1.- AND BACKGROUND.
1.1.- INTRODUCTION
This case examine demonstrates using Geospatial applied sciences to handle a enterprise problem within the improvement of the pharmacy community within the Neighborhood of Madrid, Spain. This evaluation relies on a mission that features authorized, city planning, engineering, administrative legislation and enterprise issues, however these features are exterior the scope of this evaluation. Right here we focus completely on the appliance of superior geospatial applied sciences, akin to OSMnx and NetworkX, to beat the geospatial challenges concerned within the deployment of the pharmacy community, particularly tips on how to discover gaps within the city pharmacy community the place it’s doable to put in a brand new pharmacy whereas respecting the authorized restrictions on the minimal distance between pharmacies.
1.2.- BACKGROUND
The pharmaceutical sector in Spain is regulated by the federal government with the intention of making certain the provision and dishing out of medicines beneath acceptable high quality and value circumstances. Inside this sector, distribution is affected by quite a few limitations akin to: the possession, location and technical-economic circumstances of pharmacies by way of state legal guidelines [1] and quite a few laws of the Autonomous Communities. This publication will cope with the constraints relating to location within the Autonomous Neighborhood of Madrid.
In relation to funding within the community of pharmacies in Spain normally, and within the Autonomous Neighborhood of Madrid particularly, the attention-grabbing drawback of discovering appropriate places for establishing a pharmacy arises. Though this seek for places could be in new city areas beneath improvement, probably the most attention-grabbing is consolidated city land. It’s because the funding maturity interval is shorter, as there may be already a inhabitants residing within the space, and the inhabitants density is normally larger than that deliberate for improvement areas. Nonetheless, the issue is that in these consolidated city areas there are already pharmacies in operation and the minimal distances between them should be revered by legislation.
The Spanish authorized framework for the pharmaceutical sector establishes a minimal distance limitation of 250 m between pharmacies to be able to find a pharmacy workplace [2], [3]. This distance must be measured by following a route in response to the next issues:
- It must be a route just like that which a pedestrian would comply with.
- It ought to join the centres of the fronts of pharmacies, not the entrances to pharmacies.
As well as, it should be ensured that the space to public well being amenities is greater than 150 m measured alongside a pedestrian route.
Some points are highlighted beneath:
- Pharmacies established prior to those legal guidelines don’t comply with these guidelines, with the end result that some pharmacies are situated at a distance of lower than 250m. Regardless of this, there are nonetheless city openings for the placement of recent pharmacies in areas of curiosity from the perspective of the pharmaceutical enterprise.
- The existence of those city openings shouldn’t be sufficient and requires further fieldwork to analyse the existence of obtainable properties to deal with the pharmacy in these areas and to check the likelihood supplied by city planning to really set up a pharmacy in these areas. That is due to this fact a primary step within the funding course of.
The effectiveness of open-source instruments akin to OSMnx [4] and Networkx [5] in addressing advanced issues associated to city cloth evaluation, city transport and mobility has been demonstrated in quite a few publications [6]–[8]. The intention of this publication is to current a technique primarily based on OSMnx and NerworkX to disclose potential openings (alternatives) within the city cloth for the placement of pharmacies bearing in mind the authorized restrictions.
NetworkX is a Python library designed for the appliance of graph concept [9] to analyse advanced networks of relationships. It operates by way of an advanced framework of objects, the place the fundamental components are nodes, that are interconnected by edges, representing relationships between nodes. This instrument is extensively employed within the examine, evaluation, and backbone of real-world issues, together with however not restricted to geospatial transportation networks, city geospatial networks, and social networks. OSMnx is a specialised open-source python library that makes use of OpenStreetMap geospatial information to vectorize the road networks of cities globally as NetworkX graphs, facilitating their evaluation by way of Python code. This strategy is exemplified in [10], the place numerous city areas worldwide are systematically analyzed.
