diff --git a/.gitignore b/.gitignore
index 2fc8820..547f116 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,6 +1,7 @@
 .cache/
 **/*.egg-info/
 .env
+.idea/
 **/.ipynb_checkpoints/
 .python-version
 .venv/
diff --git a/migrations/versions/rev_20210301_16_b4dd0b8903a5_add_distance_matrix.py b/migrations/versions/rev_20210301_16_b4dd0b8903a5_add_distance_matrix.py
new file mode 100644
index 0000000..d8f1606
--- /dev/null
+++ b/migrations/versions/rev_20210301_16_b4dd0b8903a5_add_distance_matrix.py
@@ -0,0 +1,96 @@
+"""Add distance matrix.
+
+Revision: #b4dd0b8903a5 at 2021-03-01 16:14:06
+Revises: #8bfb928a31f8
+"""
+
+import os
+
+import sqlalchemy as sa
+from alembic import op
+from sqlalchemy.dialects import postgresql
+
+from urban_meal_delivery import configuration
+
+
+revision = 'b4dd0b8903a5'
+down_revision = '8bfb928a31f8'
+branch_labels = None
+depends_on = None
+
+
+config = configuration.make_config('testing' if os.getenv('TESTING') else 'production')
+
+
+def upgrade():
+    """Upgrade to revision b4dd0b8903a5."""
+    op.create_table(
+        'addresses_addresses',
+        sa.Column('first_address_id', sa.Integer(), nullable=False),
+        sa.Column('second_address_id', sa.Integer(), nullable=False),
+        sa.Column('city_id', sa.SmallInteger(), nullable=False),
+        sa.Column('air_distance', sa.Integer(), nullable=False),
+        sa.Column('bicycle_distance', sa.Integer(), nullable=True),
+        sa.Column('bicycle_duration', sa.Integer(), nullable=True),
+        sa.Column('directions', postgresql.JSON(), nullable=True),
+        sa.PrimaryKeyConstraint(
+            'first_address_id',
+            'second_address_id',
+            name=op.f('pk_addresses_addresses'),
+        ),
+        sa.ForeignKeyConstraint(
+            ['first_address_id', 'city_id'],
+            [
+                f'{config.CLEAN_SCHEMA}.addresses.id',
+                f'{config.CLEAN_SCHEMA}.addresses.city_id',
+            ],
+            name=op.f(
+                'fk_addresses_addresses_to_addresses_via_first_address_id_city_id',
+            ),
+            onupdate='RESTRICT',
+            ondelete='RESTRICT',
+        ),
+        sa.ForeignKeyConstraint(
+            ['second_address_id', 'city_id'],
+            [
+                f'{config.CLEAN_SCHEMA}.addresses.id',
+                f'{config.CLEAN_SCHEMA}.addresses.city_id',
+            ],
+            name=op.f(
+                'fk_addresses_addresses_to_addresses_via_second_address_id_city_id',
+            ),
+            onupdate='RESTRICT',
+            ondelete='RESTRICT',
+        ),
+        sa.UniqueConstraint(
+            'first_address_id',
+            'second_address_id',
+            name=op.f('uq_addresses_addresses_on_first_address_id_second_address_id'),
+        ),
+        sa.CheckConstraint(
+            'first_address_id < second_address_id',
+            name=op.f('ck_addresses_addresses_on_distances_are_symmetric_for_bicycles'),
+        ),
+        sa.CheckConstraint(
+            '0 <= air_distance AND air_distance < 20000',
+            name=op.f('ck_addresses_addresses_on_realistic_air_distance'),
+        ),
+        sa.CheckConstraint(
+            'bicycle_distance < 25000',
+            name=op.f('ck_addresses_addresses_on_realistic_bicycle_distance'),
+        ),
+        sa.CheckConstraint(
+            'air_distance <= bicycle_distance',
+            name=op.f('ck_addresses_addresses_on_air_distance_is_shortest'),
+        ),
+        sa.CheckConstraint(
+            '0 <= bicycle_duration AND bicycle_duration <= 3600',
+            name=op.f('ck_addresses_addresses_on_realistic_bicycle_travel_time'),
+        ),
+        schema=config.CLEAN_SCHEMA,
+    )
+
+
+def downgrade():
+    """Downgrade to revision 8bfb928a31f8."""
+    op.drop_table('addresses_addresses', schema=config.CLEAN_SCHEMA)
diff --git a/noxfile.py b/noxfile.py
index eac123e..f79025c 100644
--- a/noxfile.py
+++ b/noxfile.py
@@ -135,7 +135,6 @@ def lint(session):
         'flake8',
         'flake8-annotations',
         'flake8-black',
-        'flake8-expression-complexity',
         'flake8-pytest-style',
         'mypy',
         'wemake-python-styleguide',
@@ -197,7 +196,6 @@ def test(session):
         'pytest-cov',
         'pytest-env',
         'pytest-mock',
-        'pytest-randomly',
         'xdoctest[optional]',
     )
 
@@ -207,7 +205,7 @@ def test(session):
     # test cases that require the slow installation of R and some packages.
     if session.env.get('_slow_ci_tests'):
         session.run(
-            'pytest', '--randomly-seed=4287', '-m', 'r and not db', PYTEST_LOCATION,
+            'pytest', '-m', 'r and not db', PYTEST_LOCATION,
         )
 
         # In the "ci-tests-slow" session, we do not run any test tool
@@ -219,7 +217,6 @@ def test(session):
     # Therefore, the CI server does not measure coverage.
     elif session.env.get('_fast_ci_tests'):
         pytest_args = (
-            '--randomly-seed=4287',
             '-m',
             'not (db or r)',
             PYTEST_LOCATION,
@@ -235,7 +232,6 @@ def test(session):
             '--cov-branch',
             '--cov-fail-under=100',
             '--cov-report=term-missing:skip-covered',
-            '--randomly-seed=4287',
             PYTEST_LOCATION,
         )
 
diff --git a/poetry.lock b/poetry.lock
index 5b0958b..415130c 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -8,18 +8,20 @@ python-versions = "*"
 
 [[package]]
 name = "alembic"
-version = "1.5.4"
+version = "1.7.1"
 description = "A database migration tool for SQLAlchemy."
 category = "main"
 optional = false
-python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,>=2.7"
+python-versions = ">=3.6"
 
 [package.dependencies]
+importlib-resources = {version = "*", markers = "python_version < \"3.9\""}
 Mako = "*"
-python-dateutil = "*"
-python-editor = ">=0.3"
 SQLAlchemy = ">=1.3.0"
 
+[package.extras]
+tz = ["python-dateutil"]
+
 [[package]]
 name = "appdirs"
 version = "1.4.4"
@@ -38,7 +40,7 @@ python-versions = "*"
 
 [[package]]
 name = "argcomplete"
-version = "1.12.2"
+version = "1.12.3"
 description = "Bash tab completion for argparse"
 category = "dev"
 optional = false
@@ -49,19 +51,18 @@ test = ["coverage", "flake8", "pexpect", "wheel"]
 
 [[package]]
 name = "argon2-cffi"
-version = "20.1.0"
+version = "21.1.0"
 description = "The secure Argon2 password hashing algorithm."
 category = "main"
 optional = true
-python-versions = "*"
+python-versions = ">=3.5"
 
 [package.dependencies]
 cffi = ">=1.0.0"
-six = "*"
 
 [package.extras]
-dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pytest", "sphinx", "wheel", "pre-commit"]
-docs = ["sphinx"]
+dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pytest", "sphinx", "furo", "wheel", "pre-commit"]
+docs = ["sphinx", "furo"]
 tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pytest"]
 
 [[package]]
@@ -72,25 +73,6 @@ category = "dev"
 optional = false
 python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
 
-[[package]]
-name = "astpretty"
-version = "2.1.0"
-description = "Pretty print the output of python stdlib `ast.parse`."
-category = "dev"
-optional = false
-python-versions = ">=3.6.1"
-
-[package.extras]
-typed = ["typed-ast"]
-
-[[package]]
-name = "async-generator"
-version = "1.10"
-description = "Async generators and context managers for Python 3.5+"
-category = "main"
-optional = true
-python-versions = ">=3.5"
-
 [[package]]
 name = "atomicwrites"
 version = "1.4.0"
@@ -101,17 +83,17 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "attrs"
-version = "20.3.0"
+version = "21.2.0"
 description = "Classes Without Boilerplate"
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [package.extras]
-dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface", "furo", "sphinx", "pre-commit"]
-docs = ["furo", "sphinx", "zope.interface"]
-tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "zope.interface"]
-tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six"]
+dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit"]
+docs = ["furo", "sphinx", "zope.interface", "sphinx-notfound-page"]
+tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface"]
+tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins"]
 
 [[package]]
 name = "autoflake"
@@ -126,7 +108,7 @@ pyflakes = ">=1.1.0"
 
 [[package]]
 name = "babel"
-version = "2.9.0"
+version = "2.9.1"
 description = "Internationalization utilities"
 category = "dev"
 optional = false
@@ -143,6 +125,29 @@ category = "main"
 optional = true
 python-versions = "*"
 
+[[package]]
+name = "backports.entry-points-selectable"
+version = "1.1.0"
+description = "Compatibility shim providing selectable entry points for older implementations"
+category = "dev"
+optional = false
+python-versions = ">=2.7"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-flake8", "pytest-cov", "pytest-black (>=0.3.7)", "pytest-mypy", "pytest-checkdocs (>=2.4)", "pytest-enabler (>=1.0.1)"]
+
+[[package]]
+name = "backports.zoneinfo"
+version = "0.2.1"
+description = "Backport of the standard library zoneinfo module"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.extras]
+tzdata = ["tzdata"]
+
 [[package]]
 name = "bandit"
 version = "1.7.0"
@@ -180,11 +185,11 @@ d = ["aiohttp (>=3.3.2)", "aiohttp-cors"]
 
 [[package]]
 name = "bleach"
-version = "3.3.0"
+version = "4.1.0"
 description = "An easy safelist-based HTML-sanitizing tool."
 category = "main"
 optional = true
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = ">=3.6"
 
 [package.dependencies]
 packaging = "*"
@@ -204,7 +209,7 @@ jinja2 = "*"
 
 [[package]]
 name = "certifi"
-version = "2020.12.5"
+version = "2021.5.30"
 description = "Python package for providing Mozilla's CA Bundle."
 category = "main"
 optional = false
@@ -212,7 +217,7 @@ python-versions = "*"
 
 [[package]]
 name = "cffi"
-version = "1.14.4"
+version = "1.14.6"
 description = "Foreign Function Interface for Python calling C code."
 category = "main"
 optional = false
@@ -223,19 +228,22 @@ pycparser = "*"
 
 [[package]]
 name = "cfgv"
-version = "3.2.0"
+version = "3.3.1"
 description = "Validate configuration and produce human readable error messages."
 category = "dev"
 optional = false
 python-versions = ">=3.6.1"
 
 [[package]]
-name = "chardet"
-version = "4.0.0"
-description = "Universal encoding detector for Python 2 and 3"
+name = "charset-normalizer"
+version = "2.0.4"
+description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = ">=3.5.0"
+
+[package.extras]
+unicode_backport = ["unicodedata2"]
 
 [[package]]
 name = "click"
@@ -255,7 +263,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [[package]]
 name = "colorlog"
-version = "4.7.2"
+version = "4.8.0"
 description = "Log formatting with colors!"
 category = "dev"
 optional = false
@@ -266,7 +274,7 @@ colorama = {version = "*", markers = "sys_platform == \"win32\""}
 
 [[package]]
 name = "coverage"
-version = "5.4"
+version = "5.5"
 description = "Code coverage measurement for Python"
 category = "dev"
 optional = false
@@ -288,23 +296,31 @@ six = "*"
 
 [[package]]
 name = "darglint"
-version = "1.6.0"
+version = "1.8.0"
 description = "A utility for ensuring Google-style docstrings stay up to date with the source code."
 category = "dev"
 optional = false
 python-versions = ">=3.6,<4.0"
 
+[[package]]
+name = "debugpy"
+version = "1.4.3"
+description = "An implementation of the Debug Adapter Protocol for Python"
+category = "main"
+optional = true
+python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*"
+
 [[package]]
 name = "decorator"
-version = "4.4.2"
+version = "5.1.0"
 description = "Decorators for Humans"
 category = "main"
 optional = true
-python-versions = ">=2.6, !=3.0.*, !=3.1.*"
+python-versions = ">=3.5"
 
 [[package]]
 name = "defusedxml"
-version = "0.6.0"
+version = "0.7.1"
 description = "XML bomb protection for Python stdlib modules"
 category = "main"
 optional = true
@@ -312,7 +328,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [[package]]
 name = "distlib"
-version = "0.3.1"
+version = "0.3.2"
 description = "Distribution utilities"
 category = "dev"
 optional = false
@@ -379,27 +395,27 @@ python-versions = "*"
 
 [[package]]
 name = "flake8"
-version = "3.8.4"
+version = "3.9.2"
 description = "the modular source code checker: pep8 pyflakes and co"
 category = "dev"
 optional = false
-python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
 
 [package.dependencies]
 mccabe = ">=0.6.0,<0.7.0"
-pycodestyle = ">=2.6.0a1,<2.7.0"
-pyflakes = ">=2.2.0,<2.3.0"
+pycodestyle = ">=2.7.0,<2.8.0"
+pyflakes = ">=2.3.0,<2.4.0"
 
 [[package]]
 name = "flake8-annotations"
-version = "2.5.0"
+version = "2.6.2"
 description = "Flake8 Type Annotation Checks"
 category = "dev"
 optional = false
 python-versions = ">=3.6.1,<4.0.0"
 
 [package.dependencies]
-flake8 = ">=3.7,<3.9"
+flake8 = ">=3.7,<4.0"
 
 [[package]]
 name = "flake8-bandit"
@@ -417,7 +433,7 @@ pycodestyle = "*"
 
 [[package]]
 name = "flake8-black"
-version = "0.2.1"
+version = "0.2.3"
 description = "flake8 plugin to call black as a code style validator"
 category = "dev"
 optional = false
@@ -426,6 +442,7 @@ python-versions = "*"
 [package.dependencies]
 black = "*"
 flake8 = ">=3.0.0"
+toml = "*"
 
 [[package]]
 name = "flake8-broken-line"
@@ -463,7 +480,7 @@ flake8 = ">=2,<4.0.0"
 
 [[package]]
 name = "flake8-comprehensions"
-version = "3.3.1"
+version = "3.6.1"
 description = "A flake8 plugin to help you write better list/set/dict comprehensions."
 category = "dev"
 optional = false
@@ -486,7 +503,7 @@ pycodestyle = "*"
 
 [[package]]
 name = "flake8-docstrings"
-version = "1.5.0"
+version = "1.6.0"
 description = "Extension for flake8 which uses pydocstyle to check docstrings"
 category = "dev"
 optional = false
@@ -509,18 +526,6 @@ attrs = "*"
 eradicate = ">=1.0,<2.0"
 flake8 = ">=3.5,<4.0"
 
-[[package]]
-name = "flake8-expression-complexity"
-version = "0.0.8"
-description = "A flake8 extension that checks expressions complexity"
-category = "dev"
-optional = false
-python-versions = ">=3.6"
-
-[package.dependencies]
-astpretty = "*"
-flake8 = "*"
-
 [[package]]
 name = "flake8-isort"
 version = "3.0.1"
@@ -539,7 +544,7 @@ test = ["pytest (>=4.0.2,<6)"]
 
 [[package]]
 name = "flake8-plugin-utils"
-version = "1.3.1"
+version = "1.3.2"
 description = "The package provides base classes and utils for flake8 plugin writing"
 category = "dev"
 optional = false
@@ -558,14 +563,14 @@ flake8 = "*"
 
 [[package]]
 name = "flake8-pytest-style"
-version = "1.3.0"
+version = "1.5.0"
 description = "A flake8 plugin checking common style issues or inconsistencies with pytest-based tests."
 category = "dev"
 optional = false
 python-versions = ">=3.6,<4.0"
 
 [package.dependencies]
-flake8-plugin-utils = ">=1.3.1,<2.0.0"
+flake8-plugin-utils = ">=1.3.2,<2.0.0"
 
 [[package]]
 name = "flake8-quotes"
@@ -620,17 +625,17 @@ testing = ["pytest"]
 
