 Hello global supply chainers and welcome to our second SC2X live event today. I'm pleased to have Milena with me. Welcome Milena So Dr. Milena Janjevic is a postdoctoral associate at MIT Center for Transportation and Logistics And she's also part of the mega city logistic lab She's a polytechnical engineer and holds a PhD in transport and logistic engineering from the University Libre The Brussels in Brussels, Belgium She's also a lecturer there at the Center for Mobility Studies Her current research focuses on urban logistics and last mile delivery with particular focus on distribution network design in the context of peak commerce Deliveries and urban freight logistic policy. We are really happy to have you here today. Milena. Welcome. Welcome again Okay, so the plan for today is the follow-up so up to this point We are almost in the middle of the of the course so we're really presented four weeks of content and in these two weeks of content a what we cover mainly was about a Network network design. So basically the first two weeks of the course was network design and The topic of this life event is gonna be a network design So Milena is gonna be sharing with us and experiences about implementing this type of project But mainly a covering last mile distribution network design. Okay, without further ado and Milena, so the floor is yours. Thank you So, hello everyone I was asked today to give you some insight about some of the work that we are doing in a mega city logistics lab With regards to the last mile distribution network design Which focuses mainly on urban markets Before going into a further description about the work that we are doing I will first give you just a short Overview of why do we particularly focus on these urban markets? And what are some of the challenges that we encountered there and basically why so much of our works is focused on this particular part of supply chain so The first reason for that is that we are living in a urban world So today we have half of the urban population that lives in urban areas This generates around 80% of global GDP But as we look at the projections, the urban economic story is becoming even more concentrated So this chart shows you the projected cumulative contribution to GDP growth between 2007 and 2025 And we can see that in 2025 First 100 cities, first 100 largest urban areas in the world are expected to account For 35% of global growth and only 600 of them are expected to account for 62% of global growth And when we look more closely to these 600 cities, we can also see that Although they account for only 25% of a global population, they account for 60% of global GDP What this means is that the increase in both the urban population and the GDPs will result in increased demands for goods in urban areas So the demand for urban logistics is increasingly high And this will bring some specific challenges, especially when we are transitioning towards these large mega cities which are typically highly congested areas On the other hand, not only is the demand for urban goods mobility growing, but we also witness a fragmentation of urban deliveries So on the first picture on this slide, you can see a container ship And this illustrates that on the long-distance transportation, we have increasingly consolidated transportation So with, for example, container ships that can transport up to 15,000 containers However, this we can call this a kind of a massification on the long-distance freight transportation But then when we look at the last part of the supply chain that occurs in urban areas here, due to some trends Notably e-commerce, we witness a atomization in the urban leg of freight transportation So this will generate an increase in number of vehicle trips disproportionately to the increase of the overall demand for urban goods On the city level, this will of course have impacts in terms of congestion, in terms of pollution But it will also present some specific challenges for logistics companies that have to operate in these environments And so to illustrate some of these challenges, I have two questions that I would like to address to you So the first question is related to the cost effects of the last mile logistics So please, in your opinion, what is the percentage of transportation costs that occur in the last mile? Okay, so the poll is open, you can reply And we are getting some results So the poll should be in the right hand side of your screen Please select the one that you believe is the correct answer So the question is what is the percentage of transportation costs occurring in the last mile? So so far we have 12 people, so most of them are answering that 28% Is it something that you were expecting, Elena? Yes, so 28% is indeed the average cost of transportation costs occurring in the last mile So your answer is correct, this will of course depend on the type of supply chain that we are considering But on average it is 28% This is a very large portion of cost And just to illustrate the cost, intensive nature of the supply chain We can for example look at this slide here that illustrates one particular supply chain For textile industry that originates in India and goes to Europe, to Paris in particular So we can see that there is a set of different links between production facilities, transportation facilities and different transportation services that are employed And when we look at the urban leg of this particular supply chain We can see that in terms of distance it will account for around 1% of distance And it will account in this specific case to 25% of logistics costs So companies are looking into ways of optimising this part of supply chain And decreasing the costs relative to last mile To illustrate the complexity of the optimisation of last mile logistics I have another question for you which is related to the way that we can sequence different stops So let's imagine that you have five vehicles They are departing from one single depot and you need to serve 50 customers And you can sequence these customers in many different ways And the question is in how many different ways you can sequence the stops Of these five vehicles towards these 50 customers So here we have four different choices and we're expecting your best guess Okay, are we talking about more or