Generating your own travel time matrices

There are a wide range of options for generating your own travel time matrices, including various travel time APIs.

You can find an example of how to use the routingpy package, which supports a wide range of APIs, here: https://geographic.hsma.co.uk/mtt_travel_time_apis.html

One good way is the r5py package.

This takes an output from the open street map project as well as bus and light rail (e.g. tram) public tranport data in the gtfs format.

OSM data: https://download.geofabrik.de/europe/united-kingdom/england.html

UK Bus/light rail Data: https://data.bus-data.dft.gov.uk/search/

(at the time of writing, heavy rail data is a bit more of a challenge!)

Because you’re running this locally, you aren’t contending with the number of requests you can make to the online services (API rate limits). Some free services like the openrouteservice don’t provide public transport routing support by default either.

Tip

If you’re comfortable with the R language, you might also find the UK2GTFS package useful

Warning

One limitation of r5py is that it requires the install of a JDK. This may be challenging if you are working in an organisation and your IT department has concerns about Java.

One option may be to use a service like GitHub codespaces to install the required software - a tutorial on this will be released at a later date.

We’ll kick off with a couple of standard imports.

import datetime
import pandas as pd
import geopandas

Let’s start by importing our data to set up a transport network.

import r5py

transport_network = r5py.TransportNetwork(
    "../../datasets/devon-260422.osm.pbf",
    [
        "../../datasets/itm_south_west_gtfs.zip",
    ]
)

Let’s then read in a dataset of destinations - in this case, minor injury units in Devon.

devon_mius = pd.read_csv("../../datasets/devon_miu.csv")
devon_mius
Facility_Name Latitude Longitude
0 North Devon District Hospital 51.09217 -4.05043
1 Honiton Hospital 50.79492 -3.18659
2 Tiverton & District Hospital 50.90933 -3.49308
3 Exmouth Minor Injury Unit 50.62083 -3.40198
4 Victoria Hospital (Sidmouth) 50.68161 -3.23966
5 Newton Abbot Community Hospital 50.53926 -3.61224
6 Totnes Community Hospital 50.43283 -3.68406
7 NHS Walk in Centre (Exeter) 50.72658 -3.52521
8 Tavistock Hospital 50.54708 -4.15376
9 South Hams Hospital (Kingsbridge) 50.28929 -3.78143
10 Cumberland Centre (Plymouth) 50.37004 -4.16873
11 Derriford Hospital (UTC) 50.41802 -4.11890
12 Ilfracombe & District Tyrrell Hospital 51.20468 -4.12454
13 South Molton Hospital 51.01681 -3.83823
14 Dawlish Community Hospital 50.58057 -3.47482

Let’s turn this into a geodataframe.

devon_mius_gdf = geopandas.GeoDataFrame(
    devon_mius,
    geometry = geopandas.points_from_xy(
        devon_mius['Longitude'],
        devon_mius['Latitude']
        ),
    crs = 'EPSG:4326'
    )

devon_mius_gdf
Facility_Name Latitude Longitude geometry
0 North Devon District Hospital 51.09217 -4.05043 POINT (-4.05043 51.09217)
1 Honiton Hospital 50.79492 -3.18659 POINT (-3.18659 50.79492)
2 Tiverton & District Hospital 50.90933 -3.49308 POINT (-3.49308 50.90933)
3 Exmouth Minor Injury Unit 50.62083 -3.40198 POINT (-3.40198 50.62083)
4 Victoria Hospital (Sidmouth) 50.68161 -3.23966 POINT (-3.23966 50.68161)
5 Newton Abbot Community Hospital 50.53926 -3.61224 POINT (-3.61224 50.53926)
6 Totnes Community Hospital 50.43283 -3.68406 POINT (-3.68406 50.43283)
7 NHS Walk in Centre (Exeter) 50.72658 -3.52521 POINT (-3.52521 50.72658)
8 Tavistock Hospital 50.54708 -4.15376 POINT (-4.15376 50.54708)
9 South Hams Hospital (Kingsbridge) 50.28929 -3.78143 POINT (-3.78143 50.28929)
10 Cumberland Centre (Plymouth) 50.37004 -4.16873 POINT (-4.16873 50.37004)
11 Derriford Hospital (UTC) 50.41802 -4.11890 POINT (-4.1189 50.41802)
12 Ilfracombe & District Tyrrell Hospital 51.20468 -4.12454 POINT (-4.12454 51.20468)
13 South Molton Hospital 51.01681 -3.83823 POINT (-3.83823 51.01681)
14 Dawlish Community Hospital 50.58057 -3.47482 POINT (-3.47482 50.58057)