 [[package]]
 name = "geographiclib"
-version = "1.50"
+version = "1.52"
 description = "The geodesic routines from GeographicLib"
-category = "dev"
+category = "main"
 optional = false
 python-versions = "*"
 
 [[package]]
 name = "geopy"
-version = "2.1.0"
+version = "2.2.0"
 description = "Python Geocoding Toolbox"
-category = "dev"
+category = "main"
 optional = false
 python-versions = ">=3.5"
 
@@ -639,53 +644,76 @@ geographiclib = ">=1.49,<2"
 
 [package.extras]
 aiohttp = ["aiohttp"]
-dev = ["async-generator", "flake8 (>=3.8.0,<3.9.0)", "isort (>=5.6.0,<5.7.0)", "coverage", "pytest-aiohttp", "pytest (>=3.10)", "readme-renderer", "sphinx", "sphinx-issues", "sphinx-rtd-theme (>=0.5.0)"]
+dev = ["async-generator", "coverage", "flake8 (>=3.8.0,<3.9.0)", "isort (>=5.6.0,<5.7.0)", "pytest-aiohttp", "pytest (>=3.10)", "readme-renderer", "sphinx", "sphinx-issues", "sphinx-rtd-theme (>=0.5.0)"]
 dev-docs = ["readme-renderer", "sphinx", "sphinx-issues", "sphinx-rtd-theme (>=0.5.0)"]
 dev-lint = ["async-generator", "flake8 (>=3.8.0,<3.9.0)", "isort (>=5.6.0,<5.7.0)"]
-dev-test = ["async-generator", "coverage", "pytest-aiohttp", "pytest (>=3.10)"]
+dev-test = ["async-generator", "coverage", "pytest-aiohttp", "pytest (>=3.10)", "sphinx"]
 requests = ["urllib3 (>=1.24.2)", "requests (>=2.16.2)"]
 timezone = ["pytz"]
 
 [[package]]
 name = "gitdb"
-version = "4.0.5"
+version = "4.0.7"
 description = "Git Object Database"
 category = "dev"
 optional = false
 python-versions = ">=3.4"
 
 [package.dependencies]
-smmap = ">=3.0.1,<4"
+smmap = ">=3.0.1,<5"
 
 [[package]]
 name = "gitpython"
-version = "3.1.12"
-description = "Python Git Library"
+version = "3.1.23"
+description = "GitPython is a python library used to interact with Git repositories"
 category = "dev"
 optional = false
-python-versions = ">=3.4"
+python-versions = ">=3.7"
 
 [package.dependencies]
 gitdb = ">=4.0.1,<5"
+typing-extensions = {version = ">=3.7.4.3", markers = "python_version < \"3.10\""}
+
+[[package]]
+name = "googlemaps"
+version = "4.5.3"
+description = "Python client library for Google Maps Platform"
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
+[package.dependencies]
+requests = ">=2.20.0,<3.0"
+
+[[package]]
+name = "greenlet"
+version = "1.1.1"
+description = "Lightweight in-process concurrent programming"
+category = "main"
+optional = false
+python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*"
+
+[package.extras]
+docs = ["sphinx"]
 
 [[package]]
 name = "identify"
-version = "1.5.13"
+version = "2.2.14"
 description = "File identification library for Python"
 category = "dev"
 optional = false
-python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
+python-versions = ">=3.6.1"
 
 [package.extras]
-license = ["editdistance"]
+license = ["editdistance-s"]
 
 [[package]]
 name = "idna"
-version = "2.10"
+version = "3.2"
 description = "Internationalized Domain Names in Applications (IDNA)"
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+python-versions = ">=3.5"
 
 [[package]]
 name = "imagesize"
@@ -695,6 +723,21 @@ category = "dev"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
+[[package]]
+name = "importlib-resources"
+version = "5.2.2"
+description = "Read resources from Python packages"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.dependencies]
+zipp = {version = ">=3.1.0", markers = "python_version < \"3.10\""}
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "pytest-black (>=0.3.7)", "pytest-mypy"]
+
 [[package]]
 name = "iniconfig"
 version = "1.1.1"
@@ -705,25 +748,28 @@ python-versions = "*"
 
 [[package]]
 name = "ipykernel"
-version = "5.4.3"
+version = "6.4.1"
 description = "IPython Kernel for Jupyter"
 category = "main"
 optional = true
-python-versions = ">=3.5"
+python-versions = ">=3.7"
 
 [package.dependencies]
 appnope = {version = "*", markers = "platform_system == \"Darwin\""}
-ipython = ">=5.0.0"
-jupyter-client = "*"
-tornado = ">=4.2"
-traitlets = ">=4.1.0"
+debugpy = ">=1.0.0,<2.0"
+ipython = ">=7.23.1,<8.0"
+ipython-genutils = "*"
+jupyter-client = "<8.0"
+matplotlib-inline = ">=0.1.0,<0.2.0"
+tornado = ">=4.2,<7.0"
+traitlets = ">=4.1.0,<6.0"
 
 [package.extras]
-test = ["pytest (!=5.3.4)", "pytest-cov", "flaky", "nose", "jedi (<=0.17.2)"]
+test = ["pytest (!=5.3.4)", "pytest-cov", "flaky", "nose", "ipyparallel"]
 
 [[package]]
 name = "ipython"
-version = "7.20.0"
+version = "7.27.0"
 description = "IPython: Productive Interactive Computing"
 category = "main"
 optional = true
@@ -735,6 +781,7 @@ backcall = "*"
 colorama = {version = "*", markers = "sys_platform == \"win32\""}
 decorator = "*"
 jedi = ">=0.16"
+matplotlib-inline = "*"
 pexpect = {version = ">4.3", markers = "sys_platform != \"win32\""}
 pickleshare = "*"
 prompt-toolkit = ">=2.0.0,<3.0.0 || >3.0.0,<3.0.1 || >3.0.1,<3.1.0"
@@ -742,7 +789,7 @@ pygments = "*"
 traitlets = ">=4.2"
 
 [package.extras]
-all = ["Sphinx (>=1.3)", "ipykernel", "ipyparallel", "ipywidgets", "nbconvert", "nbformat", "nose (>=0.10.1)", "notebook", "numpy (>=1.14)", "pygments", "qtconsole", "requests", "testpath"]
+all = ["Sphinx (>=1.3)", "ipykernel", "ipyparallel", "ipywidgets", "nbconvert", "nbformat", "nose (>=0.10.1)", "notebook", "numpy (>=1.17)", "pygments", "qtconsole", "requests", "testpath"]
 doc = ["Sphinx (>=1.3)"]
 kernel = ["ipykernel"]
 nbconvert = ["nbconvert"]
@@ -750,7 +797,7 @@ nbformat = ["nbformat"]
 notebook = ["notebook", "ipywidgets"]
 parallel = ["ipyparallel"]
 qtconsole = ["qtconsole"]
-test = ["nose (>=0.10.1)", "requests", "testpath", "pygments", "nbformat", "ipykernel", "numpy (>=1.14)"]
+test = ["nose (>=0.10.1)", "requests", "testpath", "pygments", "nbformat", "ipykernel", "numpy (>=1.17)"]
 
 [[package]]
 name = "ipython-genutils"
@@ -794,21 +841,21 @@ testing = ["Django (<3.1)", "colorama", "docopt", "pytest (<6.0.0)"]
 
 [[package]]
 name = "jinja2"
-version = "2.11.3"
+version = "3.0.1"
 description = "A very fast and expressive template engine."
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = ">=3.6"
 
 [package.dependencies]
-MarkupSafe = ">=0.23"
+MarkupSafe = ">=2.0"
 
 [package.extras]
-i18n = ["Babel (>=0.8)"]
+i18n = ["Babel (>=2.7)"]
 
 [[package]]
 name = "json5"
-version = "0.9.5"
+version = "0.9.6"
 description = "A Python implementation of the JSON5 data format."
 category = "main"
 optional = true
@@ -836,22 +883,24 @@ format_nongpl = ["idna", "jsonpointer (>1.13)", "webcolors", "rfc3986-validator
 
 [[package]]
 name = "jupyter-client"
-version = "6.1.11"
+version = "7.0.2"
 description = "Jupyter protocol implementation and client libraries"
 category = "main"
 optional = true
-python-versions = ">=3.5"
+python-versions = ">=3.6.1"
 
 [package.dependencies]
+entrypoints = "*"
 jupyter-core = ">=4.6.0"
+nest-asyncio = ">=1.5"
 python-dateutil = ">=2.1"
 pyzmq = ">=13"
 tornado = ">=4.1"
 traitlets = "*"
 
 [package.extras]
-doc = ["sphinx (>=1.3.6)", "sphinx-rtd-theme", "sphinxcontrib-github-alt"]
-test = ["jedi (<=0.17.2)", "ipykernel", "ipython", "mock", "pytest", "pytest-asyncio", "async-generator", "pytest-timeout"]
+doc = ["myst-parser", "sphinx (>=1.3.6)", "sphinx-rtd-theme", "sphinxcontrib-github-alt"]
+test = ["codecov", "coverage", "ipykernel", "ipython", "mock", "mypy", "pre-commit", "pytest", "pytest-asyncio", "pytest-cov", "pytest-timeout", "jedi (<0.18)"]
 
 [[package]]
 name = "jupyter-core"
@@ -867,7 +916,7 @@ traitlets = "*"
 
 [[package]]
 name = "jupyterlab"
-version = "2.2.9"
+version = "2.3.2"
 description = "The JupyterLab notebook server extension."
 category = "main"
 optional = true
@@ -914,15 +963,15 @@ test = ["pytest", "requests"]
 
 [[package]]
 name = "kiwisolver"
-version = "1.3.1"
+version = "1.3.2"
 description = "A fast implementation of the Cassowary constraint solver"
 category = "main"
 optional = false
-python-versions = ">=3.6"
+python-versions = ">=3.7"
 
 [[package]]
 name = "mako"
-version = "1.1.4"
+version = "1.1.5"
 description = "A super-fast templating language that borrows the  best ideas from the existing templating languages."
 category = "main"
 optional = false
@@ -937,27 +986,38 @@ lingua = ["lingua"]
 
 [[package]]
 name = "markupsafe"
-version = "1.1.1"
+version = "2.0.1"
 description = "Safely add untrusted strings to HTML/XML markup."
 category = "main"
 optional = false
-python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*"
-
-[[package]]
-name = "matplotlib"
-version = "3.3.4"
-description = "Python plotting package"
-category = "main"
-optional = false
 python-versions = ">=3.6"
 
+[[package]]
+name = "matplotlib"
+version = "3.4.3"
+description = "Python plotting package"
+category = "main"
+optional = false
+python-versions = ">=3.7"
+
 [package.dependencies]
 cycler = ">=0.10"
 kiwisolver = ">=1.0.1"
-numpy = ">=1.15"
+numpy = ">=1.16"
 pillow = ">=6.2.0"
-pyparsing = ">=2.0.3,<2.0.4 || >2.0.4,<2.1.2 || >2.1.2,<2.1.6 || >2.1.6"
-python-dateutil = ">=2.1"
+pyparsing = ">=2.2.1"
+python-dateutil = ">=2.7"
+
+[[package]]
+name = "matplotlib-inline"
+version = "0.1.3"
+description = "Inline Matplotlib backend for Jupyter"
+category = "main"
+optional = true
+python-versions = ">=3.5"
+
+[package.dependencies]
+traitlets = "*"
 
 [[package]]
 name = "mccabe"
@@ -1012,14 +1072,13 @@ ipython = "*"
 
 [[package]]
 name = "nbclient"
-version = "0.5.1"
+version = "0.5.4"
 description = "A client library for executing notebooks. Formerly nbconvert's ExecutePreprocessor."
 category = "main"
 optional = true
-python-versions = ">=3.6"
+python-versions = ">=3.6.1"
 
 [package.dependencies]
-async-generator = "*"
 jupyter-client = ">=6.1.5"
 nbformat = ">=5.0"
 nest-asyncio = "*"
@@ -1032,11 +1091,11 @@ test = ["codecov", "coverage", "ipython", "ipykernel", "ipywidgets", "pytest (>=
 
 [[package]]
 name = "nbconvert"
-version = "6.0.7"
+version = "6.1.0"
 description = "Converting Jupyter Notebooks"
 category = "main"
 optional = true
-python-versions = ">=3.6"
+python-versions = ">=3.7"
 
 [package.dependencies]
 bleach = "*"
@@ -1051,7 +1110,7 @@ nbformat = ">=4.4"
 pandocfilters = ">=1.4.1"
 pygments = ">=2.4.1"
 testpath = "*"
-traitlets = ">=4.2"
+traitlets = ">=5.0"
 
 [package.extras]
 all = ["pytest", "pytest-cov", "pytest-dependency", "ipykernel", "ipywidgets (>=7)", "pyppeteer (==0.2.2)", "tornado (>=4.0)", "sphinx (>=1.5.1)", "sphinx-rtd-theme", "nbsphinx (>=0.2.12)", "ipython"]
@@ -1062,7 +1121,7 @@ webpdf = ["pyppeteer (==0.2.2)"]
 
 [[package]]
 name = "nbformat"
-version = "5.1.2"
+version = "5.1.3"
 description = "The Jupyter Notebook format"
 category = "main"
 optional = true
@@ -1088,7 +1147,7 @@ python-versions = ">=3.5"
 
 [[package]]
 name = "nodeenv"
-version = "1.5.0"
+version = "1.6.0"
 description = "Node.js virtual environment builder"
 category = "dev"
 optional = false
@@ -1096,11 +1155,11 @@ python-versions = "*"
 
 [[package]]
 name = "notebook"
-version = "6.2.0"
+version = "6.4.3"
 description = "A web-based notebook environment for interactive computing"
 category = "main"
 optional = true
-python-versions = ">=3.5"
+python-versions = ">=3.6"
 
 [package.dependencies]
 argon2-cffi = "*"
@@ -1119,7 +1178,7 @@ tornado = ">=6.1"
 traitlets = ">=4.2.1"
 
 [package.extras]
-docs = ["sphinx", "nbsphinx", "sphinxcontrib-github-alt", "sphinx-rtd-theme"]
+docs = ["sphinx", "nbsphinx", "sphinxcontrib-github-alt", "sphinx-rtd-theme", "myst-parser"]
 json-logging = ["json-logging"]
 test = ["pytest", "coverage", "requests", "nbval", "selenium", "pytest-cov", "requests-unixsocket"]
 
@@ -1142,12 +1201,20 @@ tox_to_nox = ["jinja2", "tox"]
 
 [[package]]
 name = "numpy"
-version = "1.20.0"
+version = "1.21.1"
 description = "NumPy is the fundamental package for array computing with Python."
 category = "main"
 optional = false
 python-versions = ">=3.7"
 
+[[package]]
+name = "ordered-set"
+version = "4.0.2"
+description = "A set that remembers its order, and allows looking up its items by their index in that order."
+category = "main"
+optional = false
+python-versions = ">=3.5"
+
 [[package]]
 name = "packaging"
 version = "20.9"
@@ -1161,19 +1228,19 @@ pyparsing = ">=2.0.2"
 
 [[package]]
 name = "pandas"
-version = "1.2.1"
+version = "1.3.2"
 description = "Powerful data structures for data analysis, time series, and statistics"
 category = "main"
 optional = false
 python-versions = ">=3.7.1"
 
 [package.dependencies]
-numpy = ">=1.16.5"
+numpy = ">=1.17.3"
 python-dateutil = ">=2.7.3"
 pytz = ">=2017.3"
 
 [package.extras]
-test = ["pytest (>=5.0.1)", "pytest-xdist", "hypothesis (>=3.58)"]
+test = ["hypothesis (>=3.58)", "pytest (>=6.0)", "pytest-xdist"]
 
 [[package]]
 name = "pandocfilters"
@@ -1185,7 +1252,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "parso"
-version = "0.8.1"
+version = "0.8.2"
 description = "A Python Parser"
 category = "main"
 optional = true
@@ -1197,11 +1264,11 @@ testing = ["docopt", "pytest (<6.0.0)"]
 
 [[package]]
 name = "pathspec"
-version = "0.8.1"
+version = "0.9.0"
 description = "Utility library for gitignore style pattern matching of file paths."
 category = "dev"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
 