less a common typical last mile operation? So 50 customers, something reasonable Five vehicles may be just a small fleet but let's see some of the options So yes here we have a rather small fleet of five vehicles 50 customers of 10 per vehicle which is much less than we usually serve But you will hopefully see that this is already a quite complex problem To solve Okay, so if you haven't answered the poll yet please do it So we'll share the results immediately So we're getting some results So 40 percent more or less of the people are saying the third option The third option, so actually it is the fourth option The first option, yes So 10 to the fifth Okay, so actually it is the fourth option So it's 2.4 then exponent 70 possibilities So which is a lot So indeed only for five vehicles and 50 customers This is the number of possibilities that we have We can then take a real life example to illustrate this complexity And we can take that off of UPS So UPS does not deliver 10 customers per vehicle route But an average on 120 delivery stops per route And if we look at the slides now We can see a very large number with a lot of zeros That I will show you right away So according to the counting of these little zeros This is actually an order of magnitude of 10 exponents 198 So this shows you the complexity of optimizing last mile operations And just to give you an overview of how this optimization actually can affect the cost Let's again take an example of UPS So they perform around 55,000 delivery routes in US per day And if you were to apply a cost reduction of just one mile per route This will generate 50 millions of annual cost savings in the US So companies have it is in their best interest to indeed make sure that the last mile Part of their supply chain is well optimized Yeah So in order to adapt their distribution strategies to this particular challenges of last mile We can work on several areas One of them is distribution network design And this will be the focus of our events today But we can also look in vehicle technologies And some measures that are more relative to for example operational planning So let's go directly into distribution network design And see some of the ways that companies can optimize their networks In order to best adapt them to last mile environment So when we think about last mile distribution design We are thinking about several different decisions that need to be made One of them is how do we locate facilities? The second one is how do we define service areas? And the third one would be what type of vehicles we use To actually serve customers in urban areas And we can underline a several let's say archetypes of network designs That we can deploy in urban areas So here you see three different possibilities The most basic one is the first one Which is a single tier system Where we have one distribution center That is typically located in the outskirts of the city And that will serve individual customers With vehicle routes directly departing from the distribution center However, when we look at these mega cities and these large congested areas We also see that it's typically more efficient to introduce A second layer of consolidation or a second layer of facilities We can refer to them here as satellite facilities for example And these are the small squares that you can see on the scheme And so here we have a two tier system So a system that is composed out of two layers of facilities And in these two tier systems We can have two different options So either individual customers are only served With vehicle routes departing from satellite facilities Or we allow for a mixed system Where the distribution center can also serve some individual customers Introducing this multi-layered system So two tier, three tier or more tier systems Brings some advantages So it allows us to increase the vehicle utilization To form more efficient routes And consequently reduce the number of vehicles That are required and the costs But also on the city level It allows us to reduce the pollutant emissions Fuel consumption, congestion rates And the time that vehicles are spent in traffic And so the illustration that I will give today Of one project that our lab has worked on Is relevant to a two tier system in a urban area And here we take an example of a major Brazilian e-commerce company That operates a multi-layered distribution network in the country So we can look at their distribution network on several levels So on the country or state level They will typically have large fulfillment centers That concentrate all of their inventory So this is where all of the order preparation takes place But then if we look at the city level They also have a multi-layered two tiered system So an example here is relevant to Sao Paulo They have one distribution hub That is located in the outskirts of the city And they have seven operational centers Which are in fact those satellite facilities That we have introduced in the previous slide And that allow to serve as locations From where vehicle routes depart So just to make sure that this is clear The operational centers are typically only Performing transport operations So in this particular setting They do not hold any inventory They are only performing transport operations From larger vehicles to smaller vehicles That are more adapted to the urban environment In which they have to perform last mile delivery And to give you an indication About the size of the problem So this particular company delivers Around 15,000 customers on a daily basis So the project that I will refer to Was how do we redesign their last mile distribution network In order to minimize the overall cost of operations So here we focus on what's happening on a city level So again, distribution hub operational centers So we can look at some of the decisions That are typically made in network design problems And to introduce them Let's look at this particular example So the first level of decisions that we have to make Is relevant to the locations of different logistics facilities So this can refer to both distribution centers And satellite facilities And here we typically have a set of candidate locations That we have identified And that can be suitable for implementing these logistics facilities So in this particular