We can save this out for easier reuse too.

devon_mius_gdf.to_file("../../../sample_data/devon_mius.geojson", driver="GeoJSON")

For using this with r5py, we’ll need to rename our ‘Facility_Name’ column to ‘id’.

devon_mius_gdf = devon_mius_gdf.rename(columns={'Facility_Name':'id'})
devon_mius_gdf.head(2)
id Latitude Longitude geometry
0 North Devon District Hospital 51.09217 -4.05043 POINT (-4.05043 51.09217)
1 Honiton Hospital 50.79492 -3.18659 POINT (-3.18659 50.79492)

Let’s just have a quick look at these on the map.

devon_mius_gdf.explore()
Make this Notebook Trusted to load map: File -> Trust Notebook

Now we need to grab our sources (where our patients will travel from). We’ll use LSOA centroids for this.

lsoa_centroids = pd.read_csv(
    "https://github.com/hsma-programme/h6_3c_interactive_plots_travel/raw/main/h6_3c_interactive_plots_travel/example_code/england_lsoa_2011_centroids.csv"
    )
lsoa_centroids.head()
name code x y
0 Middlesbrough 012A E01012007 449119.175 517017.509
1 Middlesbrough 010D E01012085 451722.550 517577.735
2 Hartlepool 014G E01012005 448657.056 533984.633
3 Middlesbrough 010C E01012084 451977.348 517832.468
4 Hartlepool 006D E01012002 449565.447 533268.699

To sense check our filtering, though, we’ll take a look at an LSOA boundary file, which contains the LSOA names in the same format. The ‘name’ column in our centroids file is the same as the LSOA11NM in the boundaries geodataframe.

lsoa_boundaries = geopandas.read_file(
    "https://github.com/hsma-programme/h6_3c_interactive_plots_travel/raw/main/h6_3c_interactive_plots_travel/example_code/LSOA_2011_Boundaries_Super_Generalised_Clipped_BSC_EW_V4.geojson"
    )
lsoa_boundaries.head()
FID LSOA11CD LSOA11NM LSOA11NMW BNG_E BNG_N LONG LAT GlobalID geometry
0 1 E01000001 City of London 001A City of London 001A 532123 181632 -0.097140 51.51816 a758442e-7679-45d0-95a8-ed4c968ecdaa POLYGON ((532282.629 181906.496, 532248.25 181...
1 2 E01000002 City of London 001B City of London 001B 532480 181715 -0.091970 51.51882 861dbb53-dfaf-4f57-be96-4527e2ec511f POLYGON ((532746.814 181786.892, 532248.25 181...
2 3 E01000003 City of London 001C City of London 001C 532239 182033 -0.095320 51.52174 9f765b55-2061-484a-862b-fa0325991616 POLYGON ((532293.068 182068.422, 532419.592 18...
3 4 E01000005 City of London 001E City of London 001E 533581 181283 -0.076270 51.51468 a55c4c31-ef1c-42fc-bfa9-07c8f2025928 POLYGON ((533604.245 181418.129, 533743.689 18...
4 5 E01000006 Barking and Dagenham 016A Barking and Dagenham 016A 544994 184274 0.089317 51.53875 9cdabaa8-d9bd-4a94-bb3b-98a933ceedad POLYGON ((545271.918 184183.948, 545296.314 18...
Tip

We could also use a geopandas function to get centroids from our boundary dataframe!

We might also want to look for an option like population-weighted centroids.

Note

We may also need to consider looking at smaller units of area, particularly if we’re interested in options like public transport or walking, as LSOAs can cover a vast area compared to something like a postcode sector. However, for the sake of this example, we’re going to stick with LSOAs.