 [[package]]
 name = "patsy"
@@ -1217,7 +1284,7 @@ six = "*"
 
 [[package]]
 name = "pbr"
-version = "5.5.1"
+version = "5.6.0"
 description = "Python Build Reasonableness"
 category = "dev"
 optional = false
@@ -1255,26 +1322,39 @@ python-versions = "*"
 
 [[package]]
 name = "pillow"
-version = "8.1.0"
+version = "8.3.2"
 description = "Python Imaging Library (Fork)"
 category = "main"
 optional = false
 python-versions = ">=3.6"
 
+[[package]]
+name = "platformdirs"
+version = "2.3.0"
+description = "A small Python module for determining appropriate platform-specific dirs, e.g. a \"user data dir\"."
+category = "dev"
+optional = false
+python-versions = ">=3.6"
+
+[package.extras]
+docs = ["Sphinx (>=4)", "furo (>=2021.7.5b38)", "proselint (>=0.10.2)", "sphinx-autodoc-typehints (>=1.12)"]
+test = ["appdirs (==1.4.4)", "pytest (>=6)", "pytest-cov (>=2.7)", "pytest-mock (>=3.6)"]
+
 [[package]]
 name = "pluggy"
-version = "0.13.1"
+version = "1.0.0"
 description = "plugin and hook calling mechanisms for python"
 category = "dev"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+python-versions = ">=3.6"
 
 [package.extras]
 dev = ["pre-commit", "tox"]
+testing = ["pytest", "pytest-benchmark"]
 
 [[package]]
 name = "pre-commit"
-version = "2.10.0"
+version = "2.15.0"
 description = "A framework for managing and maintaining multi-language pre-commit hooks."
 category = "dev"
 optional = false
@@ -1290,33 +1370,33 @@ virtualenv = ">=20.0.8"
 
 [[package]]
 name = "prometheus-client"
-version = "0.9.0"
+version = "0.11.0"
 description = "Python client for the Prometheus monitoring system."
 category = "main"
 optional = true
-python-versions = "*"
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [package.extras]
 twisted = ["twisted"]
 
 [[package]]
 name = "prompt-toolkit"
-version = "3.0.14"
+version = "3.0.20"
 description = "Library for building powerful interactive command lines in Python"
 category = "main"
 optional = true
-python-versions = ">=3.6.1"
+python-versions = ">=3.6.2"
 
 [package.dependencies]
 wcwidth = "*"
 
 [[package]]
 name = "psycopg2"
-version = "2.8.6"
+version = "2.9.1"
 description = "psycopg2 - Python-PostgreSQL Database Adapter"
 category = "main"
 optional = false
-python-versions = ">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*"
+python-versions = ">=3.6"
 
 [[package]]
 name = "ptyprocess"
@@ -1336,7 +1416,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "pycodestyle"
-version = "2.6.0"
+version = "2.7.0"
 description = "Python style guide checker"
 category = "dev"
 optional = false
@@ -1352,18 +1432,21 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "pydocstyle"
-version = "5.1.1"
+version = "6.1.1"
 description = "Python docstring style checker"
 category = "dev"
 optional = false
-python-versions = ">=3.5"
+python-versions = ">=3.6"
 
 [package.dependencies]
 snowballstemmer = "*"
 
+[package.extras]
+toml = ["toml"]
+
 [[package]]
 name = "pyflakes"
-version = "2.2.0"
+version = "2.3.1"
 description = "passive checker of Python programs"
 category = "dev"
 optional = false
@@ -1371,7 +1454,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [[package]]
 name = "pygments"
-version = "2.7.4"
+version = "2.10.0"
 description = "Pygments is a syntax highlighting package written in Python."
 category = "main"
 optional = false
@@ -1387,15 +1470,15 @@ python-versions = ">=2.6, !=3.0.*, !=3.1.*, !=3.2.*"
 
 [[package]]
 name = "pyrsistent"
-version = "0.17.3"
+version = "0.18.0"
 description = "Persistent/Functional/Immutable data structures"
 category = "main"
 optional = true
-python-versions = ">=3.5"
+python-versions = ">=3.6"
 
 [[package]]
 name = "pytest"
-version = "6.2.2"
+version = "6.2.5"
 description = "pytest: simple powerful testing with Python"
 category = "dev"
 optional = false
@@ -1407,7 +1490,7 @@ attrs = ">=19.2.0"
 colorama = {version = "*", markers = "sys_platform == \"win32\""}
 iniconfig = "*"
 packaging = "*"
-pluggy = ">=0.12,<1.0.0a1"
+pluggy = ">=0.12,<2.0"
 py = ">=1.8.2"
 toml = "*"
 
@@ -1416,7 +1499,7 @@ testing = ["argcomplete", "hypothesis (>=3.56)", "mock", "nose", "requests", "xm
 
 [[package]]
 name = "pytest-cov"
-version = "2.11.1"
+version = "2.12.1"
 description = "Pytest plugin for measuring coverage."
 category = "dev"
 optional = false
@@ -1425,9 +1508,10 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 [package.dependencies]
 coverage = ">=5.2.1"
 pytest = ">=4.6"
+toml = "*"
 
 [package.extras]
-testing = ["fields", "hunter", "process-tests (==2.0.2)", "six", "pytest-xdist", "virtualenv"]
+testing = ["fields", "hunter", "process-tests", "six", "pytest-xdist", "virtualenv"]
 
 [[package]]
 name = "pytest-env"
@@ -1442,11 +1526,11 @@ pytest = ">=2.6.0"
 
 [[package]]
 name = "pytest-mock"
-version = "3.5.1"
+version = "3.6.1"
 description = "Thin-wrapper around the mock package for easier use with pytest"
 category = "dev"
 optional = false
-python-versions = ">=3.5"
+python-versions = ">=3.6"
 
 [package.dependencies]
 pytest = ">=5.0"
@@ -1454,20 +1538,9 @@ pytest = ">=5.0"
 [package.extras]
 dev = ["pre-commit", "tox", "pytest-asyncio"]
 
-[[package]]
-name = "pytest-randomly"
-version = "3.5.0"
-description = "Pytest plugin to randomly order tests and control random.seed."
-category = "dev"
-optional = false
-python-versions = ">=3.5"
-
-[package.dependencies]
-pytest = "*"
-
 [[package]]
 name = "python-dateutil"
-version = "2.8.1"
+version = "2.8.2"
 description = "Extensions to the standard Python datetime module"
 category = "main"
 optional = false
@@ -1476,14 +1549,6 @@ python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,>=2.7"
 [package.dependencies]
 six = ">=1.5"
 
-[[package]]
-name = "python-editor"
-version = "1.0.4"
-description = "Programmatically open an editor, capture the result."
-category = "main"
-optional = false
-python-versions = "*"
-
 [[package]]
 name = "pytz"
 version = "2020.5"
@@ -1494,7 +1559,7 @@ python-versions = "*"
 
 [[package]]
 name = "pywin32"
-version = "300"
+version = "301"
 description = "Python for Window Extensions"
 category = "main"
 optional = true
@@ -1502,11 +1567,11 @@ python-versions = "*"
 
 [[package]]
 name = "pywinpty"
-version = "0.5.7"
-description = "Python bindings for the winpty library"
+version = "1.1.4"
+description = "Pseudo terminal support for Windows from Python."
 category = "main"
 optional = true
-python-versions = "*"
+python-versions = ">=3.6"
 
 [[package]]
 name = "pyyaml"
@@ -1518,7 +1583,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*"
 
 [[package]]
 name = "pyzmq"
-version = "22.0.2"
+version = "22.2.1"
 description = "Python bindings for 0MQ"
 category = "main"
 optional = true
@@ -1530,7 +1595,7 @@ py = {version = "*", markers = "implementation_name == \"pypy\""}
 
 [[package]]
 name = "regex"
-version = "2020.11.13"
+version = "2021.8.28"
 description = "Alternative regular expression module, to replace re."
 category = "dev"
 optional = false
@@ -1538,21 +1603,21 @@ python-versions = "*"
 
 [[package]]
 name = "requests"
-version = "2.25.1"
+version = "2.26.0"
 description = "Python HTTP for Humans."
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*"
 
 [package.dependencies]
 certifi = ">=2017.4.17"
-chardet = ">=3.0.2,<5"
-idna = ">=2.5,<3"
+charset-normalizer = {version = ">=2.0.0,<2.1.0", markers = "python_version >= \"3\""}
+idna = {version = ">=2.5,<4", markers = "python_version >= \"3\""}
 urllib3 = ">=1.21.1,<1.27"
 
 [package.extras]
-security = ["pyOpenSSL (>=0.14)", "cryptography (>=1.3.4)"]
 socks = ["PySocks (>=1.5.6,!=1.5.7)", "win-inet-pton"]
+use_chardet_on_py3 = ["chardet (>=3.0.2,<5)"]
 
 [[package]]
 name = "restructuredtext-lint"
@@ -1567,7 +1632,7 @@ docutils = ">=0.11,<1.0"
 
 [[package]]
 name = "rpy2"
-version = "3.4.2"
+version = "3.4.5"
 description = "Python interface to the R language (embedded R)"
 category = "main"
 optional = false
@@ -1580,14 +1645,14 @@ pytz = "*"
 tzlocal = "*"
 
 [package.extras]
-all = ["pandas", "numpy", "pytest"]
+all = ["numpy", "pandas", "pytest"]
 numpy = ["pandas"]
 pandas = ["numpy", "pandas"]
 test = ["pytest"]
 
 [[package]]
 name = "scipy"
-version = "1.6.0"
+version = "1.6.1"
 description = "SciPy: Scientific Library for Python"
 category = "main"
 optional = false
@@ -1598,12 +1663,17 @@ numpy = ">=1.16.5"
 
 [[package]]
 name = "send2trash"
-version = "1.5.0"
+version = "1.8.0"
 description = "Send file to trash natively under Mac OS X, Windows and Linux."
 category = "main"
 optional = true
 python-versions = "*"
 
+[package.extras]
+nativelib = ["pyobjc-framework-cocoa", "pywin32"]
+objc = ["pyobjc-framework-cocoa"]
+win32 = ["pywin32"]
+
 [[package]]
 name = "shapely"
 version = "1.7.1"
@@ -1619,7 +1689,7 @@ vectorized = ["numpy"]
 
 [[package]]
 name = "six"
-version = "1.15.0"
+version = "1.16.0"
 description = "Python 2 and 3 compatibility utilities"
 category = "main"
 optional = false
@@ -1627,11 +1697,11 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*"
 
 [[package]]
 name = "smmap"
-version = "3.0.5"
+version = "4.0.0"
 description = "A pure Python implementation of a sliding window memory map manager"
 category = "dev"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+python-versions = ">=3.5"
 
 [[package]]
 name = "snowballstemmer"
@@ -1643,7 +1713,7 @@ python-versions = "*"
 
 [[package]]
 name = "sphinx"
-version = "3.4.3"
+version = "3.5.4"
 description = "Python documentation generator"
 category = "dev"
 optional = false
@@ -1653,7 +1723,7 @@ python-versions = ">=3.5"
 alabaster = ">=0.7,<0.8"
 babel = ">=1.3"
 colorama = {version = ">=0.3.5", markers = "sys_platform == \"win32\""}
-docutils = ">=0.12"
+docutils = ">=0.12,<0.17"
 imagesize = "*"
 Jinja2 = ">=2.3"
 packaging = "*"
@@ -1669,16 +1739,16 @@ sphinxcontrib-serializinghtml = "*"
 
 [package.extras]
 docs = ["sphinxcontrib-websupport"]
-lint = ["flake8 (>=3.5.0)", "isort", "mypy (>=0.790)", "docutils-stubs"]
+lint = ["flake8 (>=3.5.0)", "isort", "mypy (>=0.800)", "docutils-stubs"]
 test = ["pytest", "pytest-cov", "html5lib", "cython", "typed-ast"]
 
 [[package]]
 name = "sphinx-autodoc-typehints"
-version = "1.11.1"
+version = "1.12.0"
 description = "Type hints (PEP 484) support for the Sphinx autodoc extension"
 category = "dev"
 optional = false
-python-versions = ">=3.5.2"
+python-versions = ">=3.6"
 
 [package.dependencies]
 Sphinx = ">=3.0"
@@ -1713,11 +1783,11 @@ test = ["pytest"]
 
 [[package]]
 name = "sphinxcontrib-htmlhelp"
-version = "1.0.3"
+version = "2.0.0"
 description = "sphinxcontrib-htmlhelp is a sphinx extension which renders HTML help files"
 category = "dev"
 optional = false
-python-versions = ">=3.5"
+python-versions = ">=3.6"
 
 [package.extras]
 lint = ["flake8", "mypy", "docutils-stubs"]
@@ -1748,7 +1818,7 @@ test = ["pytest"]
 
 [[package]]
 name = "sphinxcontrib-serializinghtml"
-version = "1.1.4"
+version = "1.1.5"
 description = "sphinxcontrib-serializinghtml is a sphinx extension which outputs \"serialized\" HTML files (json and pickle)."
 category = "dev"
 optional = false
@@ -1760,23 +1830,34 @@ test = ["pytest"]
 
 [[package]]
 name = "sqlalchemy"
-version = "1.3.23"
+version = "1.4.23"
 description = "Database Abstraction Library"
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,!=3.5.*,>=2.7"
+
+[package.dependencies]
+greenlet = {version = "!=0.4.17", markers = "python_version >= \"3\" and platform_machine in \"x86_64 X86_64 aarch64 AARCH64 ppc64le PPC64LE amd64 AMD64 win32 WIN32\""}
 
 [package.extras]
+aiomysql = ["greenlet (!=0.4.17)", "aiomysql"]
+aiosqlite = ["greenlet (!=0.4.17)", "aiosqlite"]
+asyncio = ["greenlet (!=0.4.17)"]
+mariadb_connector = ["mariadb (>=1.0.1)"]
 mssql = ["pyodbc"]
 mssql_pymssql = ["pymssql"]
 mssql_pyodbc = ["pyodbc"]
-mysql = ["mysqlclient"]
-oracle = ["cx-oracle"]
-postgresql = ["psycopg2"]
-postgresql_pg8000 = ["pg8000 (<1.16.6)"]
+mypy = ["sqlalchemy2-stubs", "mypy (>=0.910)"]
+mysql = ["mysqlclient (>=1.4.0,<2)", "mysqlclient (>=1.4.0)"]
+mysql_connector = ["mysqlconnector"]
+oracle = ["cx_oracle (>=7,<8)", "cx_oracle (>=7)"]
+postgresql = ["psycopg2 (>=2.7)"]
+postgresql_asyncpg = ["greenlet (!=0.4.17)", "asyncpg"]
+postgresql_pg8000 = ["pg8000 (>=1.16.6)"]
 postgresql_psycopg2binary = ["psycopg2-binary"]
 postgresql_psycopg2cffi = ["psycopg2cffi"]
 pymysql = ["pymysql (<1)", "pymysql"]
+sqlcipher = ["sqlcipher3-binary"]
 
 [[package]]
 name = "statsmodels"
@@ -1799,7 +1880,7 @@ docs = ["sphinx", "nbconvert", "jupyter-client", "ipykernel", "matplotlib", "nbf
 
 [[package]]
 name = "stevedore"
-version = "3.3.0"
+version = "3.4.0"
 description = "Manage dynamic plugins for Python applications"
 category = "dev"
 optional = false
@@ -1810,7 +1891,7 @@ pbr = ">=2.0.0,<2.1.0 || >2.1.0"
 
 [[package]]
 name = "terminado"
-version = "0.9.2"
+version = "0.12.1"
 description = "Tornado websocket backend for the Xterm.js Javascript terminal emulator library."
 category = "main"
 optional = true
@@ -1818,12 +1899,15 @@ python-versions = ">=3.6"
 
 [package.dependencies]
 ptyprocess = {version = "*", markers = "os_name != \"nt\""}
-pywinpty = {version = ">=0.5", markers = "os_name == \"nt\""}
+pywinpty = {version = ">=1.1.0", markers = "os_name == \"nt\""}
 tornado = ">=4"
 