Given the quite a few variables and alternate options to think about when using these instruments to handle geospatial challenges, a broad number of publications on the topic has been reviewed. Because of the modern and quickly evolving nature of those instruments, a few of these sources are completely accessible by way of on-line boards, akin to https://stackoverflow.com/, or in web-native scientific journals. A key subject that has prompted appreciable debate in these sources is the strategy for connecting factors of curiosity (POIs) to town graphs of OSMnx, as mentioned in [11] – [12], to allow computations over these graphs to unravel issues associated to the POIs. For the precise case addressed on this paper—the localization of pharmacy workplaces (POIs) in compliance with authorized distance necessities—a brand new methodology has been developed to greatest swimsuit the case, drawing on the related literature and on-line assets consulted. This system can be introduced within the methodology part and is anticipated to be relevant to related instances.
2.- METHOD
After accumulating the mandatory information: UTM coordinates of the pharmacies and the suitable OSMnx graph of town of Madrid, a primary part of this technique consists of projecting the UTM coordinates of the pharmacies onto the OSMnx grid of Madrid as nodes. To do that, first, the perimeters of the OSMnx graph closest to every pharmacy can be recognized within the “Information Placement on the Grid” part of this technique. That is achieved by importing the OSMnx graph with out simplifying it. This fashion, all of the curved strains of the Madrid city graph could be approximated by a number of strains of lowered dimension, appropriate for subsequent vector calculation. Moreover, on this case it’s essential to mission the UTM coordinates of the pharmacy workplaces, that are normally situated inside their institutions, onto the OSMnx graph. That is achieved within the ‘Vector calculation’ part of the methodology. On this manner, the placement of the midpoints of their façades on the general public street is approximated.
Thirdly, as soon as the UTM coordinates of the pharmacies have been projected as nodes of the OSMnx graph of town of Madrid, within the subsequent ‘Grid Overlay’ part, the areas of the community which are lower than 250 m from every of the pharmacy-nodes are calculated. For this goal, we don’t contemplate the Euclidean distance however the topological distance, in response to the walkable city graph. Thus, n networks are obtained, one per pharmacy. Then, all of them are superimposed. Lastly, the results of this superposition is subtracted from the OSMnx graph of Madrid. The results of this subtraction is a brand new community with the perimeters which are greater than 250 m away from any pharmacy. Lastly, this result’s visualised as the ultimate resolution, since these edges represent the axes on which a pharmacy workplace could be housed from the topological perspective.
As an instance this publication and check the methodology, an city space with a really difficult city cloth has been chosen, centred on the Madrid district of Tetuán, the place pharmacies are additionally very shut to one another, as a few of them have been put in earlier than the inclusion of the space limitation within the authorized framework.
To simplify the preliminary exposition of the methodology, the minimal authorized distance situation of 150 m to well being centres has been distributed with, contemplating solely the minimal distance between pharmacies as a limiting issue. As soon as the methodology has been defined in its entirety, will probably be seen how this situation is definitely launched within the ‘dialogue’ part.
Every part of the methodology is defined intimately beneath.
2.1.- Information assortment
The Neighborhood of Madrid has publicly accessible information on its pharmacies and well being centres: addresses, codes, geographic coordinates, pharmacist in cost, and so on. These information can be found on the internet [13]. The csv recordsdata used on this publication have been extracted from it [14]. Because the factors to be thought-about for the calculation of distances must be the midpoints of the facades, and never the accesses to the pharmacies, it’s a higher approximation to make use of the UTM coordinates of the centre of the pharmacy institutions and mission them onto the OSMnx graph, as a substitute of geocoding the addresses of the pharmacies. On this manner, the centre of the pharmacy institutions could be higher approximated. That is notably necessary within the case of pharmacy premises with lengthy facades or nook facades, the place the geolocation of the premises is assigned to the doorway and to not the center level of the facade, which is the purpose referred to within the distance measurement regulation.
As for the OSMnx community to be thought-about, will probably be of kind ‘stroll’ (network_type=’stroll’) [15], which incorporates all public pedestrian routes in Madrid. Since a part of the methodology makes use of vector calculations, the default simplification of the OSMnx community is discarded (therefore, simplify= ’False’) to be able to get hold of the totality of the community nodes [16]. Thus, the curved elements of the community could be approximated by straight strains between the ‘nodes’ of the ‘edges’. With respect to this earlier publication, on this case, as well as the centre of the pharmacy institutions also needs to be projected onto the OSMnx community. As a conclusion of the above dialogue, the Madrid graph can be imported as follows in code 1:
Madrid_graph = ox.graph_from_place('Madrid, Spain', network_type='stroll',
simplify= False )Code 1. Python 3.11.5.