Let’s try out our filter and confirm we’ve correctly filtered by all the right LSOA names.

lsoa_boundaries[lsoa_boundaries["LSOA11NM"].str.contains(
    "Devon|Torbay|South Hams|Exeter|Torridge|Teignbridge|Plymouth"
    )].plot()

We can also take a look on an interactive plot.

lsoa_boundaries[lsoa_boundaries["LSOA11NM"].str.contains(
    "Devon|Torbay|South Hams|Exeter|Torridge|Teignbridge|Plymouth"
    )].explore()
Make this Notebook Trusted to load map: File -> Trust Notebook

Let’s now turn this into a geodataframe and convert it from BNH (Northings/Eastings) to latitude and longitude to match our other data (and what r5py expects).

devon_lsoas_with_coords = lsoa_centroids[lsoa_centroids["name"].str.contains(
    "Devon|Torbay|South Hams|Exeter|Torridge|Teignbridge|Plymouth"
    )]

devon_lsoas_with_coords_gdf = geopandas.GeoDataFrame(
    devon_lsoas_with_coords,
    geometry = geopandas.points_from_xy(
        devon_lsoas_with_coords['x'],
        devon_lsoas_with_coords['y']
        ),
    crs = 'EPSG:27700' # as our current dataset is in BNG (northings/eastings)
    ).to_crs('EPSG:4326').rename(columns={'name':'id'})

devon_lsoas_with_coords_gdf
id code x y geometry
29583 Torbay 006C E01015216 292132.142 64632.566 POINT (-3.52139 50.47156)
29585 Torbay 008A E01015217 291749.626 64295.856 POINT (-3.52668 50.46846)
29587 Torbay 006A E01015214 291750.141 64630.567 POINT (-3.52677 50.47147)
29589 Torbay 006B E01015215 292381.278 64581.160 POINT (-3.51787 50.47115)
29591 Torbay 019C E01015212 290286.739 64323.402 POINT (-3.54729 50.46844)
... ... ... ... ... ...
32825 East Devon 005B E01019887 329961.723 98655.512 POINT (-2.99485 50.78323)
32828 Torbay 017A E01015183 292872.985 55875.060 POINT (-3.50845 50.39297)
32829 Torbay 017G E01015189 292320.564 56248.741 POINT (-3.51632 50.39623)
32833 Torridge 008B E01020293 234408.086 104233.376 POINT (-4.35192 50.81392)
32836 Plymouth 014C E01015041 245338.352 56546.556 POINT (-4.17702 50.38841)

707 rows × 5 columns

Generating the matrix

Car travel

travel_time_matrix_car = r5py.TravelTimeMatrix(
    transport_network,
    origins=devon_lsoas_with_coords_gdf,
    destinations=devon_mius_gdf,
    transport_modes=[r5py.TransportMode.CAR],
    departure=datetime.datetime(2026, 4, 23, 14, 0, 0),
)
travel_time_matrix_car
from_id to_id travel_time
0 Torbay 006C North Devon District Hospital 94.0
1 Torbay 006C Honiton Hospital 47.0
2 Torbay 006C Tiverton & District Hospital 51.0
3 Torbay 006C Exmouth Minor Injury Unit 44.0
4 Torbay 006C Victoria Hospital (Sidmouth) 49.0
... ... ... ...
10600 Plymouth 014C Cumberland Centre (Plymouth) 7.0
10601 Plymouth 014C Derriford Hospital (UTC) 11.0
10602 Plymouth 014C Ilfracombe & District Tyrrell Hospital NaN
10603 Plymouth 014C South Molton Hospital 90.0
10604 Plymouth 014C Dawlish Community Hospital 56.0

10605 rows × 3 columns

This isn’t in the format lokigi expects - we just need to turn it into a wide format dataframe, where we have one row per source (where our patients will travel from) and one column per destination (where they might turn up to).