+[package.extras]
+test = ["pytest"]
+
 [[package]]
 name = "testfixtures"
-version = "6.17.1"
+version = "6.18.1"
 description = "A collection of helpers and mock objects for unit tests and doc tests."
 category = "dev"
 optional = false
@@ -1836,14 +1920,14 @@ test = ["pytest (>=3.6)", "pytest-cov", "pytest-django", "zope.component", "sybi
 
 [[package]]
 name = "testpath"
-version = "0.4.4"
+version = "0.5.0"
 description = "Test utilities for code working with files and commands"
 category = "main"
 optional = true
-python-versions = "*"
+python-versions = ">= 3.5"
 
 [package.extras]
-test = ["pathlib2"]
+test = ["pytest", "pathlib2"]
 
 [[package]]
 name = "text-unidecode"
@@ -1871,21 +1955,18 @@ python-versions = ">= 3.5"
 
 [[package]]
 name = "traitlets"
-version = "5.0.5"
+version = "5.1.0"
 description = "Traitlets Python configuration system"
 category = "main"
 optional = true
 python-versions = ">=3.7"
 
-[package.dependencies]
-ipython-genutils = "*"
-
 [package.extras]
 test = ["pytest"]
 
 [[package]]
 name = "typed-ast"
-version = "1.4.2"
+version = "1.4.3"
 description = "a fork of Python 2 and 3 ast modules with type comment support"
 category = "dev"
 optional = false
@@ -1893,26 +1974,38 @@ python-versions = "*"
 
 [[package]]
 name = "typing-extensions"
-version = "3.7.4.3"
+version = "3.10.0.2"
 description = "Backported and Experimental Type Hints for Python 3.5+"
 category = "dev"
 optional = false
 python-versions = "*"
 
+[[package]]
+name = "tzdata"
+version = "2021.1"
+description = "Provider of IANA time zone data"
+category = "main"
+optional = false
+python-versions = ">=2"
+
 [[package]]
 name = "tzlocal"
-version = "2.1"
+version = "3.0"
 description = "tzinfo object for the local timezone"
 category = "main"
 optional = false
-python-versions = "*"
+python-versions = ">=3.6"
 
 [package.dependencies]
-pytz = "*"
+"backports.zoneinfo" = {version = "*", markers = "python_version < \"3.9\""}
+tzdata = {version = "*", markers = "platform_system == \"Windows\""}
+
+[package.extras]
+test = ["pytest-mock (>=3.3)", "pytest (>=4.3)"]
 
 [[package]]
 name = "urllib3"
-version = "1.26.3"
+version = "1.26.6"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 category = "main"
 optional = false
@@ -1933,21 +2026,22 @@ python-versions = "*"
 
 [[package]]
 name = "virtualenv"
-version = "20.4.2"
+version = "20.7.2"
 description = "Virtual Python Environment builder"
 category = "dev"
 optional = false
-python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
+python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
 
 [package.dependencies]
-appdirs = ">=1.4.3,<2"
+"backports.entry-points-selectable" = ">=1.0.4"
 distlib = ">=0.3.1,<1"
 filelock = ">=3.0.0,<4"
+platformdirs = ">=2,<3"
 six = ">=1.9.0,<2"
 
 [package.extras]
 docs = ["proselint (>=0.10.2)", "sphinx (>=3)", "sphinx-argparse (>=0.2.5)", "sphinx-rtd-theme (>=0.4.3)", "towncrier (>=19.9.0rc1)"]
-testing = ["coverage (>=4)", "coverage-enable-subprocess (>=1)", "flaky (>=3)", "pytest (>=4)", "pytest-env (>=0.6.2)", "pytest-freezegun (>=0.4.1)", "pytest-mock (>=2)", "pytest-randomly (>=1)", "pytest-timeout (>=1)", "packaging (>=20.0)", "xonsh (>=0.9.16)"]
+testing = ["coverage (>=4)", "coverage-enable-subprocess (>=1)", "flaky (>=3)", "pytest (>=4)", "pytest-env (>=0.6.2)", "pytest-freezegun (>=0.4.1)", "pytest-mock (>=2)", "pytest-randomly (>=1)", "pytest-timeout (>=1)", "packaging (>=20.0)"]
 
 [[package]]
 name = "wcwidth"
@@ -2012,13 +2106,25 @@ all = ["six", "pytest", "pytest-cov", "codecov", "scikit-build", "cmake", "ninja
 optional = ["pygments", "colorama"]
 tests = ["pytest", "pytest-cov", "codecov", "scikit-build", "cmake", "ninja", "pybind11"]
 
+[[package]]
+name = "zipp"
+version = "3.5.0"
+description = "Backport of pathlib-compatible object wrapper for zip files"
+category = "main"
+optional = false
+python-versions = ">=3.6"
+
+[package.extras]
+docs = ["sphinx", "jaraco.packaging (>=8.2)", "rst.linker (>=1.9)"]
+testing = ["pytest (>=4.6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest-cov", "pytest-enabler (>=1.0.1)", "jaraco.itertools", "func-timeout", "pytest-black (>=0.3.7)", "pytest-mypy"]
+
 [extras]
 research = ["jupyterlab", "nb_black", "numpy", "pytz"]
 
 [metadata]
 lock-version = "1.1"
 python-versions = "^3.8"
-content-hash = "9a2253e699e28998cb3ef8d8dadd8bf15a891c5e0cec4709671afe22159d5d86"
+content-hash = "8fb55f96f74960bcdff195a20747ea93778f33fdf36f392d553e51565d442947"
 
 [metadata.files]
 alabaster = [
@@ -2026,7 +2132,8 @@ alabaster = [
     {file = "alabaster-0.7.12.tar.gz", hash = "sha256:a661d72d58e6ea8a57f7a86e37d86716863ee5e92788398526d58b26a4e4dc02"},
 ]
 alembic = [
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+    {file = "alembic-1.7.1-py3-none-any.whl", hash = "sha256:25f996b7408b11493d6a2d669fd9d2ff8d87883fe7434182bc7669d6caa526ab"},
+    {file = "alembic-1.7.1.tar.gz", hash = "sha256:aea964d3dcc9c205b8759e4e9c1c3935ea3afeee259bffd7ed8414f8085140fb"},
 ]
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@@ -2037,60 +2144,67 @@ appnope = [
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 ]
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+    {file = "argcomplete-1.12.3-py2.py3-none-any.whl", hash = "sha256:291f0beca7fd49ce285d2f10e4c1c77e9460cf823eef2de54df0c0fec88b0d81"},
+    {file = "argcomplete-1.12.3.tar.gz", hash = "sha256:2c7dbffd8c045ea534921e63b0be6fe65e88599990d8dc408ac8c542b72a5445"},
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 virtualenv = [
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-    {file = "virtualenv-20.4.2.tar.gz", hash = "sha256:147b43894e51dd6bba882cf9c282447f780e2251cd35172403745fc381a0a80d"},
+    {file = "virtualenv-20.7.2-py2.py3-none-any.whl", hash = "sha256:e4670891b3a03eb071748c569a87cceaefbf643c5bac46d996c5a45c34aa0f06"},
+    {file = "virtualenv-20.7.2.tar.gz", hash = "sha256:9ef4e8ee4710826e98ff3075c9a4739e2cb1040de6a2a8d35db0055840dc96a0"},
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@@ -3226,3 +3505,7 @@ xdoctest = [
     {file = "xdoctest-0.13.0-py2.py3-none-any.whl", hash = "sha256:de861fd5230a46bd26c054b4981169dd963f813768cb62b62e104e4d2644ac94"},
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 ]
+zipp = [
+    {file = "zipp-3.5.0-py3-none-any.whl", hash = "sha256:957cfda87797e389580cb8b9e3870841ca991e2125350677b2ca83a0e99390a3"},
+    {file = "zipp-3.5.0.tar.gz", hash = "sha256:f5812b1e007e48cff63449a5e9f4e7ebea716b4111f9c4f9a645f91d579bf0c4"},
+]
diff --git a/pyproject.toml b/pyproject.toml
index ac86668..0e301da 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -9,7 +9,7 @@ target-version = ["py38"]
 
 [tool.poetry]
 name = "urban-meal-delivery"
-version = "0.3.0"
+version = "0.4.0"
 
 authors = ["Alexander Hess <alexander@webartifex.biz>"]
 description = "Optimizing an urban meal delivery platform"
@@ -32,7 +32,10 @@ Shapely = "^1.7.1"
 alembic = "^1.4.2"
 click = "^7.1.2"
 folium = "^0.12.1"
+geopy = "^2.1.0"
+googlemaps = "^4.4.2"
 matplotlib = "^3.3.3"
+ordered-set = "^4.0.2"
 pandas = "^1.1.0"
 psycopg2 = "^2.8.5"  # adapter for PostgreSQL
 rpy2 = "^3.4.1"
@@ -69,7 +72,6 @@ isort = "^4.3.21"  # TODO (isort): not ^5.5.4 due to wemake-python-styleguide
 flake8 = "^3.8.3"
 flake8-annotations = "^2.3.0"
 flake8-black = "^0.2.1"
-flake8-expression-complexity = "^0.0.8"
 flake8-pytest-style = "^1.2.2"
 mypy = "^0.782"
 wemake-python-styleguide = "^0.14.1"  # flake8 plug-in
@@ -83,7 +85,6 @@ pytest = "^6.0.1"
 pytest-cov = "^2.10.0"
 pytest-env = "^0.6.2"
 pytest-mock = "^3.5.1"
-pytest-randomly = "^3.5.0"
 xdoctest = { version="^0.13.0", extras=["optional"] }
 
 # Documentation
diff --git a/setup.cfg b/setup.cfg
index 47924d4..e91e277 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -72,8 +72,6 @@ select =
     ANN0, ANN2, ANN3,
     # flake8-black => complain if black would make changes
     BLK1, BLK9,
-    # flake8-expression-complexity => not too many expressions at once
-    ECE001,
     # flake8-pytest-style => enforce a consistent style with pytest
     PT0,
 
@@ -89,6 +87,8 @@ extend-ignore =
     # Comply with black's style.
     # Source: https://github.com/psf/black/blob/master/docs/compatible_configs.md#flake8
     E203, W503, WPS348,
+    # Let's not do `@pytest.mark.no_cover()` instead of `@pytest.mark.no_cover`.
+    PT023,
     # Google's Python Style Guide is not reStructuredText
     # until after being processed by Sphinx Napoleon.
     # Source: https://github.com/peterjc/flake8-rst-docstrings/issues/17
@@ -144,6 +144,9 @@ per-file-ignores =
     src/urban_meal_delivery/console/forecasts.py:
         # The module is not too complex.
         WPS232,
+    src/urban_meal_delivery/db/addresses_addresses.py:
+        # The module does not have too many imports.
+        WPS201,
     src/urban_meal_delivery/db/customers.py:
         # The module is not too complex.
         WPS232,
@@ -200,7 +203,7 @@ max-complexity = 10
 max-local-variables = 8
 
 # Allow more than wemake-python-styleguide's 7 methods per class.
-max-methods = 12
+max-methods = 15
 
 # Comply with black's style.
 # Source: https://github.com/psf/black/blob/master/docs/the_black_code_style.md#line-length
@@ -217,6 +220,7 @@ allowed-domain-names =
     obj,
     param,
     result,
+    results,
     value,
 max-name-length = 40
 # darglint
@@ -265,14 +269,35 @@ single_line_exclusions = typing
 [mypy]
 cache_dir = .cache/mypy
 
+# Check the interior of functions without type annotations.
+check_untyped_defs = true
+
+# Disallow generic types without explicit type parameters.
+disallow_any_generics = true
+
+# Disallow functions with incomplete type annotations.
+disallow_incomplete_defs = true
+
+# Disallow calling functions without type annotations.
+disallow_untyped_calls = true
+
+# Disallow functions without type annotations (or incomplete annotations).
+disallow_untyped_defs = true
+
 [mypy-folium.*]
 ignore_missing_imports = true
+[mypy-geopy.*]
+ignore_missing_imports = true
+[mypy-googlemaps.*]
+ignore_missing_imports = true
 [mypy-matplotlib.*]
 ignore_missing_imports = true
 [mypy-nox.*]
 ignore_missing_imports = true
 [mypy-numpy.*]
 ignore_missing_imports = true
+[mypy-ordered_set.*]
+ignore_missing_imports = true
 [mypy-packaging]
 ignore_missing_imports = true
 [mypy-pandas]
diff --git a/src/urban_meal_delivery/configuration.py b/src/urban_meal_delivery/configuration.py
index e303523..2e4247e 100644
--- a/src/urban_meal_delivery/configuration.py
+++ b/src/urban_meal_delivery/configuration.py
@@ -59,11 +59,13 @@ class Config:
     # Colors for the visualizations ins `folium`.
     RESTAURANT_COLOR = 'red'
     CUSTOMER_COLOR = 'blue'
+    NEUTRAL_COLOR = 'black'
 
     # Implementation-specific settings
     # --------------------------------
 
     DATABASE_URI = os.getenv('DATABASE_URI')
+    GOOGLE_MAPS_API_KEY = os.getenv('GOOGLE_MAPS_API_KEY')
 
     # The PostgreSQL schema that holds the tables with the original data.
     ORIGINAL_SCHEMA = os.getenv('ORIGINAL_SCHEMA') or 'public'
@@ -122,7 +124,7 @@ def make_config(env: str = 'production') -> Config:
     # the warning is only emitted if the code is not run by pytest.
     # We see the bad configuration immediately as all "db" tests fail.
     if config.DATABASE_URI is None and not os.getenv('TESTING'):
-        warnings.warn('Bad configurartion: no DATABASE_URI set in the environment')
+        warnings.warn('Bad configuration: no DATABASE_URI set in the environment')
 
     # Some functionalities require R and some packages installed.
     # To ensure isolation and reproducibility, the projects keeps the R dependencies
diff --git a/src/urban_meal_delivery/console/decorators.py b/src/urban_meal_delivery/console/decorators.py
index ef416dd..74d3714 100644
--- a/src/urban_meal_delivery/console/decorators.py
+++ b/src/urban_meal_delivery/console/decorators.py
@@ -9,10 +9,12 @@ from typing import Any, Callable
 import click
 
 
-def db_revision(rev: str) -> Callable:  # pragma: no cover -> easy to check visually
+def db_revision(
+    rev: str,
+) -> Callable[..., Callable[..., Any]]:  # pragma: no cover -> easy to check visually
     """A decorator ensuring the database is at a given revision."""
 