case We had around 200 potential locations So you can see this as small dots on the map And the location decisions are aiming in establishing Which of those 200 facilities should be activated And which should not be So in this particular case We ended up with the following configuration So this is one of the scenarios that we have analyzed And so in the left side You can see a little brown dot This is actually the distribution hub And then we can see a number of satellite facilities That were located throughout the city And that are used for this last mile part of the operations The second type of decisions that we can make In the network design problems And that we are making Is relevant to service areas So here we have an entire city That presents different demand patterns And the idea is to basically segment the city Into a number of service areas And to define which service area Should be served from which particular facility So here in different colors You have different service areas And each one of them is attached to a specific logistics facility So as you can see here We are a multi-tier mixed network Where we have some of the customers That are served through a distribution hub While others are served through satellite facilities And so these service areas are typically fixed So given that the network design problems Are strategic problems So we will not redesign our network every day We will only do it once every few years maybe We will typically define service areas that are fixed So each facility will serve one particular part of the city We can introduce additional level of complexity And introduce some variability on a daily basis If this is necessary But this is something we can discuss later And then the third type of the decisions That we are trying to make in network design problems Is with regards to the model choice Or the type of vehicles that we want to deploy To serve each of those service areas So here again in the specific case Of this e-commerce operator in Sao Paulo We had three different types of vehicles That are presented here by different colors And the idea is to define For each particular segment of the city And that segment can be a neighborhood It can be a zip code It can be defined in any way that we Or the company wishes to define it Which type of vehicle is most appropriate to serve customers As you can see on one hand we define the locations On the other hand we define the service areas And then within each of the service areas We allow for potentially different types of vehicles That can be deployed So this gives you just an overview Of the type of the decisions That we are trying to make in network design problems And now we can go more into detail About the type of methods that we are employing To address some of these decisions So typically in order to model multi-tier distribution networks We used mixed-integral linear programming So when we look at typical mixed-integral linear program We have on one hand decision variables And then optimization objective And then constraints Decision variables relative to this specific type of problems Are relevant to the three types of decisions That we are making in network design Namely facility locations, service zones, and model choice So in order to model these for the first part Which is network architecture And defines active facility locations and their type We will usually use binary variables So for example for each of those 200 facilities That we have identified as potential Facilities that can accommodate Either distribution centers or satellite facilities We will define one binary variable That will take a value one If the facility is active or zero If it's not For the facility influence areas We typically divide the city into a set of discrete segments That as I mentioned this can be zip codes Or neighborhoods or any other unit of geographical analysis And for each of those specific segments We use one typical binary variable That signifies if a certain segment Is allocated to a certain facility And the third one is relevant to model choice Here a very similar approach We use binary variables to assign each of the city segments To a certain vehicle type So these as I mentioned correspond directly To the three types of decisions that we are trying to make And the optimization objective that we have used In this particular project Was a minimization of total costs of operation So this total costs can contain several categories of costs So there is indeed the cost linked to routing And less than our distribution But also cost relevant to vehicle equipment Facility fixed costs, handling costs, etc, etc We can also think about ways of extending This optimization objective So we can, for example, include other objectives Such as maximizing the total market reach Or maximizing the revenue or the profits Or decreasing the time that is required To reach certain customers And we can also think about multi-objective optimization Where we integrate several of those objectives Into a single objective function However, most commonly the cost that we are looking at The objective function that we are looking at Is relevant to the cost minimization And then we will also include a certain number Of constraints in our mixed integer linear program And these constraints are, of course, relevant To the feasibility of solutions that we are developing But also reflect some operational constraints In terms of carrying capacity of vehicles Or capacity of facilities Because each vehicle or facility Can only accommodate a limited number of shipments And this is something that we want to include in our model In a more advanced approach We can also, for example, include vehicle access restrictions So typically in some urban areas There are access restrictions To the vehicle size or the environmental performance Of the vehicles that can be used in certain areas And so this is something that we can also include In our mixed integer linear program And so when we look at this program You see that we have actually two types of decisions That we are looking into simultaneously So one is relevant to the location And the second one is relevant to the routing Because in order to have a full metal design problem We need to simultaneously look at the location Of different