 10 trucks available, or 10 trailers available. And then we have established two contracts, one with 30 trucks and one with 40 trucks. The 30 truck contract comes in 12 hours into a disaster and is ready to be sent out. And the second contract comes in 17 hours into a disaster. If that is not sufficient, I can go to the spot market and procure the rest of the carrier capacity that I need to serve need. And we are assuming here, just to make it simple, that I'm going in to the spot market 26 hours into a disaster. And I have these carrier tiers in each place that are made that made this overview up. This is how we set up the carriers. We're going to do a lot more about transportation in SC1X and SC2X. We have a lot of lessons about that. So this is just a preview of what you all have to consider when setting up or thinking about transportation. So now without further ado, I want to show you some results. Here we go. So on the left is just the current setting, my current setup of inventory. And keep in mind that I have also a current setup of carrier portfolio. And what I do in the system assessment is answering the question of how well does my current portfolio of inventory and carrier actually respond to my risk portfolio? And we can see that here. So the fraction of demand served is how many people I can serve on average, 93%. And the fraction of disasters completely served tells me how many of the disasters that are in my risk portfolio, I have served the entire need of 26% of our population, 99%. And that shouldn't be too surprising because I have a lot of inventory in my setting here. So my fraction of demand served metrics should be high in general. I can also produce an effectiveness measure. And that effectiveness measure is showing about 32 hours. It takes me on average to send out the trucks to the need. And then in the end, I can come up with a carrier contract metric to tell me how valuable the contracts are that I've set up. And what I'm doing here is I'm comparing using the contracts and the spot market to only having the spot market available as a reference point. And if I would only have the carrier contract, sorry, the spot market available, then I would only, that I would use my time to serve increases by about 15%. So you can characterize how your system actually works and how well you are serving need with aggregate measures to get a feeling of how well you're doing. But how well you're doing is only half the story. You want to know how well we could do. And that's where I asked you to respond to, let's see how what you're thinking, and you're getting already the right intuition that we should move something down south, right? I skewed the portfolio of inventory towards the east and this is how the result looks like. This is what the model suggests. The model moves a lot of the inventory that was in the east to the southeast to the south and the west. And that's pretty intuitive if you remember our heat map, right? There were a lot of disasters here. There are a lot of disasters here. And sending all that inventory from here just takes a long time. And of course, our model notices that and moves the inventory to the south and the west. Pretty intuitive, right? So the model is doing what we expected to do if you will. More importantly, I'm interested in how well I'm doing in terms of time. So of course, I'm serving the same number of people. So the fraction of demand served metric is still 93%. That doesn't change. But what changes is how quickly I'm serving them. So if you look at that, this is one day into the disaster. It is two days into the disaster. Within one day, not a lot changes because I'm still sending out the same carriers. I don't have much chance to reduce that because my carriers are coming in on average within 12, 13 hours. And then it needs time to send them out. But after two days, a lot changes because essentially what happens is those people that get served within only three days move to the two days. And that makes a huge difference, right? Because one day can decide whether you may live or die in such a disaster setting. And it's important that. So you can see that a lot of people are served far quicker just by repositioning the inventory in the network. No additional cost, right? This is just moving inventory into the right place. Yes. So what we can actually, if we are comparing, it's about, in my case, it's about 15% improvement in average time to serve. This is what you can get out of such a model on a quick overview. So there are a lot of other metrics that we can come up with to characterize that as just a peek into how we can set something like that up. One thing, how am I doing on time? I'm good. I'm good. So one thing that I wanted to mention, just because I'm very excited about that and people that work with linear programs usually like to look at that very much, and Chris covered that actually in his lesson just briefly, is shadow prices, right? So remember that shadow prices or the dual variables of a problem, they tell you what it is worth to you as a decision maker when you increase capacity by one unit. In our setting here, it means how much our expected time to serve is reduced. So how much quicker we are going to serve the people in need. And I'm here showing the carrier duals for each location in these bars. The larger the bar, the more valuable it is to me to increase the capacity by one unit. So what you see here is, for example, in the southeast, I should mention that I'm running this dual shadow prices on the original setting. So how my assets were distributed without optimization, so with a heavily skewed inventory to the west, to the east. And you can see that the first carrier tier, so these preloaded trucks that are sitting in the lot, they are of course the most valuable to me because they are coming in within four hours. I