-    def decorator(func: Callable) -> Callable:
+    def decorator(func: Callable[..., Any]) -> Callable[..., Any]:
         @functools.wraps(func)
         def ensure(*args: Any, **kwargs: Any) -> Any:  # noqa:WPS430
             """Do not execute the `func` if the revision does not match."""
diff --git a/src/urban_meal_delivery/console/forecasts.py b/src/urban_meal_delivery/console/forecasts.py
index fd1f707..5d2a20d 100644
--- a/src/urban_meal_delivery/console/forecasts.py
+++ b/src/urban_meal_delivery/console/forecasts.py
@@ -103,8 +103,8 @@ def tactical_heuristic(  # noqa:C901,WPS213,WPS216,WPS231
         # Important: this check may need to be adapted once further
         # commands are added the make `Forecast`s without the heuristic!
         # Continue with forecasting on the day the last prediction was made ...
-        last_predict_at = (  # noqa:ECE001
-            db.session.query(func.max(db.Forecast.start_at))
+        last_predict_at = (
+            db.session.query(func.max(db.Forecast.start_at))  # noqa:WPS221
             .join(db.Pixel, db.Forecast.pixel_id == db.Pixel.id)
             .join(db.Grid, db.Pixel.grid_id == db.Grid.id)
             .filter(db.Forecast.pixel == pixel)
diff --git a/src/urban_meal_delivery/console/gridify.py b/src/urban_meal_delivery/console/gridify.py
index 3024f14..440a900 100644
--- a/src/urban_meal_delivery/console/gridify.py
+++ b/src/urban_meal_delivery/console/gridify.py
@@ -34,8 +34,9 @@ def gridify() -> None:  # pragma: no cover  note:b1f68d24
 
             click.echo(f' -> created {len(grid.pixels)} pixels')
 
-        # The number of assigned addresses is the same across different `side_length`s.
-        db.session.flush()  # necessary for the query to work
+        # Because the number of assigned addresses is the same across
+        # different `side_length`s, we can take any `grid` from the `city`.
+        grid = db.session.query(db.Grid).filter_by(city=city).first()
         n_assigned = (
             db.session.query(db.AddressPixelAssociation)
             .filter(db.AddressPixelAssociation.grid_id == grid.id)
diff --git a/src/urban_meal_delivery/db/__init__.py b/src/urban_meal_delivery/db/__init__.py
index ecd9fa1..6161657 100644
--- a/src/urban_meal_delivery/db/__init__.py
+++ b/src/urban_meal_delivery/db/__init__.py
@@ -1,6 +1,7 @@
 """Provide the ORM models and a connection to the database."""
 
 from urban_meal_delivery.db.addresses import Address
+from urban_meal_delivery.db.addresses_addresses import Path
 from urban_meal_delivery.db.addresses_pixels import AddressPixelAssociation
 from urban_meal_delivery.db.cities import City
 from urban_meal_delivery.db.connection import connection
diff --git a/src/urban_meal_delivery/db/addresses.py b/src/urban_meal_delivery/db/addresses.py
index 8ce7193..d75f59b 100644
--- a/src/urban_meal_delivery/db/addresses.py
+++ b/src/urban_meal_delivery/db/addresses.py
@@ -2,6 +2,7 @@
 
 from __future__ import annotations
 
+import functools
 from typing import Any
 
 import folium
@@ -10,6 +11,7 @@ from sqlalchemy import orm
 from sqlalchemy.dialects import postgresql
 from sqlalchemy.ext import hybrid
 
+from urban_meal_delivery import config
 from urban_meal_delivery.db import meta
 from urban_meal_delivery.db import utils
 
@@ -70,9 +72,6 @@ class Address(meta.Base):
     )
     pixels = orm.relationship('AddressPixelAssociation', back_populates='address')
 
-    # We do not implement a `.__init__()` method and leave that to SQLAlchemy.
-    # Instead, we use `hasattr()` to check for uninitialized attributes.  grep:b1f68d24
-
     def __repr__(self) -> str:
         """Non-literal text representation."""
         return '<{cls}({street} in {city})>'.format(
@@ -90,7 +89,7 @@ class Address(meta.Base):
         """
         return self.id == self.primary_id
 
-    @property
+    @functools.cached_property
     def location(self) -> utils.Location:
         """The location of the address.
 
@@ -102,10 +101,9 @@ class Address(meta.Base):
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_location'):  # noqa:WPS421  note:b1f68d24
-            self._location = utils.Location(self.latitude, self.longitude)
-            self._location.relate_to(self.city.southwest)
-        return self._location
+        location = utils.Location(self.latitude, self.longitude)
+        location.relate_to(self.city.southwest)
+        return location
 
     @property
     def x(self) -> int:  # noqa=WPS111
@@ -154,7 +152,7 @@ class Address(meta.Base):
             `.city.map` for convenience in interactive usage
         """
         defaults = {
-            'color': 'black',
+            'color': f'{config.NEUTRAL_COLOR}',
             'popup': f'{self.street}, {self.zip_code} {self.city_name}',
         }
         defaults.update(kwargs)
diff --git a/src/urban_meal_delivery/db/addresses_addresses.py b/src/urban_meal_delivery/db/addresses_addresses.py
new file mode 100644
index 0000000..02fd978
--- /dev/null
+++ b/src/urban_meal_delivery/db/addresses_addresses.py
@@ -0,0 +1,316 @@
+"""Model for the `Path` relationship between two `Address` objects."""
+
+from __future__ import annotations
+
+import functools
+import itertools
+import json
+from typing import List
+
+import folium
+import googlemaps as gm
+import ordered_set
+import sqlalchemy as sa
+from geopy import distance as geo_distance
+from sqlalchemy import orm
+from sqlalchemy.dialects import postgresql
+
+from urban_meal_delivery import config
+from urban_meal_delivery import db
+from urban_meal_delivery.db import meta
+from urban_meal_delivery.db import utils
+
+
+class Path(meta.Base):
+    """Path between two `Address` objects.
+
+    Models the path between two `Address` objects, including directions
+    for a `Courier` to get from one `Address` to another.
+
+    As the couriers are on bicycles, we model the paths as
+    a symmetric graph (i.e., same distance in both directions).
+
+    Implements an association pattern between `Address` and `Address`.
+
+    Further info:
+        https://docs.sqlalchemy.org/en/stable/orm/basic_relationships.html#association-object  # noqa:E501
+    """
+
+    __tablename__ = 'addresses_addresses'
+
+    # Columns
+    first_address_id = sa.Column(sa.Integer, primary_key=True)
+    second_address_id = sa.Column(sa.Integer, primary_key=True)
+    city_id = sa.Column(sa.SmallInteger, nullable=False)
+    # Distances are measured in meters.
+    air_distance = sa.Column(sa.Integer, nullable=False)
+    bicycle_distance = sa.Column(sa.Integer, nullable=True)
+    # The duration is measured in seconds.
+    bicycle_duration = sa.Column(sa.Integer, nullable=True)
+    # An array of latitude-longitude pairs approximating a courier's way.
+    _directions = sa.Column('directions', postgresql.JSON, nullable=True)
+
+    # Constraints
+    __table_args__ = (
+        # The two `Address` objects must be in the same `.city`.
+        sa.ForeignKeyConstraint(
+            ['first_address_id', 'city_id'],
+            ['addresses.id', 'addresses.city_id'],
+            onupdate='RESTRICT',
+            ondelete='RESTRICT',
+        ),
+        sa.ForeignKeyConstraint(
+            ['second_address_id', 'city_id'],
+            ['addresses.id', 'addresses.city_id'],
+            onupdate='RESTRICT',
+            ondelete='RESTRICT',
+        ),
+        # Each `Address`-`Address` pair only has one distance.
+        sa.UniqueConstraint('first_address_id', 'second_address_id'),
+        sa.CheckConstraint(
+            'first_address_id < second_address_id',
+            name='distances_are_symmetric_for_bicycles',
+        ),
+        sa.CheckConstraint(
+            '0 <= air_distance AND air_distance < 20000', name='realistic_air_distance',
+        ),
+        sa.CheckConstraint(
+            'bicycle_distance < 25000',  # `.bicycle_distance` may not be negative
+            name='realistic_bicycle_distance',  # due to the constraint below.
+        ),
+        sa.CheckConstraint(
+            'air_distance <= bicycle_distance', name='air_distance_is_shortest',
+        ),
+        sa.CheckConstraint(
+            '0 <= bicycle_duration AND bicycle_duration <= 3600',
+            name='realistic_bicycle_travel_time',
+        ),
+    )
+
+    # Relationships
+    first_address = orm.relationship(
+        'Address', foreign_keys='[Path.first_address_id, Path.city_id]',
+    )
+    second_address = orm.relationship(
+        'Address',
+        foreign_keys='[Path.second_address_id, Path.city_id]',
+        overlaps='first_address',
+    )
+
+    @classmethod
+    def from_addresses(
+        cls, *addresses: db.Address, google_maps: bool = False,
+    ) -> List[Path]:
+        """Calculate pair-wise paths for `Address` objects.
+
+        This is the main constructor method for the class.
+
+        It handles the "sorting" of the `Address` objects by `.id`, which is
+        the logic that enforces the symmetric graph behind the paths.
+
+        Args:
+            *addresses: to calculate the pair-wise paths for;
+                must contain at least two `Address` objects
+            google_maps: if `.bicycle_distance` and `._directions` should be
+                populated with a query to the Google Maps Directions API;
+                by default, only the `.air_distance` is calculated with `geopy`
+
+        Returns:
+            paths
+        """
+        paths = []
+
+        # We consider all 2-tuples of `Address`es. The symmetric graph is ...
+        for first, second in itertools.combinations(addresses, 2):
+            # ... implicitly enforced by a precedence constraint for the `.id`s.
+            first, second = (  # noqa:WPS211
+                (first, second) if first.id < second.id else (second, first)
+            )
+
+            # If there is no `Path` object in the database ...
+            path = (
+                db.session.query(db.Path)
+                .filter(db.Path.first_address == first)
+                .filter(db.Path.second_address == second)
+                .first()
+            )
+            # ... create a new one.
+            if path is None:
+                air_distance = geo_distance.great_circle(
+                    first.location.lat_lng, second.location.lat_lng,
+                )
+
+                path = cls(
+                    first_address=first,
+                    second_address=second,
+                    air_distance=round(air_distance.meters),
+                )
+
+                db.session.add(path)
+                db.session.commit()
+
+            paths.append(path)
+
+        if google_maps:
+            for path in paths:  # noqa:WPS440
+                path.sync_with_google_maps()
+
+        return paths
+
+    @classmethod
+    def from_order(cls, order: db.Order, google_maps: bool = False) -> Path:
+        """Calculate the path for an `Order` object.
+
+        The path goes from the `Order.pickup_address` to the `Order.delivery_address`.
+
+        Args:
+            order: to calculate the path for
+            google_maps: if `.bicycle_distance` and `._directions` should be
+                populated with a query to the Google Maps Directions API;
+                by default, only the `.air_distance` is calculated with `geopy`
+
+        Returns:
+            path
+        """
+        return cls.from_addresses(
+            order.pickup_address, order.delivery_address, google_maps=google_maps,
+        )[0]
+
+    def sync_with_google_maps(self) -> None:
+        """Fill in `.bicycle_distance` and `._directions` with Google Maps.
+
+        `._directions` will NOT contain the coordinates
+        of `.first_address` and `.second_address`.
+
+        This uses the Google Maps Directions API.
+
+        Further info:
+            https://developers.google.com/maps/documentation/directions
+        """
+        # To save costs, we do not make an API call
+        # if we already have data from Google Maps.
+        if self.bicycle_distance is not None:
+            return
+
+        client = gm.Client(config.GOOGLE_MAPS_API_KEY)
+        response = client.directions(
+            origin=self.first_address.location.lat_lng,
+            destination=self.second_address.location.lat_lng,
+            mode='bicycling',
+            alternatives=False,
+        )
+        # Without "alternatives" and "waypoints", the `response` contains
+        # exactly one "route" that consists of exactly one "leg".
+        # Source: https://developers.google.com/maps/documentation/directions/get-directions#Legs  # noqa:E501
+        route = response[0]['legs'][0]
+
+        self.bicycle_distance = route['distance']['value']  # noqa:WPS601
+        self.bicycle_duration = route['duration']['value']  # noqa:WPS601
+
+        # Each route consists of many "steps" that are instructions as to how to
+        # get from A to B. As a step's "start_location" may equal the previous step's
+        # "end_location", we use an `OrderedSet` to find the unique latitude-longitude
+        # pairs that make up the path from `.first_address` to `.second_address`.
+        steps = ordered_set.OrderedSet()
+        for step in route['steps']:
+            steps.add(  # noqa:WPS221
+                (step['start_location']['lat'], step['start_location']['lng']),
+            )
+            steps.add(  # noqa:WPS221
+                (step['end_location']['lat'], step['end_location']['lng']),
+            )
+
+        steps.discard(self.first_address.location.lat_lng)
+        steps.discard(self.second_address.location.lat_lng)
+
+        self._directions = json.dumps(list(steps))  # noqa:WPS601
+
+        db.session.add(self)
+        db.session.commit()
+
+    @property  # pragma: no cover
+    def map(self) -> folium.Map:  # noqa:WPS125
+        """Convenience property to obtain the underlying `City.map`."""
+        return self.first_address.city.map
+
+    @functools.cached_property
+    def waypoints(self) -> List[utils.Location]:
+        """The couriers' route from `.first_address` to `.second_address`.
+
+        The returned `Location`s all relate to `.first_address.city.southwest`.
+
+        Implementation detail: This property is cached as none of the
+        underlying attributes (i.e., `._directions`) are to be changed.
+        """
+        points = [utils.Location(*point) for point in json.loads(self._directions)]
+        for point in points:
+            point.relate_to(self.first_address.city.southwest)
+
+        return points
+
+    def draw(  # noqa:WPS211
+        self,
+        *,
+        reverse: bool = False,
+        start_tooltip: str = 'Start',
+        end_tooltip: str = 'End',
+        start_color: str = 'green',
+        end_color: str = 'red',
+        path_color: str = 'black',
+    ) -> folium.Map:  # pragma: no cover
+        """Draw the `.waypoints` from `.first_address` to `.second_address`.
+
+        Args:
+            reverse: by default, `.first_address` is used as the start;
+                set to `False` to make `.second_address` the start
+            start_tooltip: text shown on marker at the path's start
+            end_tooltip: text shown on marker at the path's end
+            start_color: `folium` color for the path's start
+            end_color: `folium` color for the path's end
+            path_color: `folium` color along the path, which
+                is the line between the `.waypoints`
+
+        Returns:
+            `.map` for convenience in interactive usage
+        """
+        # Without `self._directions` synced from Google Maps,
+        # the `.waypoints` are not available.
+        self.sync_with_google_maps()
+
+        # First, plot the couriers' path between the start and
+        # end locations, so that it is below the `folium.Circle`s.
+        line = folium.PolyLine(
+            locations=(
+                self.first_address.location.lat_lng,
+                *(point.lat_lng for point in self.waypoints),
+                self.second_address.location.lat_lng,
+            ),
+            color=path_color,
+            weight=2,
+        )
+        line.add_to(self.map)
+
+        # Draw the path's start and end locations, possibly reversed,
+        # on top of the couriers' path.
+
+        if reverse:
+            start, end = self.second_address, self.first_address
+        else:
+            start, end = self.first_address, self.second_address
+
+        start.draw(
+            radius=5,
+            color=start_color,
+            fill_color=start_color,
+            fill_opacity=1,
+            tooltip=start_tooltip,
+        )
+        end.draw(
+            radius=5,
+            color=end_color,
+            fill_color=end_color,
+            fill_opacity=1,
+            tooltip=end_tooltip,
+        )
+
+        return self.map
diff --git a/src/urban_meal_delivery/db/addresses_pixels.py b/src/urban_meal_delivery/db/addresses_pixels.py
index 293bde7..4d5c07b 100644
--- a/src/urban_meal_delivery/db/addresses_pixels.py
+++ b/src/urban_meal_delivery/db/addresses_pixels.py
@@ -10,7 +10,7 @@ class AddressPixelAssociation(meta.Base):
     """Association pattern between `Address` and `Pixel`.
 
     This approach is needed here mainly because it implicitly
-    updates the `_city_id` and `_grid_id` columns.
+    updates the `city_id` and `grid_id` columns.
 
     Further info:
         https://docs.sqlalchemy.org/en/stable/orm/basic_relationships.html#association-object  # noqa:E501
diff --git a/src/urban_meal_delivery/db/cities.py b/src/urban_meal_delivery/db/cities.py
index b6cf4e0..926b3ae 100644
--- a/src/urban_meal_delivery/db/cities.py
+++ b/src/urban_meal_delivery/db/cities.py
@@ -2,6 +2,8 @@
 
 from __future__ import annotations
 
+import functools
+
 import folium
 import sqlalchemy as sa
 from sqlalchemy import orm
@@ -38,51 +40,39 @@ class City(meta.Base):
     addresses = orm.relationship('Address', back_populates='city')
     grids = orm.relationship('Grid', back_populates='city')
 
-    # We do not implement a `.__init__()` method and leave that to SQLAlchemy.
-    # Instead, we use `hasattr()` to check for uninitialized attributes.  grep:d334120e
+    # We do not implement a `.__init__()` method and use SQLAlchemy's default.
+    # The uninitialized attribute `._map` is computed on the fly.  note:d334120ei
 
     def __repr__(self) -> str:
         """Non-literal text representation."""
         return '<{cls}({name})>'.format(cls=self.__class__.__name__, name=self.name)
 
-    @property
+    @functools.cached_property
     def center(self) -> utils.Location:
         """Location of the city's center.
 
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_center'):  # noqa:WPS421  note:d334120e
-            self._center = utils.Location(self.center_latitude, self.center_longitude)
-        return self._center
+        return utils.Location(self.center_latitude, self.center_longitude)
 
-    @property
+    @functools.cached_property
     def northeast(self) -> utils.Location:
         """The city's northeast corner of the Google Maps viewport.
 