facilities and the routing of the vehicles From those facilities towards the end customers And so this brings us actually to a category of problems That is called location routing problems And that simultaneously looks into those two types of decisions So we can break down this type of problem into two sub-problems So the first sub-problem that we can look at Is a location allocation problem So here you have a very simple example Where we have again a set of candidate allocations For distribution centers So these are noted by D And there we have also a set of customers That need to be delivered So in a location allocation problem We are typically looking into Which of those candidate locations For distribution centers need to be activated So here we have two of them that are activated And how do we allocate different customers To those distribution centers So which distribution center should serve which customers And we can look at the formulation of this problem We can again formulate this as a mixed integer linear program With a certain number of decision variables That are relevant to the location and allocation However, what we notice is that When we move from this very simple toy problem That is presented here on the screen To real life instances that contain a very large number of customers The problem becomes NP-hard Or in simple terms a very hard to solve Very hard to solve means requires a very long computational time In order to get to an optimal solution Another problem that is integrated in a location routing problem Is the vehicle routing problem And so this brings us back to that discussion About how in how many ways we can sequence Different customers within one vehicle route So you have seen that there are many different possibilities The reason for that is that we will define For each potential arc between two customers A separate decision variable So this problem can become very hard to solve And very time consuming to solve to optimality So we have here two problems that are very hard to solve And we want to combine them And when we combine these two problems And we come up with a single formulation What happens is that for real life instances Where we have for example thousands of customers So we've seen 15,000 customers In the case of this Brazilian e-commerce company This problem becomes impossible and tractable to solve Again, let's think about the number of possibilities That we have for vehicle routing And we can add to that the number of possibilities That we have really got to facility locations And so this shows you very clearly That if you want to combine the two problems This becomes impossible to solve for real life instances And so this is where a lot of research That we're doing in our lab comes into play Because we are developing techniques That allows us to simplify these problems And to formulate problems that are possible To solve while maintaining all of the complexities Of the urban environment And so one approach that we are commonly using In the projects that we are currently working on Is called continuum approximation And so continuum approximation allows us to Basically combine these two types of location routing problems But to bring them back to a simple location allocation problem And so the basic idea behind the continuum approximation Is that if we have some characteristics of demand That are satisfied in some hypotheses Such as for example that we have a homogeneous stop density Of within a certain area We can make some approximations So for example we can estimate the average distance per stop For an area with a given density With a given size And considering a given distance to a serving facility And so we can introduce additional elements For example global service time for vehicles So we can say for example all of the routes Need to be under eight hours Vehicle carrying capacities and different speeds But at the end of the day We are able to establish closed form A formula for these For vehicle routes And to actually approximate the cost of an optimal vehicle route In a given setting Without performing the explicit vehicle routing Towards each customer And so this is something that is very interesting For the network design Because network design is a decision that is taken on a strategic level So we do not have to basically establish Each specific vehicle route towards each individual customer So we only want to have information About how the cost of these routes Will affect other decisions with regards to the location And the definition of service areas And furthermore in the case of an e-commerce company For example the demand The specific demand will change daily So we will never have the exact same two customers That are located in the same area We will have variable locations for the demand So we do not want to solve the problem For a specific instance of demand We want to solve it for an average demand scenario So as I mentioned before These approximations work But they only work if we are able to enforce A certain number of hypotheses So for example that the demand density Is homogeneous in a zone that we are considering However when you think about a given urban market This is really the case So typically there are areas of the city There are more dens that present high population density And that will therefore present a higher density of the demand On the other hand different areas of the city Will also have different characteristics In terms of infrastructure So some areas will be typically characterized By very small streets Narrow access and one-way streets While others will be characterized By different infrastructure And so if you want to apply this approximation Direct to the whole service area We will not be able to capture the granularity Of those characteristics And the characteristics of each of the zones That we are considering So what we are doing in order to still be able To capture the urban geographies And the demand patterns Is that we segment the city Into a certain number of areas So we have one area here We can see the outline of the service area in red And we apply sort of a grid to this area And we define a certain number of This discrete demand zones So each of these small pixels here We refer to them as pixels Will be defined as a