travel_time_matrix_car_wide = travel_time_matrix_car.pivot(columns="to_id", index="from_id", values="travel_time").reset_index()
travel_time_matrix_car_wide
to_id from_id Cumberland Centre (Plymouth) Dawlish Community Hospital Derriford Hospital (UTC) Exmouth Minor Injury Unit Honiton Hospital Ilfracombe & District Tyrrell Hospital NHS Walk in Centre (Exeter) Newton Abbot Community Hospital North Devon District Hospital South Hams Hospital (Kingsbridge) South Molton Hospital Tavistock Hospital Tiverton & District Hospital Totnes Community Hospital Victoria Hospital (Sidmouth)
0 East Devon 001A 75.0 44.0 70.0 38.0 16.0 86.0 35.0 47.0 77.0 71.0 55.0 72.0 34.0 56.0 29.0
1 East Devon 001B 71.0 40.0 66.0 33.0 12.0 92.0 31.0 43.0 83.0 67.0 61.0 67.0 40.0 52.0 27.0
2 East Devon 001C 83.0 52.0 77.0 45.0 25.0 104.0 43.0 55.0 94.0 79.0 72.0 79.0 52.0 64.0 39.0
3 East Devon 002A 67.0 36.0 61.0 29.0 3.0 84.0 27.0 39.0 75.0 63.0 53.0 63.0 33.0 48.0 19.0
4 East Devon 002B 67.0 36.0 61.0 29.0 5.0 82.0 27.0 39.0 73.0 63.0 51.0 63.0 30.0 48.0 19.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
702 West Devon 006D 27.0 67.0 16.0 70.0 73.0 103.0 60.0 52.0 90.0 52.0 84.0 11.0 77.0 45.0 75.0
703 West Devon 007A 34.0 74.0 23.0 77.0 81.0 110.0 68.0 60.0 97.0 60.0 92.0 16.0 85.0 52.0 83.0
704 West Devon 007B 34.0 74.0 24.0 76.0 80.0 110.0 67.0 60.0 96.0 60.0 91.0 15.0 84.0 52.0 82.0
705 West Devon 007C 29.0 69.0 18.0 74.0 78.0 109.0 67.0 54.0 96.0 54.0 91.0 17.0 82.0 47.0 79.0
706 West Devon 007D 25.0 65.0 14.0 70.0 74.0 109.0 64.0 50.0 95.0 50.0 90.0 17.0 78.0 43.0 76.0

707 rows × 16 columns

Note

r5py assumes free flowing traffic at the speed limit - so this might not be overly realistic for traffic!

Lokigi can’t handle missing values in a travel matrix, which might exist here if the time between any two points is over 2 hours or otherwise deemed to be impossible, so let’s fill any missing values with a very large travel time.

travel_time_matrix_car_wide = travel_time_matrix_car_wide.fillna(9999.0)

We can save this to a csv for convenience if we want to load it in elsewhere later.

travel_time_matrix_car_wide.to_csv("../../../sample_data/devon_miu_travel_matrix.csv", index=False)

Public transport

For public transport, we change our transport mode to TRANSIT.

By default, it assumes people can walk to where they will pick up their journey with public transport.

travel_time_matrix_transit = r5py.TravelTimeMatrix(
    transport_network,
    origins=devon_lsoas_with_coords_gdf,
    destinations=devon_mius_gdf,
    transport_modes=[r5py.TransportMode.TRANSIT],
    departure=datetime.datetime(2026, 4, 23, 14, 0, 0),
)

Let’s first just filter down to instances where it’s successfully computed a time.

travel_time_matrix_transit[~travel_time_matrix_transit["travel_time"].isna()]
from_id to_id travel_time
5 Torbay 006C Newton Abbot Community Hospital 78.0
6 Torbay 006C Totnes Community Hospital 97.0
14 Torbay 006C Dawlish Community Hospital 114.0
20 Torbay 008A Newton Abbot Community Hospital 70.0
21 Torbay 008A Totnes Community Hospital 79.0
... ... ... ...
10551 Torbay 017A Totnes Community Hospital 82.0
10566 Torbay 017G Totnes Community Hospital 77.0
10598 Plymouth 014C Tavistock Hospital 83.0
10600 Plymouth 014C Cumberland Centre (Plymouth) 25.0
10601 Plymouth 014C Derriford Hospital (UTC) 29.0

2283 rows × 3 columns

Now let’s make a wide version of this too.

travel_time_matrix_transit_wide = travel_time_matrix_transit.pivot(columns="to_id", index="from_id", values="travel_time").reset_index()
travel_time_matrix_transit_wide
to_id from_id Cumberland Centre (Plymouth) Dawlish Community Hospital Derriford Hospital (UTC) Exmouth Minor Injury Unit Honiton Hospital Ilfracombe & District Tyrrell Hospital NHS Walk in Centre (Exeter) Newton Abbot Community Hospital North Devon District Hospital South Hams Hospital (Kingsbridge) South Molton Hospital Tavistock Hospital Tiverton & District Hospital Totnes Community Hospital Victoria Hospital (Sidmouth)
0 East Devon 001A NaN NaN NaN NaN 101.0 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
1 East Devon 001B NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2 East Devon 001C NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
3 East Devon 002A NaN NaN NaN NaN 14.0 NaN 86.0 NaN NaN NaN NaN NaN NaN NaN 63.0
4 East Devon 002B NaN NaN NaN NaN 18.0 NaN 82.0 NaN NaN NaN NaN NaN NaN NaN 63.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
702 West Devon 006D 83.0 NaN 51.0 NaN NaN NaN NaN NaN NaN NaN NaN 41.0 NaN NaN NaN
703 West Devon 007A NaN NaN 113.0 NaN NaN NaN NaN NaN NaN NaN NaN 63.0 NaN NaN NaN
704 West Devon 007B NaN NaN 113.0 NaN NaN NaN NaN NaN NaN NaN NaN 63.0 NaN NaN NaN
705 West Devon 007C NaN NaN 87.0 NaN NaN NaN NaN NaN NaN NaN NaN 80.0 NaN NaN NaN
706 West Devon 007D 109.0 NaN 70.0 NaN NaN NaN NaN NaN NaN NaN NaN 78.0 NaN NaN NaN