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_northeast'):  # noqa:WPS421  note:d334120e
-            self._northeast = utils.Location(
-                self.northeast_latitude, self.northeast_longitude,
-            )
+        return utils.Location(self.northeast_latitude, self.northeast_longitude)
 
-        return self._northeast
-
-    @property
+    @functools.cached_property
     def southwest(self) -> utils.Location:
         """The city's southwest corner of the Google Maps viewport.
 
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_southwest'):  # noqa:WPS421  note:d334120e
-            self._southwest = utils.Location(
-                self.southwest_latitude, self.southwest_longitude,
-            )
-
-        return self._southwest
+        return utils.Location(self.southwest_latitude, self.southwest_longitude)
 
     @property
     def total_x(self) -> int:
@@ -103,16 +93,17 @@ class City(meta.Base):
     def clear_map(self) -> City:  # pragma: no cover
         """Create a new `folium.Map` object aligned with the city's viewport.
 
-        The map is available via the `.map` property. Note that it is a
-        mutable objects that is changed from various locations in the code base.
+        The map is available via the `.map` property. Note that it is mutable
+        and changed from various locations in the code base.
 
         Returns:
             self: enabling method chaining
-        """  # noqa:DAR203
+        """  # noqa:DAR203  note:d334120e
         self._map = folium.Map(
             location=[self.center_latitude, self.center_longitude],
             zoom_start=self.initial_zoom,
         )
+
         return self
 
     @property  # pragma: no cover
@@ -138,7 +129,7 @@ class City(meta.Base):
             `.map` for convenience in interactive usage
         """
         # Obtain all primary `Address`es in the city that host `Restaurant`s.
-        addresses = (  # noqa:ECE001
+        addresses = (
             db.session.query(db.Address)
             .filter(
                 db.Address.id.in_(
@@ -155,7 +146,7 @@ class City(meta.Base):
         for address in addresses:
             # Show the restaurant's name if there is only one.
             # Otherwise, list all the restaurants' ID's.
-            restaurants = (  # noqa:ECE001
+            restaurants = (
                 db.session.query(db.Restaurant)
                 .join(db.Address, db.Restaurant.address_id == db.Address.id)
                 .filter(db.Address.primary_id == address.id)
@@ -170,7 +161,7 @@ class City(meta.Base):
 
             if order_counts:
                 # Calculate the number of orders for ALL restaurants ...
-                n_orders = (  # noqa:ECE001
+                n_orders = (
                     db.session.query(db.Order.id)
                     .join(db.Address, db.Order.pickup_address_id == db.Address.id)
                     .filter(db.Address.primary_id == address.id)
@@ -221,11 +212,11 @@ class City(meta.Base):
                 sa.text(
                     f"""  -- # noqa:S608
                     SELECT DISTINCT
-                        zip_code
+                        {config.CLEAN_SCHEMA}.addresses.zip_code
                     FROM
-                        {config.CLEAN_SCHEMA}.addresses
+                        {config.CLEAN_SCHEMA}.addresses AS addresses
                     WHERE
-                        city_id = {self.id};
+                        {config.CLEAN_SCHEMA}.addresses.city_id = {self.id};
                     """,
                 ),
             )
diff --git a/src/urban_meal_delivery/db/customers.py b/src/urban_meal_delivery/db/customers.py
index f6d59c2..fcbfd58 100644
--- a/src/urban_meal_delivery/db/customers.py
+++ b/src/urban_meal_delivery/db/customers.py
@@ -63,15 +63,18 @@ class Customer(meta.Base):
 
         # Obtain all primary `Address`es where
         # at least one delivery was made to `self`.
-        delivery_addresses = (  # noqa:ECE001
+        delivery_addresses = (
             db.session.query(db.Address)
             .filter(
                 db.Address.id.in_(
-                    db.session.query(db.Address.primary_id)  # noqa:WPS221
-                    .join(db.Order, db.Address.id == db.Order.delivery_address_id)
-                    .filter(db.Order.customer_id == self.id)
-                    .distinct()
-                    .all(),
+                    row.primary_id
+                    for row in (
+                        db.session.query(db.Address.primary_id)  # noqa:WPS221
+                        .join(db.Order, db.Address.id == db.Order.delivery_address_id)
+                        .filter(db.Order.customer_id == self.id)
+                        .distinct()
+                        .all()
+                    )
                 ),
             )
             .all()
@@ -79,7 +82,7 @@ class Customer(meta.Base):
 
         for address in delivery_addresses:
             if order_counts:
-                n_orders = (  # noqa:ECE001
+                n_orders = (
                     db.session.query(db.Order)
                     .join(db.Address, db.Order.delivery_address_id == db.Address.id)
                     .filter(db.Order.customer_id == self.id)
@@ -111,7 +114,7 @@ class Customer(meta.Base):
                 )
 
         if restaurants:
-            pickup_addresses = (  # noqa:ECE001
+            pickup_addresses = (
                 db.session.query(db.Address)
                 .filter(
                     db.Address.id.in_(
@@ -129,7 +132,7 @@ class Customer(meta.Base):
                 # Show the restaurant's name if there is only one.
                 # Otherwise, list all the restaurants' ID's.
                 # We cannot show the `Order.restaurant.name` due to the aggregation.
-                restaurants = (  # noqa:ECE001
+                restaurants = (
                     db.session.query(db.Restaurant)
                     .join(db.Address, db.Restaurant.address_id == db.Address.id)
                     .filter(db.Address.primary_id == address.id)  # noqa:WPS441
@@ -145,7 +148,7 @@ class Customer(meta.Base):
                     )
 
                 if order_counts:
-                    n_orders = (  # noqa:ECE001
+                    n_orders = (
                         db.session.query(db.Order)
                         .join(db.Address, db.Order.pickup_address_id == db.Address.id)
                         .filter(db.Order.customer_id == self.id)
diff --git a/src/urban_meal_delivery/db/forecasts.py b/src/urban_meal_delivery/db/forecasts.py
index a85fa74..79230d9 100644
--- a/src/urban_meal_delivery/db/forecasts.py
+++ b/src/urban_meal_delivery/db/forecasts.py
@@ -31,7 +31,7 @@ class Forecast(meta.Base):
     model = sa.Column(sa.Unicode(length=20), nullable=False)
     # We also store the actual order counts for convenient retrieval.
     # A `UniqueConstraint` below ensures that redundant values that
-    # are to be expected are consistend across rows.
+    # are to be expected are consistent across rows.
     actual = sa.Column(sa.SmallInteger, nullable=False)
     # Raw `.prediction`s are stored as `float`s (possibly negative).
     # The rounding is then done on the fly if required.
@@ -157,7 +157,7 @@ class Forecast(meta.Base):
         Background: The functions in `urban_meal_delivery.forecasts.methods`
         return `pd.Dataframe`s with "start_at" (i.e., `pd.Timestamp` objects)
         values in the index and five columns "prediction", "low80", "high80",
-        "low95", and "high95" with `np.float` values. The `*Model.predic()`
+        "low95", and "high95" with `np.float` values. The `*Model.predict()`
         methods in `urban_meal_delivery.forecasts.models` then add an "actual"
         column. This constructor converts these results into ORM models.
         Also, the `np.float` values are cast as plain `float` ones as
diff --git a/src/urban_meal_delivery/db/grids.py b/src/urban_meal_delivery/db/grids.py
index dac6e48..9212d66 100644
--- a/src/urban_meal_delivery/db/grids.py
+++ b/src/urban_meal_delivery/db/grids.py
@@ -76,7 +76,7 @@ class Grid(meta.Base):
         # `Pixel`s grouped by `.n_x`-`.n_y` coordinates.
         pixels = {}
 
-        pickup_addresses = (  # noqa:ECE:001
+        pickup_addresses = (
             db.session.query(db.Address)
             .join(db.Order, db.Address.id == db.Order.pickup_address_id)
             .filter(db.Address.city == city)
diff --git a/src/urban_meal_delivery/db/orders.py b/src/urban_meal_delivery/db/orders.py
index 0b4550b..1b1341b 100644
--- a/src/urban_meal_delivery/db/orders.py
+++ b/src/urban_meal_delivery/db/orders.py
@@ -2,10 +2,13 @@
 
 import datetime
 
+import folium
 import sqlalchemy as sa
 from sqlalchemy import orm
 from sqlalchemy.dialects import postgresql
 
+from urban_meal_delivery import config
+from urban_meal_delivery import db
 from urban_meal_delivery.db import meta
 
 
@@ -524,3 +527,36 @@ class Order(meta.Base):  # noqa:WPS214
         return '<{cls}(#{order_id})>'.format(
             cls=self.__class__.__name__, order_id=self.id,
         )
+
+    def draw(self) -> folium.Map:  # pragma: no cover
+        """Draw the `.waypoints` from `.pickup_address` to `.delivery_address`.
+
+        Important: Do not put this in an automated script as a method call
+        triggers an API call to the Google Maps API and may result in costs.
+
+        Returns:
+            `...city.map` for convenience in interactive usage
+        """
+        path = db.Path.from_order(self)
+
+        restaurant_tooltip = f'{self.restaurant.name} (#{self.restaurant.id})'
+        customer_tooltip = f'Customer #{self.customer.id}'
+
+        # Because the underlying distance matrix is symmetric (i.e., a DB constraint),
+        # we must check if the `.pickup_address` is the couriers' `Path`'s start.
+        if path.first_address is self.pickup_address:
+            reverse = False
+            start_tooltip, end_tooltip = restaurant_tooltip, customer_tooltip
+        else:
+            reverse = True
+            start_tooltip, end_tooltip = customer_tooltip, restaurant_tooltip
+
+        # This triggers `Path.sync_with_google_maps()` behind the scenes.
+        return path.draw(
+            reverse=reverse,
+            start_tooltip=start_tooltip,
+            end_tooltip=end_tooltip,
+            start_color=config.RESTAURANT_COLOR,
+            end_color=config.CUSTOMER_COLOR,
+            path_color=config.NEUTRAL_COLOR,
+        )
diff --git a/src/urban_meal_delivery/db/pixels.py b/src/urban_meal_delivery/db/pixels.py
index 9461d4d..f063634 100644
--- a/src/urban_meal_delivery/db/pixels.py
+++ b/src/urban_meal_delivery/db/pixels.py
@@ -2,6 +2,7 @@
 
 from __future__ import annotations
 
+import functools
 from typing import List
 
 import folium
@@ -68,66 +69,58 @@ class Pixel(meta.Base):
         """The area of a pixel in square kilometers."""
         return self.grid.pixel_area
 
-    @property
+    @functools.cached_property
     def northeast(self) -> utils.Location:
         """The pixel's northeast corner, relative to `.grid.city.southwest`.
 
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_northeast'):  # noqa:WPS421  note:d334120e
-            # The origin is the southwest corner of the `.grid.city`'s viewport.
-            easting_origin = self.grid.city.southwest.easting
-            northing_origin = self.grid.city.southwest.northing
+        easting, northing = (
+            self.grid.city.southwest.easting + ((self.n_x + 1) * self.side_length),
+            self.grid.city.southwest.northing + ((self.n_y + 1) * self.side_length),
+        )
+        latitude, longitude = utm.to_latlon(
+            easting, northing, *self.grid.city.southwest.zone_details,
+        )
 
-            # `+1` as otherwise we get the pixel's `.southwest` corner.
-            easting = easting_origin + ((self.n_x + 1) * self.side_length)
-            northing = northing_origin + ((self.n_y + 1) * self.side_length)
-            zone, band = self.grid.city.southwest.zone_details
-            latitude, longitude = utm.to_latlon(easting, northing, zone, band)
+        location = utils.Location(latitude, longitude)
+        location.relate_to(self.grid.city.southwest)
 
-            self._northeast = utils.Location(latitude, longitude)
-            self._northeast.relate_to(self.grid.city.southwest)
+        return location
 
-        return self._northeast
-
-    @property
+    @functools.cached_property
     def southwest(self) -> utils.Location:
-        """The pixel's northeast corner, relative to `.grid.city.southwest`.
+        """The pixel's southwest corner, relative to `.grid.city.southwest`.
 
         Implementation detail: This property is cached as none of the
         underlying attributes to calculate the value are to be changed.
         """
-        if not hasattr(self, '_southwest'):  # noqa:WPS421  note:d334120e
-            # The origin is the southwest corner of the `.grid.city`'s viewport.
-            easting_origin = self.grid.city.southwest.easting
-            northing_origin = self.grid.city.southwest.northing
+        easting, northing = (
+            self.grid.city.southwest.easting + (self.n_x * self.side_length),
+            self.grid.city.southwest.northing + (self.n_y * self.side_length),
+        )
+        latitude, longitude = utm.to_latlon(
+            easting, northing, *self.grid.city.southwest.zone_details,
+        )
 
-            easting = easting_origin + (self.n_x * self.side_length)
-            northing = northing_origin + (self.n_y * self.side_length)
-            zone, band = self.grid.city.southwest.zone_details
-            latitude, longitude = utm.to_latlon(easting, northing, zone, band)
+        location = utils.Location(latitude, longitude)
+        location.relate_to(self.grid.city.southwest)
 
-            self._southwest = utils.Location(latitude, longitude)
-            self._southwest.relate_to(self.grid.city.southwest)
+        return location
 
-        return self._southwest
-
-    @property
+    @functools.cached_property
     def restaurants(self) -> List[db.Restaurant]:  # pragma: no cover
         """Obtain all `Restaurant`s in `self`."""
-        if not hasattr(self, '_restaurants'):  # noqa:WPS421  note:d334120e
-            self._restaurants = (  # noqa:ECE001
-                db.session.query(db.Restaurant)
-                .join(
-                    db.AddressPixelAssociation,
-                    db.Restaurant.address_id == db.AddressPixelAssociation.address_id,
-                )
-                .filter(db.AddressPixelAssociation.pixel_id == self.id)
-                .all()
+        return (
+            db.session.query(db.Restaurant)
+            .join(
+                db.AddressPixelAssociation,
+                db.Restaurant.address_id == db.AddressPixelAssociation.address_id,
             )
-
-        return self._restaurants
+            .filter(db.AddressPixelAssociation.pixel_id == self.id)
+            .all()
+        )
 
     def clear_map(self) -> Pixel:  # pragma: no cover
         """Shortcut to the `.city.clear_map()` method.
@@ -182,7 +175,7 @@ class Pixel(meta.Base):
         if restaurants:
             # Obtain all primary `Address`es in the city that host `Restaurant`s
             # and are in the `self` `Pixel`.
-            addresses = (  # noqa:ECE001
+            addresses = (
                 db.session.query(db.Address)
                 .filter(
                     db.Address.id.in_(
@@ -208,7 +201,7 @@ class Pixel(meta.Base):
             for address in addresses:
                 # Show the restaurant's name if there is only one.
                 # Otherwise, list all the restaurants' ID's.
-                restaurants = (  # noqa:ECE001
+                restaurants = (
                     db.session.query(db.Restaurant)
                     .join(db.Address, db.Restaurant.address_id == db.Address.id)
                     .filter(db.Address.primary_id == address.id)
@@ -225,7 +218,7 @@ class Pixel(meta.Base):
 
                 if order_counts:
                     # Calculate the number of orders for ALL restaurants ...
-                    n_orders = (  # noqa:ECE001
+                    n_orders = (
                         db.session.query(db.Order.id)
                         .join(db.Address, db.Order.pickup_address_id == db.Address.id)
                         .filter(db.Address.primary_id == address.id)
diff --git a/src/urban_meal_delivery/db/restaurants.py b/src/urban_meal_delivery/db/restaurants.py
index cf02e53..31df7f8 100644
--- a/src/urban_meal_delivery/db/restaurants.py
+++ b/src/urban_meal_delivery/db/restaurants.py
@@ -45,7 +45,11 @@ class Restaurant(meta.Base):
 
     # Relationships
     address = orm.relationship('Address', back_populates='restaurants')
-    orders = orm.relationship('Order', back_populates='restaurant')
+    orders = orm.relationship(
+        'Order',
+        back_populates='restaurant',
+        overlaps='orders_picked_up,pickup_address',
+    )
 
     def __repr__(self) -> str:
         """Non-literal text representation."""
@@ -83,15 +87,20 @@ class Restaurant(meta.Base):
         if customers:
             # Obtain all primary `Address`es in the city that
             # received at least one delivery from `self`.
-            delivery_addresses = (  # noqa:ECE001
+            delivery_addresses = (
                 db.session.query(db.Address)
                 .filter(
                     db.Address.id.in_(
-                        db.session.query(db.Address.primary_id)  # noqa:WPS221
-                        .join(db.Order, db.Address.id == db.Order.delivery_address_id)
-                        .filter(db.Order.restaurant_id == self.id)
-                        .distinct()
-                        .all(),
+                        row.primary_id
+                        for row in (
+                            db.session.query(db.Address.primary_id)  # noqa:WPS221
+                            .join(
+                                db.Order, db.Address.id == db.Order.delivery_address_id,
+                            )
+                            .filter(db.Order.restaurant_id == self.id)
+                            .distinct()
+                            .all()
+                        )
                     ),
                 )
                 .all()
@@ -99,7 +108,7 @@ class Restaurant(meta.Base):
 
             for address in delivery_addresses:
                 if order_counts:
-                    n_orders = (  # noqa:ECE001
+                    n_orders = (
                         db.session.query(db.Order)
                         .join(db.Address, db.Order.delivery_address_id == db.Address.id)
                         .filter(db.Order.restaurant_id == self.id)
diff --git a/src/urban_meal_delivery/db/utils/locations.py b/src/urban_meal_delivery/db/utils/locations.py
index b6ef41e..77faa8b 100644
--- a/src/urban_meal_delivery/db/utils/locations.py
+++ b/src/urban_meal_delivery/db/utils/locations.py
@@ -7,7 +7,7 @@ from typing import Optional, Tuple
 import utm
 
 
-class Location:
+class Location:  # noqa:WPS214
     """A location represented in WGS84 and UTM coordinates.
 