can send them out. So of course, if I have the chance, I'm looking into renegotiating these carrier tiers first. Well, in fact, Alex, it's a little bit more nuanced because this initial tier, this is trailers that they can preload before the truck arrives. So it may mean we have to position some trailers at those locations as well. So additional resources to be ready to preload them and then the truck can come and hook up and go. So I'm always thinking about yeah, that's true. So that helps again, more resources thinking about trailers in the network. So the nice thing is shadow prices help give you an idea of where to focus on adding additional resources, where you get the most benefit. Exactly. And we see how the skewed inventory impacts the duals, right? Here is a lot of inventory. So we need more carrier capacity to actually reduce time. Here's very little inventory. So we only care about these first tiers because we're sending out low inventory anyways. So we get the most benefit from adding that preloaded trailer in the cell. So this is a peek behind the curtain of a linear program and how you can do that for a disaster response network. Do we have questions that we should address right now? We have, maybe. Derek says how interested in the ways we can collect data during active disaster response to feedback into these models and make them more accurate? Actually, that's an interesting point. We're actually involved with FEMA and doing ongoing research to understand how we can collect data in a better way in real time. And not only just for FEMA but also for the private sector, for the grocery stores that are also providing water to people. How can we collect data in real time to understand how well they're responding? And actually, FEMA can do some things to help them perhaps in setting up their business in a better way. For example, you have to have power at a gas station to pump fuel. So is there ways that FEMA can help prioritize restoration of power at fuel stations and at grocery stores so that then more people can be met? Remember, we only serve 26% of the demand out of FEMA. The market is supplying the other part. So how can FEMA help support that market is something we're doing. That's a good point. Real time. And we can feed that into the model in real time to assess how well we're able to perform them. Let's see here. How are models deployed and how frequently does a model need to be tuned, changed, calibrated? Well, that's an interesting point. We deployed this, as Lauren mentioned earlier, she deployed it a couple years ago when she joined FEMA. And then we determined we needed to calibrate it better. And we've just now finished doing the work to calibrate this. In fact, this may be a good time. We actually have a special guest in the lab with us today. Mr. Jeff Dorko, who is the head of logistics for FEMA, is here today. Maybe we can just ask him about how these kind of models could be used to make decisions. So maybe we want to come up here and join us at the table here and we can talk about that. You've largely explained it all. What you have done for us has been a game changer, I think, for FEMA. We'll go back to Lauren's modeling and how we've carried that forward to now. I mean, it has made a material difference. Alex made the point earlier, when you move things left, you do things faster, you take care of disaster survivors. Our mission one is to take care of disaster survivors. You have to keep people alive, just have their worst day. Make sure the life-saving, life-sustaining things that need to be done for them to get down the road in those first few days are going on. And gaps between curves are threats to life. And what this model has done for us, I mean, it's very practical. The work we're doing now to look at our warehouses, to resize our warehouses, to relocate our warehouses, what are we going to do in the mid-Atlantic now? We have a couple warehouses and the research that's going on right now is going to put a new and better warehouse. And what this work is going to tell us is how big should it be, what should be in it? I mean, how many loading docks do you need? How many trailers should we have to optimize that initial push that gets out the door? Where should it be relative to the road network so we get out better to disaster survivors? It's making a huge difference. I will tell you, for example, not to this, but you had a graduate student that looked at our pallet configuration. You think about something as simple as pallet configuration, that's not rocket science? Well, maybe in a way that it is, because we went back and looked at our pallet configuration and found a better way to build our pallets. And now we can haul with the work that you've done, we can haul in 15 trailers, what it took 18 trailers to do before. And your pallet work and some looking at the state-of-the-art racking that goes on in warehousing around the world, we now get about 59 percent more pallet positions for the same floor space that we have in some of our legacy distribution centers. So we're going to actually be able to stock more. So we can put more inventory in the warehouses because the racks are set up in a better way. But we need a model to help determine where that inventory should be put. Absolutely. Because I live in both those worlds. We've been talking about effectiveness to this point. How do you get things to a disaster survivor on the appropriate timeline at the initial point of a disaster? But I live in a very practical world that I have to go to the Office of Management Budget and I have to describe the money I need for these warehouses, what I need to store, and why I need to store. And what we know is, what we don't know is as important as what we do know. If you look at the modeling that you've done here, you're looking in the rearview mirror. I mean, I've