2.2.- Information placement on the grid
As defined above, step one is to determine the perimeters of the detailed model of the OSMnx graph of Madrid which are closest to every pharmacy. That is achieved by way of the OSMnx distances module, saving the information of every nearest edge within the corresponding row of the pharmacies DataFrame, in addition to the space, as a test, code 2.
for index, row in farmacias.iterrows():
edge = ox.distance.nearest_edges(Madrid_graph, row['lon'],
row['lat'], return_dist=True)
node = ox.distance.nearest_nodes(Madrid_graph, row['lon'],
row['lat'], return_dist=True)
farmacias.loc[index,'edge_1'] = str(edge[0][0])
farmacias.loc[index,'edge_2'] = str(edge[0][1])
farmacias.loc[index,'edge_n'] = str(edge[0][2])
farmacias.loc[index,'edge_d'] = edge[1]
farmacias.loc[index,'node'] = str(node[0])
farmacias.loc[index,'node_d'] = node[1]Code 2. Python 3.11.5. ‘lon’ and ‘lat’ stand for the geographical coordinates Longitude and Latitude.
Though not essential for the following calculations, the identification of the closest node has additionally been included for data and high quality management functions.
These are proven beneath in Fig. 1 for the chosen Madrid pilot setting.
Fig. 1. Information Placement on the grid. UTM coordinates of the pharmacies, blue factors. Nearest nodes of the graph, pink factors. Closest edges of the graph, pink segments. Personal elaboration utilizing OSMnx. Information © OpenStreetMap contributors, accessible beneath the Open Database License
2.3.- Vector calculation
With a view to mission the pharmacies on the graph of Madrid, it’s taken into consideration that what’s of curiosity on this case is to determine the midpoint of their façade on the general public methods, i.e. on the graph. As talked about above, normally, the UTM offered within the Public Administration recordsdata refer to a degree contained in the business institution. Due to this fact, it’s essential to mission these factors on the Madrid graph, remodeling them into a brand new node of the graph. On this case, it’s not appropriate to hyperlink pharmacies to the graph by way of an edge, since solely pedestrian routes on public methods are of curiosity for distance measurement. So, as a substitute, a brand new node must be created the place every pharmacy workplace is projected on the graph, on the closest edge decided within the earlier part.
The projection is carried out utilizing the Python library Numpy [17] utilizing the next vector calculation, which offers the coordinates of the brand new P nodes which are the projection of every pharmacy on the graph, Fig. 2:
Fig. 2. Vector calculation scheme. F, pharmacy UTM level. P, projected pharmacy node. E1 and E2, edge ends. L, is the size of the sting in OSMnx. Personal elaboration.
Within the case that “d” or “L2” is destructive, which may happen as a consequence of small variations between the lengths of the perimeters in OSMnx and the projections made utilizing UTM coordinates, the node the place the pharmacy is projected can be one of many excessive nodes defining the sting, relying on which of the 2 portions is destructive. If “d” is destructive, then the pharmacy can be projected as “E1”; if “L2” is destructive, then as “E2”.
Thus, a brand new edge is created that connects this new node with the nodes of the closest edge. Subsequently, the beforehand decided nearest edge is deleted, as it’s changed by the one simply created. See code 3.