     WGS84:
@@ -15,7 +15,7 @@ class Location:
         - assumes earth is a sphere and models the location in 3D
 
     UTM:
-        - the Universal Transverse Mercator sytem
+        - the Universal Transverse Mercator system
         - projects WGS84 coordinates onto a 2D map
         - can be used for visualizations and calculations directly
         - distances are in meters
@@ -67,6 +67,11 @@ class Location:
         """
         return self._longitude
 
+    @property
+    def lat_lng(self) -> Tuple[float, float]:
+        """The `.latitude` and `.longitude` as a 2-`tuple`."""
+        return self._latitude, self._longitude
+
     @property
     def easting(self) -> int:
         """The easting of the location in meters (UTM)."""
@@ -85,7 +90,7 @@ class Location:
     @property
     def zone_details(self) -> Tuple[int, str]:
         """The UTM zone of the location as the zone number and the band."""
-        return (self._zone, self._band)
+        return self._zone, self._band
 
     def __eq__(self, other: object) -> bool:
         """Check if two `Location` objects are the same location."""
diff --git a/src/urban_meal_delivery/forecasts/methods/arima.py b/src/urban_meal_delivery/forecasts/methods/arima.py
index 3abd60e..7817851 100644
--- a/src/urban_meal_delivery/forecasts/methods/arima.py
+++ b/src/urban_meal_delivery/forecasts/methods/arima.py
@@ -31,8 +31,8 @@ def predict(
     Raises:
         ValueError: if `training_ts` contains `NaN` values
     """
-    # Initialize R only if necessary as it is tested only in nox's
-    # "ci-tests-slow" session and "ci-tests-fast" should not fail.
+    # Initialize R only if it is actually used.
+    # For example, the nox session "ci-tests-fast" does not use it.
     from urban_meal_delivery import init_r  # noqa:F401,WPS433
 
     # Re-seed R every time it is used to ensure reproducibility.
diff --git a/src/urban_meal_delivery/forecasts/methods/decomposition.py b/src/urban_meal_delivery/forecasts/methods/decomposition.py
index 3be8582..c71f6be 100644
--- a/src/urban_meal_delivery/forecasts/methods/decomposition.py
+++ b/src/urban_meal_delivery/forecasts/methods/decomposition.py
@@ -154,8 +154,8 @@ def stl(  # noqa:C901,WPS210,WPS211,WPS231
     else:
         robust = False
 
-    # Initialize R only if necessary as it is tested only in nox's
-    # "ci-tests-slow" session and "ci-tests-fast" should not fail.
+    # Initialize R only if it is actually used.
+    # For example, the nox session "ci-tests-fast" does not use it.
     from urban_meal_delivery import init_r  # noqa:F401,WPS433
 
     # Re-seed R every time it is used to ensure reproducibility.
diff --git a/src/urban_meal_delivery/forecasts/methods/ets.py b/src/urban_meal_delivery/forecasts/methods/ets.py
index 5b70aef..7da9073 100644
--- a/src/urban_meal_delivery/forecasts/methods/ets.py
+++ b/src/urban_meal_delivery/forecasts/methods/ets.py
@@ -32,8 +32,8 @@ def predict(
     Raises:
         ValueError: if `training_ts` contains `NaN` values
     """
-    # Initialize R only if necessary as it is tested only in nox's
-    # "ci-tests-slow" session and "ci-tests-fast" should not fail.
+    # Initialize R only if it is actually used.
+    # For example, the nox session "ci-tests-fast" does not use it.
     from urban_meal_delivery import init_r  # noqa:F401,WPS433
 
     # Re-seed R every time it is used to ensure reproducibility.
diff --git a/src/urban_meal_delivery/forecasts/models/__init__.py b/src/urban_meal_delivery/forecasts/models/__init__.py
index c5c905f..108c7ce 100644
--- a/src/urban_meal_delivery/forecasts/models/__init__.py
+++ b/src/urban_meal_delivery/forecasts/models/__init__.py
@@ -15,7 +15,7 @@ For the paper check:
 
 This sub-package is organized as follows. The `base` module defines an abstract
 `ForecastingModelABC` class that unifies how the concrete `*Model`s work.
-While the abstact `.predict()` method returns a `pd.DataFrame` (= basically,
+While the abstract `.predict()` method returns a `pd.DataFrame` (= basically,
 the result of one of the forecasting `methods`, the concrete `.make_forecast()`
 method converts the results into `Forecast` (=ORM) objects.
 Also, `.make_forecast()` implements a caching strategy where already made
@@ -23,7 +23,7 @@ Also, `.make_forecast()` implements a caching strategy where already made
 which could be a heavier computation.
 
 The `tactical` sub-package contains all the `*Model`s used to implement the
-UDP's predictive routing strategy.
+predictive routing strategy employed by the UDP.
 
 A future `planning` sub-package will contain the `*Model`s used to plan the
 `Courier`'s shifts a week ahead.
diff --git a/src/urban_meal_delivery/forecasts/models/base.py b/src/urban_meal_delivery/forecasts/models/base.py
index 9a9cd72..9c3977a 100644
--- a/src/urban_meal_delivery/forecasts/models/base.py
+++ b/src/urban_meal_delivery/forecasts/models/base.py
@@ -75,7 +75,7 @@ class ForecastingModelABC(abc.ABC):
         # noqa:DAR401 RuntimeError
         """
         if (  # noqa:WPS337
-            cached_forecast := db.session.query(db.Forecast)  # noqa:ECE001,WPS221
+            cached_forecast := db.session.query(db.Forecast)  # noqa:WPS221
             .filter_by(pixel=pixel)
             .filter_by(start_at=predict_at)
             .filter_by(time_step=self._order_history.time_step)
diff --git a/src/urban_meal_delivery/forecasts/models/tactical/__init__.py b/src/urban_meal_delivery/forecasts/models/tactical/__init__.py
index df70622..0bb33de 100644
--- a/src/urban_meal_delivery/forecasts/models/tactical/__init__.py
+++ b/src/urban_meal_delivery/forecasts/models/tactical/__init__.py
@@ -1,8 +1,8 @@
 """Forecasting `*Model`s to predict demand for tactical purposes.
 
 The `*Model`s in this module predict only a small number (e.g., one)
-of time steps into the near future and are used to implement the UDP's
-predictive routing strategies.
+of time steps into the near future and are used to implement the
+predictive routing strategies employed by the UDP.
 
 They are classified into "horizontal", "vertical", and "real-time" models
 with respect to what historic data they are trained on and how often they
diff --git a/src/urban_meal_delivery/forecasts/models/tactical/horizontal.py b/src/urban_meal_delivery/forecasts/models/tactical/horizontal.py
index 3a18d76..ef238bf 100644
--- a/src/urban_meal_delivery/forecasts/models/tactical/horizontal.py
+++ b/src/urban_meal_delivery/forecasts/models/tactical/horizontal.py
@@ -51,7 +51,7 @@ class HorizontalETSModel(base.ForecastingModelABC):
         # Make `predictions` with the seasonal ETS method ("ZZZ" model).
         predictions = methods.ets.predict(
             training_ts=training_ts,
-            forecast_interval=actuals_ts.index,
+            forecast_interval=pd.DatetimeIndex(actuals_ts.index),
             frequency=frequency,  # `== 7`, the number of weekdays
             seasonal_fit=True,  # because there was no decomposition before
         )
@@ -59,7 +59,7 @@ class HorizontalETSModel(base.ForecastingModelABC):
         predictions.insert(loc=0, column='actual', value=actuals_ts)
 
         # Sanity checks.
-        if predictions.isnull().any().any():  # pragma: no cover
+        if predictions.isnull().sum().any():  # pragma: no cover
             raise RuntimeError('missing predictions in hets model')
         if predict_at not in predictions.index:  # pragma: no cover
             raise RuntimeError('missing prediction for `predict_at`')
diff --git a/src/urban_meal_delivery/forecasts/models/tactical/realtime.py b/src/urban_meal_delivery/forecasts/models/tactical/realtime.py
index bf30ee5..a14536d 100644
--- a/src/urban_meal_delivery/forecasts/models/tactical/realtime.py
+++ b/src/urban_meal_delivery/forecasts/models/tactical/realtime.py
@@ -59,7 +59,7 @@ class RealtimeARIMAModel(base.ForecastingModelABC):
         # Make predictions for the seasonal component by linear extrapolation.
         seasonal_predictions = methods.extrapolate_season.predict(
             training_ts=decomposed_training_ts['seasonal'],
-            forecast_interval=actuals_ts.index,
+            forecast_interval=pd.DatetimeIndex(actuals_ts.index),
             frequency=frequency,
         )
 
@@ -68,7 +68,7 @@ class RealtimeARIMAModel(base.ForecastingModelABC):
             training_ts=(
                 decomposed_training_ts['trend'] + decomposed_training_ts['residual']
             ),
-            forecast_interval=actuals_ts.index,
+            forecast_interval=pd.DatetimeIndex(actuals_ts.index),
             # Because the seasonality was taken out before,
             # the `training_ts` has, by definition, a `frequency` of `1`.
             frequency=1,
@@ -109,7 +109,7 @@ class RealtimeARIMAModel(base.ForecastingModelABC):
         # Sanity checks.
         if len(predictions) != 1:  # pragma: no cover
             raise RuntimeError('real-time models should predict exactly one time step')
-        if predictions.isnull().any().any():  # pragma: no cover
+        if predictions.isnull().sum().any():  # pragma: no cover
             raise RuntimeError('missing predictions in rtarima model')
         if predict_at not in predictions.index:  # pragma: no cover
             raise RuntimeError('missing prediction for `predict_at`')
diff --git a/src/urban_meal_delivery/forecasts/models/tactical/vertical.py b/src/urban_meal_delivery/forecasts/models/tactical/vertical.py
index caf4317..e663907 100644
--- a/src/urban_meal_delivery/forecasts/models/tactical/vertical.py
+++ b/src/urban_meal_delivery/forecasts/models/tactical/vertical.py
@@ -61,7 +61,7 @@ class VerticalARIMAModel(base.ForecastingModelABC):
         # Make predictions for the seasonal component by linear extrapolation.
         seasonal_predictions = methods.extrapolate_season.predict(
             training_ts=decomposed_training_ts['seasonal'],
-            forecast_interval=actuals_ts.index,
+            forecast_interval=pd.DatetimeIndex(actuals_ts.index),
             frequency=frequency,
         )
 
@@ -70,7 +70,7 @@ class VerticalARIMAModel(base.ForecastingModelABC):
             training_ts=(
                 decomposed_training_ts['trend'] + decomposed_training_ts['residual']
             ),
-            forecast_interval=actuals_ts.index,
+            forecast_interval=pd.DatetimeIndex(actuals_ts.index),
             # Because the seasonality was taken out before,
             # the `training_ts` has, by definition, a `frequency` of `1`.
             frequency=1,
@@ -111,7 +111,7 @@ class VerticalARIMAModel(base.ForecastingModelABC):
         # Sanity checks.
         if len(predictions) <= 1:  # pragma: no cover
             raise RuntimeError('vertical models should predict several time steps')
-        if predictions.isnull().any().any():  # pragma: no cover
+        if predictions.isnull().sum().any():  # pragma: no cover
             raise RuntimeError('missing predictions in varima model')
         if predict_at not in predictions.index:  # pragma: no cover
             raise RuntimeError('missing prediction for `predict_at`')
diff --git a/src/urban_meal_delivery/forecasts/timify.py b/src/urban_meal_delivery/forecasts/timify.py
index 6260808..55cef76 100644
--- a/src/urban_meal_delivery/forecasts/timify.py
+++ b/src/urban_meal_delivery/forecasts/timify.py
@@ -84,41 +84,50 @@ class OrderHistory:
                             pixels.pixel_id,
                             DATE_TRUNC('MINUTE', orders.placed_at)
                                 AS placed_at_without_seconds,
-                            ((
-                                EXTRACT(MINUTES FROM orders.placed_at)::INTEGER
-                                    % {self._time_step}
-                            )::TEXT || ' MINUTES')::INTERVAL
-                                AS minutes_to_be_cut
+                            (
+                                (
+                                    (
+                                        EXTRACT(MINUTES FROM orders.placed_at)::INTEGER
+                                            % {self._time_step}
+                                    )::TEXT
+                                    ||
+                                    ' MINUTES'
+                                )::INTERVAL
+                            ) AS minutes_to_be_cut
                         FROM (
                             SELECT
-                                id,
-                                placed_at,
-                                pickup_address_id
+                                {config.CLEAN_SCHEMA}.orders.id,
+                                {config.CLEAN_SCHEMA}.orders.placed_at,
+                                {config.CLEAN_SCHEMA}.orders.pickup_address_id
                             FROM
                                 {config.CLEAN_SCHEMA}.orders
                             INNER JOIN (
                                 SELECT
-                                    id AS address_id
+                                    {config.CLEAN_SCHEMA}.addresses.id AS address_id
                                 FROM
                                     {config.CLEAN_SCHEMA}.addresses
                                 WHERE
-                                    city_id = {self._grid.city.id}
+                                    {config.CLEAN_SCHEMA}.addresses.city_id
+                                        = {self._grid.city.id}
                             ) AS in_city
-                                ON orders.pickup_address_id = in_city.address_id
+                                ON {config.CLEAN_SCHEMA}.orders.pickup_address_id
+                                    = in_city.address_id
                             WHERE
-                                ad_hoc IS TRUE
+                                {config.CLEAN_SCHEMA}.orders.ad_hoc IS TRUE
                         ) AS
                             orders
                         INNER JOIN (
                             SELECT
-                                address_id,
-                                pixel_id
+                                {config.CLEAN_SCHEMA}.addresses_pixels.address_id,
+                                {config.CLEAN_SCHEMA}.addresses_pixels.pixel_id
                             FROM
                                 {config.CLEAN_SCHEMA}.addresses_pixels
                             WHERE
-                                grid_id = {self._grid.id}
+                                {config.CLEAN_SCHEMA}.addresses_pixels.grid_id
+                                    = {self._grid.id}
                                 AND
-                                city_id = {self._grid.city.id} -- -> sanity check
+                                {config.CLEAN_SCHEMA}.addresses_pixels.city_id
+                                    = {self._grid.city.id} -- -> sanity check
                         ) AS pixels
                             ON orders.pickup_address_id = pixels.address_id
                     ) AS placed_at_aggregated_into_start_at
@@ -544,7 +553,7 @@ class OrderHistory:
 