707 rows × 16 columns

There are a lot of NAs this time!

Let’s again fill this for any instances with impossibly long travel times.

travel_time_matrix_transit_wide = travel_time_matrix_transit_wide.fillna(9999.0)

Solving a problem with our travel time matrices

Let’s now use this to initialise a lokigi problem.

We’ll conceptualise this as a problem where they need to close two of the current MIUs.

Car

from lokigi.site import SiteProblem

problem = SiteProblem()

problem.add_sites(
    devon_mius_gdf,
    candidate_id_col="id"
    )

problem.add_travel_matrix(
    travel_matrix_df=travel_time_matrix_car_wide,
    source_col="from_id",
    unit="minutes",
    )

problem.add_region_geometry_layer(
    lsoa_boundaries,
    common_col="LSOA11NM"
    )
problem.plot_sites()

solution_greedy = problem.solve(p=len(problem.show_sites())-2, search_strategy="greedy")
C:\lokigi\lokigi\site.py:1414: UserWarning: No demand data was provided. Demand from all regions has been assumed to be equal.If you wish to override this, run .add_demand() to add your site dataframe before running .solve() again.You can use the .show_demand_format() to see the expected format beforehand.
  warn(
Best combination for 1 sites: [np.int64(5)]
Best combination for 2 sites: [np.int64(5), np.int64(11)]
Best combination for 3 sites: [np.int64(0), np.int64(5), np.int64(11)]
Best combination for 4 sites: [np.int64(0), np.int64(5), np.int64(7), np.int64(11)]
Best combination for 5 sites: [np.int64(0), np.int64(5), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 6 sites: [np.int64(0), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 7 sites: [np.int64(0), np.int64(2), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 8 sites: [np.int64(0), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 9 sites: [np.int64(0), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(11)]
Best combination for 10 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(11)]
Best combination for 11 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(11), np.int64(12)]
Best combination for 12 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(11), np.int64(12), np.int64(14)]
Best combination for 13 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(9), np.int64(11), np.int64(12), np.int64(14)]
fig = solution_greedy.plot_best_combination(unchosen_site_colour="magenta")
fig;

Tip

In this instance, we might want to consider the impact of boundary effects. We’ve only mapped the MIUs based in Devon. However, people on the border, where we are seeing extreme travel times, may well pass into a hospital in an adjoining county.

If that’s the case, we need to be sure we provide the OSM data for those regions when we do our initial travel time matrix generation, as otherwise the router won’t be able to work out how to get there! If we just added an extra point in Cornwall to our travel matrix calculation as currently defined, we’d get ‘NA’ for all instances.

Public Transport

Let’s solve again for public transport times.

problem_public_transport = SiteProblem()

problem_public_transport.add_sites(
    devon_mius_gdf,
    candidate_id_col="id"
    )

problem_public_transport.add_region_geometry_layer(
    lsoa_boundaries,
    common_col="LSOA11NM"
    )