for index, row in farmacias.iterrows():
# vector calculation
F = np.array( [row['localizacion_coordenada_x'], row['localizacion_coordenada_y']])
E1 = np.array([utm.from_latlon(Madrid_graph.nodes[row['edge_1']]['y'], Madrid_graph.nodes[row['edge_1']]['x'], 30,'N')[0],
utm.from_latlon(Madrid_graph.nodes[row['edge_1']]['y'], Madrid_graph.nodes[row['edge_1']]['x'], 30,'N')[1]])
E2 = np.array([utm.from_latlon(Madrid_graph.nodes[row['edge_2']]['y'], Madrid_graph.nodes[row['edge_2']]['x'], 30,'N')[0],
utm.from_latlon(Madrid_graph.nodes[row['edge_2']]['y'], Madrid_graph.nodes[row['edge_2']]['x'], 30,'N')[1]])
d = np.dot(E2-E1,F-E1)/Madrid_graph.edges[(row['edge_1'],row['edge_2'],row['edge_n'] )]['length']
d_vect = (E2-E1)*d/Madrid_graph.edges[(row['edge_1'],row['edge_2'],row['edge_n'] )]['length']
F_coord = E1 + d_vect
L_calculada = np.sqrt(np.dot(E2-E1,E2-E1))
F_coord_LL = utm.to_latlon(F_coord[0], F_coord[1], 30, 'N')
L2 = Madrid_graph.edges[(row['edge_1'],row['edge_2'],row['edge_n'] )]['length'] - d
# edge and node substitution
if d<0:
nx.relabel_nodes(Madrid_graph, {row['edge_1']: row['farmacia_nro_soe']}, copy= False)
nx.set_node_attributes(Madrid_graph, { row['farmacia_nro_soe'] :{'coloration':'r', 'dimension':10 }} )
elif L2<0:
nx.relabel_nodes(Madrid_graph, {row['edge_2']: row['farmacia_nro_soe']}, copy=False)
nx.set_node_attributes(Madrid_graph, { row['farmacia_nro_soe'] :{'coloration':'r', 'dimension':10 }} )
else:
Madrid_graph.add_edge(row['edge_1'],row['farmacia_nro_soe'],0)
nx.set_edge_attributes(Madrid_graph, { (row['edge_1'], row['farmacia_nro_soe'],
0):{'size':d, 'osmid' : row['farmacia_nro_soe'], 'coloration':'r', 'dimension':4 }})
Madrid_graph.add_edge(row['farmacia_nro_soe'],row['edge_2'],0)
nx.set_edge_attributes(Madrid_graph, { (row['farmacia_nro_soe'], row['edge_2'],
0):{'size':L2 , 'osmid' : row['farmacia_nro_soe'], 'coloration':'r', 'dimension':4 }})
Madrid_graph.remove_edge(row['edge_1'],row['edge_2'],row['edge_n'] )
nx.set_node_attributes(Madrid_graph,
{ row['farmacia_nro_soe'] :{'x':F_coord_LL[1], 'y':F_coord_LL[0], 'coloration':'r', 'dimension':10 }} )
Code 3. . Python 3.11.5. ‘farmacia_nro_soe’ stands for pharmacy code. The variables to start with (F, E1, E2, d, and so on) check with these in Fig. 2. The opposite attributes of nodes and edges (‘coloration’, ‘dimension’) are supposed to spotlight them within the drawing course of.
The results of this calculation is proven in Fig. 3
Fig. 3. Projected pharmacies as pink nodes within the Madrid graph. Personal elaboration utilizing OSMnx. Information © OpenStreetMap contributors, accessible beneath the Open Database License
2.4.- Grid overlay.
On this part we’re going to create graphs of 250 m strolling distance with centre at every of the pharmacy nodes in Madrid: nx.turbines.ego_graph([...], radius=250, centre=True, distance=’size‘). They’re then composed to kind a bigger one containing all of them: MultiGraph.nx.compose_all(). They’re then subtracted from the bottom Madrid graph initially used: MultiGraph.remove_edges_from(). This graph with the perimeters and nodes remaining after the subtraction accommodates edges that meet the situation of getting all their factors situated greater than 250 m from all the opposite pharmacy nodes, due to this fact, prone to home a brand new pharmacy, code 4.
for index, row in farmacias.iterrows():
Grph = nx.turbines.ego_graph(Madrid_graph,row['farmacia_nro_soe'] ,
undirected=True, radius=250,
middle=True, distance='size')
superposicion.append(Grph)
S = nx.compose_all(superposicion)
nx.set_edge_attributes(S, 'r', 'coloration' )
Madrid_graph.remove_edges_from(record(S.edges)) Code 4. . Python 3.11.5. ‘farmacia_nro_soe’ stands for pharmacy code.
3.- RESULTS
Fig. 4 exhibits the results of making use of the process to the set of pharmacies represented by the inexperienced dots solely in an almond-shaped space of town of Madrid. All edges containing factors which are lower than 250 m away from the given pharmacy community have been eliminated, so {that a} hole is noticed inside the illustration. The perimeters which are nonetheless current inside the hole after the elimination are these the place it might be doable to deal with a brand new pharmacy from a topological perspective. Clearly, within the precise mission it’s essential to test the city circumstances of those ‘edges’, in addition to the supply of a business actual property to deal with a pharmacy, see the next part.