had to go to OMB, the Office of Management Budget, to describe using a regression analysis, a plus-on distribution. Why do you have what you do now on a cost basis? Why does it make sense that you're doing what you're doing? Well, all that's based on historic data. And that's good. Historic data informs where we ought to be to take care of all those things that have happened from 1990 forward, or I think at one point you went back to 1974 and looked at storms and all manner of disasters. But at the same time, we have to be ready for the catastrophic. A Cascadia subduction zone earthquake scenario in the northeast of the U.S., a large Southern California earthquake, which is not what we've experienced since 1990. So we need to look at both. Your dummy note out there that tells you what we have now and how we're trying to optimize it based on our look in the rearview mirror and our experience over the last 20 or 30 years, that's really good. But where do we reach the limit that we're not able to meet need? And then how do we fill that need now? How do we plan for that with the private sector or other partners we have? And all this modeling has helped us do that. You mentioned something about working with OMB using regression and Poisson processes. That's coming up, right? We are going to cover our regression in B9. So we'll learn a lot about that. So another tool you'll learn about in this course being used with Mr. Dorco, working with the Office of Management Budget, looking at the budget side of things, to make sure that the resources are spent effectively. So maybe bridging off of that, this kind of a course, this kind of online course, is this something that is useful to FEMA and training? And I think this and other things like it, but this in particular will be a cornerstone of our going forward. Right now we have logistics planners who are good at FEMA business. We are increasingly partnering with the private sector and academic institutions, but what the MicroMasters does is it gives us the tools that I think that our folks need to have. It's not just our folks. I think we live in a world where we're very federally centric. We think about supply chains in terms of we're going to rush out the door during the first days or weeks. We're going to put this replacement federal supply chain down to fill the need that is not being filled because things have been torn up and disasters have happened. But there's the private sector capability which is virtually limitless compared to what we can bring to bear. And while our folks have the analytical skills and tools that they need, I just brought on a new supply chain advisor on board and he is starting the MicroMasters program in December. And so I think this program holds great promise for us to professionalize our planners and to get them talking and thinking and analyzing your supply chains. And it's not just us. It's partnering with the private sector, with the states and the municipalities that we serve in this business. I think if we can professionalize the whole community of folks who plan for the supply chain and against the supply chain implications and disasters, then we'll be back to that end. And with the MicroMasters, the state and the local could work with the federal taking the courses at the same time and maybe communities can form around learning together on this. Yeah, that's an interesting thing. Do we have some other questions up here for all of us here? So one of the questions that's really interesting to me is how does this come together in a real life situation? How would you know how to replenish and how would you use such a model? So for me, there are two components to that. Well, that model actually informs and how you replenish because these are perhaps two different things. Yeah, maybe talk about the replenishment cycle. We talked about inventory in the warehouse and that issue of how do you get the inventory filled again, you know, understanding how you can look at the procurement part of this too and working with suppliers? Yeah, absolutely. So you used the example earlier as we had Florence that hit South Carolina, North Carolina. And there was only a matter of a few weeks before we now had to live through the impacts of Hurricane Michael coming through Florida and up into Georgia. And we had just enough time, I will tell you, in this case in between, given that our suppliers typically had not had a lot of demands for their products and the folks I'll use meals, for an example, the companies that produce our meals are the same companies that are producing meals for outdoor stores or produce military meals for the Department of Defense. And we were able to support Florence and we were able to restock, we had just enough time and the state of the supply chains out there, when you go down two and three tiers, was just enough to be able to get the warehouses back to where they need to be for the course. But if you go back to a year ago where we had in quick succession Harvey in Texas and then we had Irma that came through the Caribbean, went up the length of Florida and into Georgia, and then we had Maria, that constant drain, our suppliers and their sub-suppliers, when you go two and three tiers deep into the supply chain, put a real strain on the system. And we had to go into, in terms of our feeding mechanisms or our methods of feeding people, activate all sorts of second and third tier ways to get enough food out there for folks. And again, so we circle back and we'll do the after action of that, we'll do the after action of this, and it takes us back to, what do we need to be prepared for? The suite of storms that we've faced now, how can we better prepared for that? Where does that put us against having to face a truly catastrophic one? That's interesting too, the idea of having thousands of disasters in the