problem_public_transport.add_travel_matrix(
    travel_matrix_df=travel_time_matrix_transit_wide,
    source_col="from_id",
    unit="minutes",
    )
solution_greedy_public_transport = problem_public_transport.solve(
    p=len(problem_public_transport.show_sites())-2,
    search_strategy="greedy"
    )
C:\lokigi\lokigi\site.py:1414: UserWarning: No demand data was provided. Demand from all regions has been assumed to be equal.If you wish to override this, run .add_demand() to add your site dataframe before running .solve() again.You can use the .show_demand_format() to see the expected format beforehand.
  warn(
Best combination for 1 sites: [np.int64(7)]
Best combination for 2 sites: [np.int64(6), np.int64(7)]
Best combination for 3 sites: [np.int64(6), np.int64(7), np.int64(11)]
Best combination for 4 sites: [np.int64(6), np.int64(7), np.int64(11), np.int64(13)]
Best combination for 5 sites: [np.int64(1), np.int64(6), np.int64(7), np.int64(11), np.int64(13)]
Best combination for 6 sites: [np.int64(1), np.int64(6), np.int64(7), np.int64(11), np.int64(12), np.int64(13)]
Best combination for 7 sites: [np.int64(1), np.int64(6), np.int64(7), np.int64(9), np.int64(11), np.int64(12), np.int64(13)]
Best combination for 8 sites: [np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(9), np.int64(11), np.int64(12), np.int64(13)]
Best combination for 9 sites: [np.int64(0), np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(9), np.int64(11), np.int64(12), np.int64(13)]
Best combination for 10 sites: [np.int64(0), np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(9), np.int64(11), np.int64(12), np.int64(13), np.int64(14)]
Best combination for 11 sites: [np.int64(0), np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(9), np.int64(11), np.int64(12), np.int64(13), np.int64(14)]
Best combination for 12 sites: [np.int64(0), np.int64(1), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(9), np.int64(11), np.int64(12), np.int64(13), np.int64(14)]
Best combination for 13 sites: [np.int64(0), np.int64(1), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(9), np.int64(10), np.int64(11), np.int64(12), np.int64(13), np.int64(14)]
fig = solution_greedy_public_transport.plot_best_combination(unchosen_site_colour="magenta")
fig;

We can see that our output has some problems!

First, we could try rerunning our public transport with

  • a higher maximum journey time
  • a wider departure window
  • a higher number of transfers

Tweaking a public transport travel matrix

travel_time_matrix_transit = r5py.TravelTimeMatrix(
    transport_network,
    origins=devon_lsoas_with_coords_gdf,
    destinations=devon_mius_gdf,
    transport_modes=[r5py.TransportMode.TRANSIT],
    departure=datetime.datetime(2026, 4, 23, 14, 0, 0),
    max_time=datetime.timedelta(minutes=600),
    departure_time_window=datetime.timedelta(minutes=60),
    max_public_transport_rides=20
)
travel_time_matrix_transit_wide = travel_time_matrix_transit.pivot(columns="to_id", index="from_id", values="travel_time").reset_index()

We can check if there are any examples where you can’t get to any hospital.

len(travel_time_matrix_transit_wide)
707
travel_time_matrix_transit_wide_extended = travel_time_matrix_transit_wide.set_index("from_id").dropna(how="all").reset_index(drop=False)
travel_time_matrix_transit_wide_extended
to_id from_id Cumberland Centre (Plymouth) Dawlish Community Hospital Derriford Hospital (UTC) Exmouth Minor Injury Unit Honiton Hospital Ilfracombe & District Tyrrell Hospital NHS Walk in Centre (Exeter) Newton Abbot Community Hospital North Devon District Hospital South Hams Hospital (Kingsbridge) South Molton Hospital Tavistock Hospital Tiverton & District Hospital Totnes Community Hospital Victoria Hospital (Sidmouth)
0 East Devon 001A 260.0 217.0 268.0 211.0 76.0 365.0 137.0 213.0 288.0 292.0 245.0 316.0 190.0 259.0 160.0
1 East Devon 001B 359.0 288.0 363.0 258.0 133.0 518.0 223.0 302.0 490.0 NaN 433.0 415.0 317.0 326.0 198.0
2 East Devon 001C 398.0 377.0 402.0 338.0 216.0 543.0 294.0 386.0 515.0 NaN 458.0 454.0 388.0 361.0 260.0
3 East Devon 002A 222.0 197.0 225.0 127.0 14.0 365.0 116.0 205.0 288.0 286.0 241.0 275.0 184.0 213.0 72.0
4 East Devon 002B 221.0 195.0 223.0 128.0 18.0 365.0 115.0 201.0 288.0 282.0 241.0 275.0 180.0 209.0 73.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
702 West Devon 006D 97.0 244.0 56.0 240.0 262.0 314.0 172.0 222.0 268.0 184.0 308.0 45.0 248.0 184.0 252.0
703 West Devon 007A 150.0 285.0 111.0 283.0 307.0 331.0 217.0 287.0 285.0 255.0 353.0 61.0 293.0 252.0 297.0
704 West Devon 007B 150.0 285.0 111.0 283.0 307.0 331.0 217.0 287.0 285.0 255.0 353.0 61.0 293.0 252.0 297.0
705 West Devon 007C 130.0 293.0 90.0 301.0 308.0 408.0 249.0 262.0 331.0 221.0 443.0 80.0 329.0 223.0 306.0
706 West Devon 007D 119.0 285.0 79.0 289.0 301.0 401.0 237.0 246.0 324.0 205.0 433.0 74.0 317.0 212.0 296.0