Fig. 4. Outcome: the perimeters the place it might be doable to host new pharmacies, given a constellation of present pharmacies as blue dots. The perimeters of the graph situated exterior the topological distance of 250 m inside the given constellation of pharmacies, proven as pink segments, are doable appropriate places for a pharmacy. Gray background: shadows of buildings. Personal elaboration utilizing OSMnx. Information © OpenStreetMap contributors, accessible beneath the Open Database License
4.- DISCUSSION AND CONCLUSIONS
4.1.-Graph choice
Provided that pharmacy workplaces in Spain can solely be situated on public pathways and that the 250 m distance limitations between pharmacy workplaces are measured by way of pedestrian routes, the community kind ‘stroll’ [15], which incorporates all public pedestrian routes in Madrid, has been chosen because the OSMnx Madrid graph, code 5.
Madrid_graph = ox.graph_from_place('Madrid, Spain', network_type='stroll',
simplify= False )Code 5. Python 3.11.5
In instances completely different from the one at hand, through which not solely public roads are helpful for the work, but additionally personal ones, a graph that features all of them—each public and personal—could possibly be chosen by utilizing the Overpass QL code to specify a customized filter [18], code 6:
Madrid_graph = ox.graph_from_place('Madrid, Spain', simplify= False,
custom_filter=
'["area"!~"yes"]'
'["highway"!~"cycleway|motor|proposed|construction|abandoned|platform|raceway"]'
'["foot"!~"no"]["service"!~"private"]["access"!~"private"]' )Code 6. Python 3.11.5
4.2.-Procesing the information.
As defined within the introduction, for vector calculation causes, the “unsimplified” OSMnx graph for Madrid has been chosen. Nonetheless, because of this the variety of nodes within the NetworkX graph is kind of massive, particularly 465,976, in comparison with 154,311 within the simplified community of Madrid. This, along with the complexity of a metropolis like Madrid, makes the calculation course of described above take fairly a very long time, relying on the {hardware} used. If there are {hardware} limitations, there are attention-grabbing publications value consulting, which may velocity up the calculations of the Python engine, as is the case of utilizing the Numba library [11].
4.3.- The Approximate Nature of the Answer.
The vary of city conditions associated to business premises is huge. For instance, there are business premises whose façades should not steady. In such instances, authorized laws require contemplating the a part of the façade that’s most related to every particular case. Even in these conditions, the answer is pretty exact. Nonetheless, it stays an approximate resolution that serves as a helpful place to begin for an in depth on-site evaluation.
4.4.-Simplification.
For the sake of readability, to date solely the minimal distance limitation between pharmacies of 250 m alongside a pedestrian route has been thought-about. As indicated in part 2.- METHOD, it is usually essential for a pharmacy to respect a minimal distance of 150 m from well being centres. Having seen the methodology, this will simply be achieved by including the well being centres of Madrid, publicly accessible as csv file within the internet of the Neighborhood of Madrid [19]. We proceed with the identical methodology as within the case of pharmacies to create the graphs containing factors situated lower than 150 m from every well being centre; on this case nx.turbines.ego_graph([...], radius=150, centre=True, distance=’size‘). Then, within the ‘Grid Overlay’ part, we superimpose this graph with the one for pharmacies within the MultiGraph.nx.compose_all() step. Subsequently subtracting this whole set from the Madrid metropolis graph.
4.5.- Purposes aside from these regarding consolidated city land.
Though this publication has handled the case of finding pharmacies on consolidated city land, NetworkX functionalities in Python will also be used to check one of the best places for pharmacies in growing city areas that don’t but have city companies and amenities put in. This may be achieved by way of centrality measures. There are very attention-grabbing examples of utilizing centrality measures to analyse an city community, for instance within the case of an city biking community [16]. Within the case of pharmacies, the NetworkX “betweenness centrality” measure could be an attention-grabbing candidate to assist decide probably the most interconnected pedestrian routes in a growing city space, which is a fascinating characteristic to host a pharmacy, as they are usually the place most pedestrians flow into. That is the criterion used to analyse the development factors of cycle lane networks in Copenhagen [20]. However this can be a completely different drawback from the one addressed on this publication, and must be handled in one other publication.