history helps you plan according to a broader set rather than just planning against what you recently experienced, which I think humans tend to do. So that's a nice thing about it. There's a technical question up here. Alex, what's the Python sufficient to do this? How did the modeling approach we use? So the question was about when we decided which tool to use. And that's a really good question. So for us, I think it's part of how much data we're expecting to feed in, how large the problem is going to be. And for us, that's usually going to Python because it's very flexible to use that. You can manage the data very easily. You have different tools that you can load in, and it's open to the public, right? So it's open source and then we are, and it'll make it easier for maybe FEMA to adopt this going forward. That's the idea. Because in the end, we can build a front-end that runs that Python code for FEMA and we don't have any issues in building that into a setting that allows external parties to use that very easily. Lorna, you're up for that? You're ready to take on some new modeling approaches here? She's got her thumbs up there on the screen. Yeah, so she's at FEMA now. We actually made the code run faster than when it was when you were a student. So it runs a lot faster now. We got an undergrad to help us optimize the code versus us professors writing the code. So we're making it better over time. There's a second component to that. How quickly we do such a project, right? And I can only speak to the recent one that I did, your four experience, maybe talking about the other projects that we could, of course, use some of the code that we developed before. But the core of the problem we solved in eight weeks, ten weeks. And you know what? And this will be something you'll learn through practices. Most of the time it's not coming up with the model of writing the code. It's getting the data, making sure the data is correct, making sure the data aligns with people who are making decisions as they build intuition with it for them effectively. And so that's our next step, Jeff, is to actually take data. We made up data for this exercise here, but we take your actual data and you've got some decisions coming up. You know, we're working on a footprint. Our warehouses are aging out. We're finding better ways to do business. All this will come together. And in the end, what does that do? It helps us take care of disaster survivors better and have a higher degree of confidence that when we get out the door, we're pretty confident as to knowing what we can do and maybe what our limitations are and we have to find other solutions at some point. And it's good to see how tools that you're learning in this course can be directly applied. The model here can be directly applied to help make decisions that they've got upcoming here. You can justify budgets with your regression analysis. A lot of these tools are directly applicable for FEMA. So maybe you can be looking at some of our MicroMasters students who are interested in this work. Absolutely. You know, there's a talent pool out there that you can tap. Always looking forward. Here's an interesting question for you two. Will AI, so artificial intelligence, play any role on this? I know there will be a new college and a teacher who has official intelligence in all subjects. So that's a really interesting one. I'll add one little one quick thing on that on that topic. So we hired a postdoc recently to work on a project sponsored by FEMA to look at private sector. And one thing we're looking at is how can we get massive data sets to understand how the private sector responding if we can get them in real time, like transactions from credit cards? How can we see a response happening in real time? You need artificial intelligence machine learning to be able to take those big data sets and do something with it. So we've actually hired a postdoc to help us. You know, those of us who weren't trained in the days of AI, we're learning by bringing in people who have been trained with those techniques and trying to apply it in this context. So there's a lot of potential for that. Integration with the private sector is huge. The private sector is infinitely bigger than anything we can bring to bear. And if we can stay out of the private sector's way and we can anything we can do to shorten the time and lessen the impact and get business back to doing business is what we want to do. Well, thanks for joining us today. We're out of time now, but we'll be glad to share links of the work we've done before. I saw one question about the link for the UN stockpiles. We can share information about what we've done in the past. We'll continue to share information about what we're doing with FEMA going forward to attract the progress of our lab and our research. But more importantly, I hope this gives you a sense of what you're learning in this course. A lot of math, a lot of analytics actually can help make decisions that may affect people's lives. And that's a really nice way to see the value of what you're learning. Hopefully that gives you some motivation to keep going weeks four or five, six and so forth, that there's a lot of potential impact there. So you want to say anything else to close out? So thank you very much for joining us. Thank you, Jeff, for joining. Thank you, Lauren, for giving us some insight into the practice component and that what we're doing here is actually going into practice. I'm very excited that you joined us today and had such an active participation in our life event here. For those of you that are doing SCSRX, good luck with the midterm. I know you're looking forward to that in one hour. Thank you very much. We'll see each other again in just five weeks for a third life event. In the meantime, stay on top of all the math. Thanks, guys. Bye.