specific area And so as a next step For each of those demand pixels We will define a certain number of characteristics So we can look at the demand density So how many customers or how many stops Do I have within that specific pixel We can look at the drop size How many items do I deliver per order, per stop We can look at the volume of the deliveries We can look at the infrastructural properties Of each segment And we can look at things like vehicle speed Etc etc etc So we will define for each of those specific segments All of these parameters And we will use that as an input to our model And just to provide you an illustration of that So here are a few maps That we have made for this Brazilian e-commerce company So the first one is relevant to demand density You can see that, for example, the areas That are located in the city center Are the most dense So they are with the red and orange colors Where as we move towards more peripheral areas The demand density decreases We can then use GPS traces of vehicles To define travel speeds within each segment of the city And use that as input data And we can also look at some infrastructural properties Of the network So one of them is, for example, travel directness Which basically describes how roads are formed in a certain area So how many, one way streets do we have What is the security of these streets Etc etc etc And this will give us some information about What is the length of a tour That we need to perform within that area By using this granular input data That is aggregate and on-site segment level We are then able to produce high resolution Last mile network design models And inform decisions through the gods to the facility Which regards to the allocation of segments To different facilities And really regards to the model choice per segment So as you can see in these pictures These pixels that we have defined That we have characterized in input data Are then used in a network design model To perform those different decisions So for example, for each of those pixels Determine what would be the optimal size of Type of the vehicle And just to give you an idea in this specific project We have considered over 2000 different pixels So we do allow our model To capture highly granular input data While still making approximations That allow us to make this problem Solvable So what I've described here Was a very basic network design problem And it is the illustrations I've used Is relevant to this one specific project But it's really representative of a way That we approach this for many of our projects In the realm of urban logistics Now we can think about some potential extensions That we can make to this network design problem And these extensions will, for example, Look into a way that we can integrate Some of the new trends in terms of Logistics operations, business models, etc, etc Into these network design models And so before going into that part of the Presentation Again, a question from our side In your opinion, what trend is most likely to disrupt Last my delivery operations Here, unfortunately, I do not think there's a right answer It's more to get a sense of What is your current understanding of this field Okay, and the option is our facility automation Crowd source deliveries The use of drones for LASMR And also autonomous ground vehicles So students are starting to answer So some are saying A tie between crowdsourced deliveries and drones Others are saying autonomous ground vehicles I can see that it's pretty well distributed Correct, and it's very Okay, I would say divided between the last study And just some of them are saying that facility automation Yeah, so indeed, there is not a right answer In a few following slides, I will try to Illustrate how we think that some of these Trends are going to impact the way that we Design networks and then also touch upon How does this impact the type of models that we are producing So what are the implications for the models That we are developing for network design problems So indeed, there are a few trends that we can consider First one that I have not mentioned here Is with regards to the product exchange options That e-commerce operators or parcel operators Can offer to their customers So increasingly we see that Parcel and e-commerce operators are proposing New products exchange options So for example, a pickup at a store A pickup at an automatic locker And then we also have some other delivery options That are technology enabled such as smart homes Or delivery stores, trucks of cars And so if you look at this first part That looks at the product exchange options With regards to, for example, the automatic lockers Or pickups at stores What this means is that we are actually required To introduce an additional layer of facilities In our network design model So so far we had a two-tier distribution network With distribution centers and satellite facilities Now we have to consider these additional facilities Such as lockers or stores And to integrate them in our model And we can also think about it in a more proactive way And if we are looking for a model That aims in maximizing the profit We can look at where should we place Those different facilities In order to capture most of the demand And in order to increase the profit of a given company So this is the first trend that is very relevant And that is, I would say, very much present And implemented today A second trend that we can look at Is relevant to the integration of multiple delivery services So the model that I've described previously Assumes that all of the customers Are served through one delivery service pipeline So basically we consolidate all the orders on a daily basis And then we perform vehicle routes Towards individual customers on a daily basis However, if we think about some recent trends in e-commerce We see the emergence of multiple delivery services With increasingly short delivery lead times So we're moving from next day delivery To same day delivery and even towards instant On-demand deliveries performed within one hour or two hours And also the location of the delivery Can be changed and can be adapted in real time So one of the extensions that we are actually working on Right now is how do we integrate Those different delivery services Within one