4.6.- Dialogue of the result.
As indicated within the introduction, the given resolution is topological in nature. For instance, in Fig. 5, the perimeters highlighted inside inexperienced squares “a” correspond to roads in a really vast road in Madrid, the “Paseo de La Castellana”, with a number of lanes at completely different ranges and boulevards, which pedestrians can solely entry by way of only a few zebra crossings following a circuitous route. These ‘edges’ have been chosen within the computation exactly for that reason: though their Euclidean distance to the closest pharmacies shouldn’t be massive, the precise route a pedestrian has to take to achieve them is for much longer, as they will solely be accessed by way of a couple of zebra crossings following a circuitous route. Nonetheless, as a consequence of city planning constraints, they aren’t appropriate places for a pharmacy.
As defined above, after figuring out the perimeters that respect the limitation of distances between pharmacies following this technique, it’s essential to additional analyse them when it comes to: availability of economic actual property in them to deal with a pharmacy and the probabilities supplied by city planning on permitted makes use of and actions on them. An instance is the highlighted inside inexperienced sq. ‘b’. This can be a massive city plot belonging to the general public water provide firm in Madrid, ‘Canal de Isabel II’, which additionally capabilities as a inexperienced area within the metropolis. On this case, regardless of having been chosen for computation, it’s not an acceptable area to deal with a pharmacy as a consequence of city planning and possession points. Regardless of its Euclidean proximity to the encompassing pharmacies, the computation has chosen these edges due to their troublesome accessibility, as they’re surrounded by a wall, which requires many detours to enter them following a pedestrian route from the encompassing places.
The chosen examine space has a excessive saturation of pharmacies, primarily as a consequence of the truth that a lot of them have been put in earlier than the regulation of distances between pharmacies got here into drive. As well as, as a result of city chaos of the world, pedestrian routes are very circuitous. Which means, regardless of the excessive density of pharmacies within the city space, the computation has been capable of finding gaps that would a priori home pharmacies. A few of them are inscribed in cyan ellipses and circles, Fig. 5.
Fig. 5. Particular instances. Personal elaboration utilizing OSMnx. Information © OpenStreetMap contributors, accessible beneath the Open Database License
5.- Information Availability and Disclaimer
The datasets utilized on this examine are publicly accessible and licensed for any use by the Autonomous Neighborhood of Madrid, Spain. Road community information was sourced from OpenStreetMap © OpenStreetMap contributors, by way of the OSMnx Python library, and is on the market beneath the Open Database License (ODbL): https://opendatacommons.org/licenses/odbl/1.0/ . Geospatial layers as pharmacy places, have been derived from publicly accessible GeoJSON and csv recordsdata hosted on https://datos.comunidad.madrid/group/salud and https://datos.comunidad.madrid/catalogo/dataset/6f407280-6ab1-43fb-bb48-ab954ec6edae/resource/130c1f6e-b131-44a1-94c9-00c9bb807ca6/download/oficinas_farmacia.csv , by the Autonomous Neighborhood of Madrid, Spain, explicitly allowing any use, as could be seen within the corresponding Phrases of Use and Licensing Info at https://www.comunidad.madrid/servicios/012-atencion-ciudadano/aviso-legal-privacidad.
The methodological design, technical implementation (e.g., community evaluation by way of NetworkX), and spatial computations introduced on this article have been developed independently by the writer. All analytical workflows, visualizations, and conclusions are authentic contributions, free from third-party mental property restrictions. For transparency, direct hyperlinks to information sources has been offered within the References and Information Availability sections of this text.
Word on Legal responsibility:
In accordance with the publicly accessible information sources employed, as defined within the earlier “Information Availability” part, the writer hereby disclaims any accountability for penalties, damages, or losses ensuing from the entry, use, or interpretation of the data introduced on this work, as achieved within the Phrases of Use of such information sources. This text is meant strictly for instructional functions and doesn’t represent skilled or business recommendation. Customers are urged to independently validate information and seek the advice of related consultants earlier than making use of any findings.
6.- REFFERENCES
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