707 rows × 16 columns

len(travel_time_matrix_transit_wide_extended)
707

Let’s agains set any NAs to a high value.

travel_time_matrix_transit_wide_extended = travel_time_matrix_transit_wide_extended.fillna(9999.0)

And save this for future use.

travel_time_matrix_transit_wide_extended.to_csv("../../../sample_data/devon_miu_travel_matrix_public_transport_extended.csv", index=False)

We can then overwrite the existing travel matrix.

problem_public_transport_extended = SiteProblem()

problem_public_transport_extended.add_sites(
    devon_mius_gdf,
    candidate_id_col="id"
    )

problem_public_transport_extended.add_region_geometry_layer(
    lsoa_boundaries,
    common_col="LSOA11NM"
    )

problem_public_transport_extended.add_travel_matrix(
    travel_matrix_df=travel_time_matrix_transit_wide_extended,
    source_col="from_id",
    unit="minutes",
    )
problem_public_transport_extended.show_travel_matrix()
to_id from_id Cumberland Centre (Plymouth) Dawlish Community Hospital Derriford Hospital (UTC) Exmouth Minor Injury Unit Honiton Hospital Ilfracombe & District Tyrrell Hospital NHS Walk in Centre (Exeter) Newton Abbot Community Hospital North Devon District Hospital South Hams Hospital (Kingsbridge) South Molton Hospital Tavistock Hospital Tiverton & District Hospital Totnes Community Hospital Victoria Hospital (Sidmouth)
0 East Devon 001A 260.0 217.0 268.0 211.0 76.0 365.0 137.0 213.0 288.0 292.0 245.0 316.0 190.0 259.0 160.0
1 East Devon 001B 359.0 288.0 363.0 258.0 133.0 518.0 223.0 302.0 490.0 9999.0 433.0 415.0 317.0 326.0 198.0
2 East Devon 001C 398.0 377.0 402.0 338.0 216.0 543.0 294.0 386.0 515.0 9999.0 458.0 454.0 388.0 361.0 260.0
3 East Devon 002A 222.0 197.0 225.0 127.0 14.0 365.0 116.0 205.0 288.0 286.0 241.0 275.0 184.0 213.0 72.0
4 East Devon 002B 221.0 195.0 223.0 128.0 18.0 365.0 115.0 201.0 288.0 282.0 241.0 275.0 180.0 209.0 73.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
702 West Devon 006D 97.0 244.0 56.0 240.0 262.0 314.0 172.0 222.0 268.0 184.0 308.0 45.0 248.0 184.0 252.0
703 West Devon 007A 150.0 285.0 111.0 283.0 307.0 331.0 217.0 287.0 285.0 255.0 353.0 61.0 293.0 252.0 297.0
704 West Devon 007B 150.0 285.0 111.0 283.0 307.0 331.0 217.0 287.0 285.0 255.0 353.0 61.0 293.0 252.0 297.0
705 West Devon 007C 130.0 293.0 90.0 301.0 308.0 408.0 249.0 262.0 331.0 221.0 443.0 80.0 329.0 223.0 306.0
706 West Devon 007D 119.0 285.0 79.0 289.0 301.0 401.0 237.0 246.0 324.0 205.0 433.0 74.0 317.0 212.0 296.0

707 rows × 16 columns

And re-solve.