network design model So we no longer characterize the demand For total parcel deliveries But we have to characterize it With regards to each of those delivery services And introduce additional decisions With regards to what facilities should deploy Which services, for example If we are then thinking about These highly responsive services We also would need to accommodate Some potential variability in the demand During one day And we would also need to integrate Inventory positions that are closer to the end customer So again, in a typical network design model We have made the assumption that all of the inventory Is located in distribution centers That are located in the outskirts of the city However, if we want to deploy Highly responsive services, for example One hour to our delivery We need to move inventory positions Closer to the customer So we see companies that are deploying Hyperlocal distribution centers That are typically located in the heart of urban areas And that are served to deploy these types of services Given that the location of the demand Will vary according to the day So typically during the day People will order in the workplace In one area of the city In the evening it will be to their homes We also need to introduce some flexibility With regards to the location of the inventory Throughout the day And one way of introducing that Is to deploy mobile warehouse Concept Which is basically a If you look at the image here It's basically a truck That can hold a certain amount of inventory And that can move throughout the day Towards different parts of the city Where, when and where it is needed One trend that was mentioned in the question Was with regards to the facility automation So what is the link between facility automation And the network design So facility automation basically allows us To better use space And this in hand will allow us To deploy these hyper-local inventories So we can work not only in horizontal But also in vertical And potentially reduce the cost of These hyper-local distribution centers That are situated in the heart of urban areas A third trend relates to the new business models And the way that we are deploying our fleet So again, in the model that I have described previously We have used three different types of vehicles And we have made the assumption that All of these vehicles are owned And operated by the company In real case instances We will most probably introduce An additional number of options And some of them are related, for example, To the outsourcing of the deliveries So we might introduce the possibilities That for some specific parts of the city We want to consider the option Of outsourcing it to a last mile specialist That, for example, operates cargo bikes That are particularly suited for a given area For some areas of the city Where we have lower density of deliveries We might want to consider collaborative operations With other operators That will allow us to increase the stop density And reduce the cost per stop And then if you're thinking about this Highly responsive delivery services Here we typically have a demand That is variable per day And we want to deploy in real time Secondary network of vehicles That can be provided, for example, By crowdsource carriers That we can integrate on the demand When and where this is necessary And the final trend that we can consider Is the integration of new vehicle technologies In the last mile delivery operations So, of course, there is always a lot of buzz About the drones And how can we use the drones in urban areas A lot of people, including our spectators here See it as a way to tackle some of the problems Of deliveries in urban areas So in our lab today we do not see drones As a solution that can perform sufficiently enough If considered separately However, when we integrate this with other types of vehicles And, for example, when we think about combined truck and drone delivery systems There we can kind of use the best of both worlds So we have the line-hole transportation That is performed by one type of vehicle That can carry sufficient capacity And then the final deliveries to individual customers That can be performed by drones And the last one would be, of course, Autonomous round vehicles for hyperlocal deliveries So this again requires us to develop additional models For the routing approximations, for example And for the routing So how do we integrate a combined truck, drone delivery system In a network design model that we have made So this is it for the presentation part I believe that we... We have some questions Thank you, thank you, Milena It was an insightful presentation And most of what you presented today Was related to what we discovered in our course So let me just stop here Okay, excellent So we have some questions from our students So the first question that we have is the following So when you were talking about the different factors Of the different characteristics Of the different features that you take into consideration To characterize a pixel Have you considered anything related to the factor? Any security factor, for example, that could be included as well? Yes, so the question of security is particularly relevant When we are thinking about the emerging markets So indeed in some of our projects We had to introduce additional constraints Which regards to the type of vehicles That can be operated in certain areas of the city So in some areas, for example, that have a very high risk of robbery It is probably not a good idea to deploy a 10 pallet truck That is full of electronics And so we would need to constrain the type of vehicle options That may be introduced And for example, use smaller trucks We can also limit the value of shipments That is carried by trucks So that way we always limit the risk And when we were looking at, for example, some options With regards to the product exchange So I have mentioned automatic lockers Again, probably not a good idea to deploy these in high risk areas So this is definitely one factor That can be integrated into network design models Okay, excellent And how common do you think that this As you said, you mentioned that this is more common in Latin America But if we talk in the project that the lab have conducted Do you have a sense in how many of this project