solution_greedy_public_transport_extended = problem_public_transport_extended.solve(
    p=len(problem_public_transport_extended.show_sites())-2,
    search_strategy="greedy"
    )
C:\lokigi\lokigi\site.py:1414: UserWarning: No demand data was provided. Demand from all regions has been assumed to be equal.If you wish to override this, run .add_demand() to add your site dataframe before running .solve() again.You can use the .show_demand_format() to see the expected format beforehand.
  warn(
Best combination for 1 sites: [np.int64(7)]
Best combination for 2 sites: [np.int64(7), np.int64(11)]
Best combination for 3 sites: [np.int64(0), np.int64(7), np.int64(11)]
Best combination for 4 sites: [np.int64(0), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 5 sites: [np.int64(0), np.int64(1), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 6 sites: [np.int64(0), np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(11)]
Best combination for 7 sites: [np.int64(0), np.int64(1), np.int64(5), np.int64(6), np.int64(7), np.int64(10), np.int64(11)]
Best combination for 8 sites: [np.int64(0), np.int64(1), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(10), np.int64(11)]
Best combination for 9 sites: [np.int64(0), np.int64(1), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(10), np.int64(11)]
Best combination for 10 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(10), np.int64(11)]
Best combination for 11 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(10), np.int64(11), np.int64(12)]
Best combination for 12 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(10), np.int64(11), np.int64(12), np.int64(14)]
Best combination for 13 sites: [np.int64(0), np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8), np.int64(10), np.int64(11), np.int64(12), np.int64(14)]

We can see that this time we get a much better output!

(Though some of these people may have had impossible journeys in a practical sense, taking over 4 hours and an unknown number of changes to get where they’re going!)

fig = solution_greedy_public_transport_extended.plot_best_combination(unchosen_site_colour="magenta")
fig;

Tip

Lokigi will be extended in future to better handle NA values in travel matrices.

fig = solution_greedy_public_transport_extended.plot_best_combination(unchosen_site_colour="magenta", plot_site_allocation=True, legend_loc="lower right", show_all_locations=False, cmap="Set3")
fig;

solution_greedy_public_transport_extended.show_solutions().problem_df.iloc[0].selected_site.unique()
<StringArray>
[                      'Honiton Hospital',
           'Victoria Hospital (Sidmouth)',
            'NHS Walk in Centre (Exeter)',
              'Exmouth Minor Injury Unit',
           'Tiverton & District Hospital',
 'Ilfracombe & District Tyrrell Hospital',
          'North Devon District Hospital',
               'Derriford Hospital (UTC)',
           'Cumberland Centre (Plymouth)',
              'Totnes Community Hospital',
             'Dawlish Community Hospital',
        'Newton Abbot Community Hospital',
                     'Tavistock Hospital']
Length: 13, dtype: str
problem.show_sites()
canonical_site_index id Latitude Longitude geometry
0 0 North Devon District Hospital 51.09217 -4.05043 POINT (256506.101 134540.134)
1 1 Honiton Hospital 50.79492 -3.18659 POINT (316466.043 100155.33)
2 2 Tiverton & District Hospital 50.90933 -3.49308 POINT (295122.857 113268.884)
3 3 Exmouth Minor Injury Unit 50.62083 -3.40198 POINT (300919.29 81063.23)
4 4 Victoria Hospital (Sidmouth) 50.68161 -3.23966 POINT (312514.661 87617.001)
5 5 Newton Abbot Community Hospital 50.53926 -3.61224 POINT (285848.833 72295.946)
6 6 Totnes Community Hospital 50.43283 -3.68406 POINT (280491.309 60575.271)
7 7 NHS Walk in Centre (Exeter) 50.72658 -3.52521 POINT (292444.533 92994.08)
8 8 Tavistock Hospital 50.54708 -4.15376 POINT (247503.629 74139.474)
9 9 South Hams Hospital (Kingsbridge) 50.28929 -3.78143 POINT (273194.03 44777.085)
10 10 Cumberland Centre (Plymouth) 50.37004 -4.16873 POINT (245868.211 54486.789)
11 11 Derriford Hospital (UTC) 50.41802 -4.11890 POINT (249563.619 59719.094)
12 12 Ilfracombe & District Tyrrell Hospital 51.20468 -4.12454 POINT (251678.187 147197.738)
13 13 South Molton Hospital 51.01681 -3.83823 POINT (271156.007 125767.813)
14 14 Dawlish Community Hospital 50.58057 -3.47482 POINT (295677.679 76686.654) 
solution_greedy_public_transport_extended.show_solutions()
site_names site_indices coverage_threshold weighted_average unweighted_average 90th_percentile max proportion_within_coverage_threshold problem_df
0 [North Devon District Hospital, Honiton Hospit... [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14] None 57.65 57.65 98.4 262.0 0.0 from_id        from_id_x  North D...
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