Or what percent have included these risk factors? So definitely in emerging markets So Latin America, India, etc This is something that was given to us by the company So typically companies we interact with them In order to establish all of the business requirements Including this type And it's typically why we discuss with them That some of these specific constraints come up And then we think about ways to integrate them in our models Excellent, thank you, thank you, Milena So we have another question that is more technical And this question was made by ANSAR And it's asking about which solver do you use primarily? So in today in our lab We mostly use Python for the modeling And then we use Gurobi for the optimization part Simply because the integration with Python is very seamless So when we process the data We use typically Python to clean it up And then sometimes MySQL, etc to make databases Okay, excellent So basically it's a combination of Python and Gurobi as a solver Yes Also he's talking about what's the largest problem You have ever had in terms of the number of variables Do you have a sense? So all of the problems that we deal with are typically quite large We here for the project that we have made in Sao Paulo We had 200 facility locations We had 2,400 city segments And then this can number of vehicle options And this can yield several million decision variables for our problem So if we this is all in our integer programming If we are moving towards some additional models That for example look in the way that the demand interacts With the supply So for example in case of product exchange options Here we end up with even more decision variables And often end up in a non-linear programming setting Okay, so we're talking about million of variables So Excel is not an option here for you guys Okay, so in the course Milena So we use Excel And also we have a couple of options SAS and Ample But I mean for this size For the size of this problem I guess that Python it would be like the The only option that they have Okay, so Mohamed is asking another question So this question is how do you formulate the milk When selecting a candidate location Based on time and weight of the product In the lectures and practice program we use distance So can you please how do we formulate the milk when When selecting a candidate location Okay, so to summarize for each of the candidate locations We have one decision variable that is binary And that presents if this is a active or inactive facility We can also allow for different size of facilities We'll typically place several facilities With different capacities on the same location To allow for different sizes And then the model will choose the one that is most suitable And then in order to account for the size Of the different orders And so typically the volume of different shipments We will introduce constraints With regards to the total flow of goods That is transitioning from within and outside of facility And the size of the facility in terms of number of items Or in terms of capacity that it can accommodate And we do a similar approach for the vehicle capacity Okay, got it. Thank you. Thank you So Agata is asking another question So let me read the question She's saying how can you manage costs or distances In your model if one stop meets more than one customer So if one stop meets more than one customer This is something that we can capture with the drop size So when we think about drop size There are two ways in which we can think about it The first one would be how many items per customer do we serve So one parcel, two parcels A second one would be how many items or customers per stop can we serve And typically in our models we integrate a Fixed time per stop which is linked to the time required to park To operate the vehicle and then a variable time per item So here especially in some highly congested urban areas We see that drivers often prefer to park their vehicle And serve multiple customers on foot Even if that requires them Requires that they walk a certain distance Then to look for a parking spot for each individual customer And so here again we can use data analytics on for example stop duration And link that to a number of customers and a number of items And the type of zone that we are working in And produce basically a prediction model that gives us Estimated time per stop with regards to all of these different parameters Okay excellent thank you I think that clarifies everything So the last question, Edmar, he's one of our CPAs also from Bolivia He's asking if a correlation in each of the pixels might not be a problem for optimization Have you considered, have you measured a correlation between pixels? So when we discretize the area into pixels Given that the density of the demand within each pixel is sufficient We can make those approximations for each of those pixels and then add them up And so basically what happens is that you can end up with 3.2 routes Towards one given pixel and then 4.2 towards a neighboring one But then when you combine those two in an approximation This gives you a very good approximation with regards to the total number of routes that are considered So we discretize and we consider each one of them separately But then when we aggregate the demand this gives us a good information about the number of vehicles And there is a number of studies that show the validity of this type of approach So this method was actually developed by director of our lab And he has compared the performance of our approximation with Vehicle routing, explicit vehicle routing towards customers And we show that above a certain demand threshold that is actually quite low This approximation performs extremely well Okay, excellent. Thank you. Thank you, Milena, for being here It was a really insightful presentation Just a final remark, guys So remember that we are releasing an exam next Wednesday, October 31st at 1500 UTC So the material that we'll be covering during the exam is going to be the first four weeks So from week one to week four And you will have the exam is going to be open for one week But you have only four hours to complete the exam Okay, thanks again for joining this live event and see you in the next one. Bye. Bye. Thank you and good luck on your exams