         # For now, we only make forecasts with 7 and 8 weeks
         # as the training horizon (note:4f79e8fa).
-        if train_horizon == 7 or train_horizon == 8:
+        if train_horizon in {7, 8}:
             if add >= 25:  # = "high demand"
                 return models.HorizontalETSModel(order_history=self)
             elif add >= 10:  # = "medium demand"
diff --git a/tests/conftest.py b/tests/conftest.py
index b7bafd5..d4b1b25 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -5,6 +5,7 @@ in the CLI layer need access to the database.
 """
 
 import os
+import warnings
 
 import pytest
 import sqlalchemy as sa
@@ -94,7 +95,9 @@ def db_session(db_connection):
 
     finally:
         session.close()
-        transaction.rollback()
+
+        with warnings.catch_warnings(record=True):
+            transaction.rollback()
 
 
 # Import the fixtures from the `fake_data` sub-package.
diff --git a/tests/db/test_addresses_addresses.py b/tests/db/test_addresses_addresses.py
new file mode 100644
index 0000000..b44ed08
--- /dev/null
+++ b/tests/db/test_addresses_addresses.py
@@ -0,0 +1,682 @@
+"""Test the ORM's `Path` model."""
+
+import json
+
+import googlemaps
+import pytest
+import sqlalchemy as sqla
+from geopy import distance
+from sqlalchemy import exc as sa_exc
+
+from urban_meal_delivery import db
+from urban_meal_delivery.db import utils
+
+
+@pytest.fixture
+def another_address(make_address):
+    """Another `Address` object in the `city`."""
+    return make_address()
+
+
+@pytest.fixture
+def path(address, another_address, make_address):
+    """A `Path` from `address` to `another_address`."""
+    air_distance = distance.great_circle(  # noqa:WPS317
+        address.location.lat_lng, another_address.location.lat_lng,
+    ).meters
+
+    # We put 5 latitude-longitude pairs as the "path" from
+    # `.first_address` to `.second_address`.
+    directions = json.dumps(
+        [
+            (float(add.latitude), float(add.longitude))
+            for add in (make_address() for _ in range(5))  # noqa:WPS335
+        ],
+    )
+
+    return db.Path(
+        first_address=address,
+        second_address=another_address,
+        air_distance=round(air_distance),
+        bicycle_distance=round(1.25 * air_distance),
+        bicycle_duration=300,
+        _directions=directions,
+    )
+
+
+class TestSpecialMethods:
+    """Test special methods in `Path`."""
+
+    def test_create_an_address_address_association(self, path):
+        """Test instantiation of a new `Path` object."""
+        assert path is not None
+
+
+@pytest.mark.db
+@pytest.mark.no_cover
+class TestConstraints:
+    """Test the database constraints defined in `Path`."""
+
+    def test_insert_into_database(self, db_session, path):
+        """Insert an instance into the (empty) database."""
+        assert db_session.query(db.Path).count() == 0
+
+        db_session.add(path)
+        db_session.commit()
+
+        assert db_session.query(db.Path).count() == 1
+
+    def test_delete_a_referenced_first_address(self, db_session, path):
+        """Remove a record that is referenced with a FK."""
+        db_session.add(path)
+        db_session.commit()
+
+        # Must delete without ORM as otherwise an UPDATE statement is emitted.
+        stmt = sqla.delete(db.Address).where(db.Address.id == path.first_address.id)
+
+        with pytest.raises(
+            sa_exc.IntegrityError,
+            match='fk_addresses_addresses_to_addresses_via_first_address',  # shortened
+        ):
+            db_session.execute(stmt)
+
+    def test_delete_a_referenced_second_address(self, db_session, path):
+        """Remove a record that is referenced with a FK."""
+        db_session.add(path)
+        db_session.commit()
+
+        # Must delete without ORM as otherwise an UPDATE statement is emitted.
+        stmt = sqla.delete(db.Address).where(db.Address.id == path.second_address.id)
+
+        with pytest.raises(
+            sa_exc.IntegrityError,
+            match='fk_addresses_addresses_to_addresses_via_second_address',  # shortened
+        ):
+            db_session.execute(stmt)
+
+    def test_reference_an_invalid_city(self, db_session, address, another_address):
+        """Insert a record with an invalid foreign key."""
+        db_session.add(address)
+        db_session.add(another_address)
+        db_session.commit()
+
+        # Must insert without ORM as otherwise SQLAlchemy figures out
+        # that something is wrong before any query is sent to the database.
+        stmt = sqla.insert(db.Path).values(
+            first_address_id=address.id,
+            second_address_id=another_address.id,
+            city_id=999,
+            air_distance=123,
+        )
+
+        with pytest.raises(
+            sa_exc.IntegrityError,
+            match='fk_addresses_addresses_to_addresses_via_first_address',  # shortened
+        ):
+            db_session.execute(stmt)
+
+    def test_redundant_addresses(self, db_session, path):
+        """Insert a record that violates a unique constraint."""
+        db_session.add(path)
+        db_session.commit()
+
+        # Must insert without ORM as otherwise SQLAlchemy figures out
+        # that something is wrong before any query is sent to the database.
+        stmt = sqla.insert(db.Path).values(
+            first_address_id=path.first_address.id,
+            second_address_id=path.second_address.id,
+            city_id=path.city_id,
+            air_distance=path.air_distance,
+        )
+
+        with pytest.raises(sa_exc.IntegrityError, match='duplicate key value'):
+            db_session.execute(stmt)
+
+    def test_symmetric_addresses(self, db_session, path):
+        """Insert a record that violates a check constraint."""
+        db_session.add(path)
+        db_session.commit()
+
+        another_path = db.Path(
+            first_address=path.second_address,
+            second_address=path.first_address,
+            air_distance=path.air_distance,
+        )
+        db_session.add(another_path)
+
+        with pytest.raises(
+            sa_exc.IntegrityError,
+            match='ck_addresses_addresses_on_distances_are_symmetric_for_bicycles',
+        ):
+            db_session.commit()
+
+    def test_negative_air_distance(self, db_session, path):
+        """Insert an instance with invalid data."""
+        path.air_distance = -1
+        db_session.add(path)
+
+        with pytest.raises(sa_exc.IntegrityError, match='realistic_air_distance'):
+            db_session.commit()
+
+    def test_air_distance_too_large(self, db_session, path):
+        """Insert an instance with invalid data."""
+        path.air_distance = 20_000
+        path.bicycle_distance = 21_000
+        db_session.add(path)
+
+        with pytest.raises(sa_exc.IntegrityError, match='realistic_air_distance'):
+            db_session.commit()
+
+    def test_bicycle_distance_too_large(self, db_session, path):
+        """Insert an instance with invalid data."""
+        path.bicycle_distance = 25_000
+        db_session.add(path)
+
+        with pytest.raises(sa_exc.IntegrityError, match='realistic_bicycle_distance'):
+            db_session.commit()
+
+    def test_air_distance_shorter_than_bicycle_distance(self, db_session, path):
+        """Insert an instance with invalid data."""
+        path.bicycle_distance = round(0.75 * path.air_distance)
+        db_session.add(path)
+
+        with pytest.raises(sa_exc.IntegrityError, match='air_distance_is_shortest'):
+            db_session.commit()
+
+    @pytest.mark.parametrize('duration', [-1, 3601])
+    def test_unrealistic_bicycle_travel_time(self, db_session, path, duration):
+        """Insert an instance with invalid data."""
+        path.bicycle_duration = duration
+        db_session.add(path)
+
+        with pytest.raises(
+            sa_exc.IntegrityError, match='realistic_bicycle_travel_time',
+        ):
+            db_session.commit()
+
+
+@pytest.mark.db
+class TestFromAddresses:
+    """Test the alternative constructor `Path.from_addresses()`.
+
+    Includes tests for the convenience method `Path.from_order()`,
+    which redirects to `Path.from_addresses()`.
+    """
+
+    @pytest.fixture
+    def _prepare_db(self, db_session, address):
+        """Put the `address` into the database.
+
+        `Address`es must be in the database as otherwise the `.city_id` column
+        cannot be resolved in `Path.from_addresses()`.
+        """
+        db_session.add(address)
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_make_path_instance(
+        self, db_session, address, another_address,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        assert db_session.query(db.Path).count() == 0
+
+        db.Path.from_addresses(address, another_address)
+
+        assert db_session.query(db.Path).count() == 1
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_make_the_same_path_instance_twice(
+        self, db_session, address, another_address,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        assert db_session.query(db.Path).count() == 0
+
+        db.Path.from_addresses(address, another_address)
+
+        assert db_session.query(db.Path).count() == 1
+
+        db.Path.from_addresses(another_address, address)
+
+        assert db_session.query(db.Path).count() == 1
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_structure_of_return_value(self, db_session, address, another_address):
+        """Test instantiation of a new `Path` instance."""
+        results = db.Path.from_addresses(address, another_address)
+
+        assert isinstance(results, list)
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_instances_must_have_air_distance(
+        self, db_session, address, another_address,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        paths = db.Path.from_addresses(address, another_address)
+
+        result = paths[0]
+
+        assert result.air_distance is not None
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_do_not_sync_instances_with_google_maps(
+        self, db_session, address, another_address,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        paths = db.Path.from_addresses(address, another_address)
+
+        result = paths[0]
+
+        assert result.bicycle_distance is None
+        assert result.bicycle_duration is None
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_sync_instances_with_google_maps(
+        self, db_session, address, another_address, monkeypatch,
+    ):
+        """Test instantiation of a new `Path` instance."""
+
+        def sync(self):
+            self.bicycle_distance = 1.25 * self.air_distance
+            self.bicycle_duration = 300
+
+        monkeypatch.setattr(db.Path, 'sync_with_google_maps', sync)
+
+        paths = db.Path.from_addresses(address, another_address, google_maps=True)
+
+        result = paths[0]
+
+        assert result.bicycle_distance is not None
+        assert result.bicycle_duration is not None
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_one_path_for_two_addresses(self, db_session, address, another_address):
+        """Test instantiation of a new `Path` instance."""
+        result = len(db.Path.from_addresses(address, another_address))
+
+        assert result == 1
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_two_paths_for_three_addresses(self, db_session, make_address):
+        """Test instantiation of a new `Path` instance."""
+        result = len(db.Path.from_addresses(*[make_address() for _ in range(3)]))
+
+        assert result == 3
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_six_paths_for_four_addresses(self, db_session, make_address):
+        """Test instantiation of a new `Path` instance."""
+        result = len(db.Path.from_addresses(*[make_address() for _ in range(4)]))
+
+        assert result == 6
+
+    # Tests for the `Path.from_order()` convenience method.
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_make_path_instance_from_order(
+        self, db_session, order,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        assert db_session.query(db.Path).count() == 0
+
+        db.Path.from_order(order)
+
+        assert db_session.query(db.Path).count() == 1
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_make_the_same_path_instance_from_order_twice(
+        self, db_session, order,
+    ):
+        """Test instantiation of a new `Path` instance."""
+        assert db_session.query(db.Path).count() == 0
+
+        db.Path.from_order(order)
+
+        assert db_session.query(db.Path).count() == 1
+
+        db.Path.from_order(order)
+
+        assert db_session.query(db.Path).count() == 1
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_structure_of_return_value_from_order(self, db_session, order):
+        """Test instantiation of a new `Path` instance."""
+        result = db.Path.from_order(order)
+
+        assert isinstance(result, db.Path)
+
+    @pytest.mark.usefixtures('_prepare_db')
+    def test_sync_instance_from_order_with_google_maps(
+        self, db_session, order, monkeypatch,
+    ):
+        """Test instantiation of a new `Path` instance."""
+
+        def sync(self):
+            self.bicycle_distance = 1.25 * self.air_distance
+            self.bicycle_duration = 300
+
+        monkeypatch.setattr(db.Path, 'sync_with_google_maps', sync)
+
+        result = db.Path.from_order(order, google_maps=True)
+
+        assert result.bicycle_distance is not None
+        assert result.bicycle_duration is not None
+
+
+@pytest.mark.db
+class TestSyncWithGoogleMaps:
+    """Test the `Path.sync_with_google_maps()` method."""
+
+    @pytest.fixture
+    def api_response(self):
+        """A typical (shortened) response by the Google Maps Directions API."""
+        return [  # noqa:ECE001
+            {
+                'bounds': {
+                    'northeast': {'lat': 44.8554284, 'lng': -0.5652398},
+                    'southwest': {'lat': 44.8342256, 'lng': -0.5708206},
+                },
+                'copyrights': 'Map data ©2021',
+                'legs': [
+                    {
+                        'distance': {'text': '3.0 km', 'value': 2999},
+                        'duration': {'text': '10 mins', 'value': 596},
+                        'end_address': '13 Place Paul et Jean Paul Avisseau, ...',
+                        'end_location': {'lat': 44.85540839999999, 'lng': -0.5672105},
+                        'start_address': '59 Rue Saint-François, 33000 Bordeaux, ...',
+                        'start_location': {'lat': 44.8342256, 'lng': -0.570372},
+                        'steps': [
+                            {
+                                'distance': {'text': '0.1 km', 'value': 138},
+                                'duration': {'text': '1 min', 'value': 43},
+                                'end_location': {
+                                    'lat': 44.83434380000001,
+                                    'lng': -0.5690105999999999,
+                                },
+                                'html_instructions': 'Head <b>east</b> on <b> ...',
+                                'polyline': {'points': '}tspGxknBKcDIkB'},
+                                'start_location': {'lat': 44.8342256, 'lng': -0.57032},
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.1 km', 'value': 115},
+                                'duration': {'text': '1 min', 'value': 22},
+                                'end_location': {'lat': 44.8353651, 'lng': -0.569199},
+                                'html_instructions': 'Turn <b>left</b> onto <b> ...',
+                                'maneuver': 'turn-left',
+                                'polyline': {'points': 'suspGhcnBc@JE@_@DiAHA?w@F'},
+                                'start_location': {
+                                    'lat': 44.83434380000001,
+                                    'lng': -0.5690105999999999,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.3 km', 'value': 268},
+                                'duration': {'text': '1 min', 'value': 59},
+                                'end_location': {'lat': 44.8362675, 'lng': -0.5660914},
+                                'html_instructions': 'Turn <b>right</b> onto <b> ...',
+                                'maneuver': 'turn-right',
+                                'polyline': {
+                                    'points': 'a|spGndnBEYEQKi@Mi@Is@CYCOE]CQIq@ ...',
+                                },
+                                'start_location': {'lat': 44.8353651, 'lng': -0.56919},
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.1 km', 'value': 95},
+                                'duration': {'text': '1 min', 'value': 29},
+                                'end_location': {'lat': 44.8368458, 'lng': -0.5652398},
+                                'html_instructions': 'Slight <b>left</b> onto <b> ...',
+                                'maneuver': 'turn-slight-left',
+                                'polyline': {
+                                    'points': 'uatpG`qmBg@aAGM?ACE[k@CICGACEGCCAAEAG?',
+                                },
+                                'start_location': {
+                                    'lat': 44.8362675,
+                                    'lng': -0.5660914,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '23 m', 'value': 23},
+                                'duration': {'text': '1 min', 'value': 4},
+                                'end_location': {'lat': 44.83697, 'lng': -0.5654425},
+                                'html_instructions': 'Slight <b>left</b> to stay ...',
+                                'maneuver': 'turn-slight-left',
+                                'polyline': {
+                                    'points': 'ietpGvkmBA@C?CBCBEHA@AB?B?B?B?@',
+                                },
+                                'start_location': {
+                                    'lat': 44.8368458,
+                                    'lng': -0.5652398,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.2 km', 'value': 185},
+                                'duration': {'text': '1 min', 'value': 23},
+                                'end_location': {'lat': 44.8382126, 'lng': -0.5669969},
+                                'html_instructions': 'Take the ramp to <b>Le Lac ...',
+                                'polyline': {
+                                    'points': 'aftpG~lmBY^[^sAdB]`@CDKLQRa@h@A@IZ',
+                                },
+                                'start_location': {'lat': 44.83697, 'lng': -0.5654425},
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.3 km', 'value': 253},
+                                'duration': {'text': '1 min', 'value': 43},
+                                'end_location': {'lat': 44.840163, 'lng': -0.5686525},
+                                'html_instructions': 'Merge onto <b>Quai Richelieu</b>',
+                                'maneuver': 'merge',
+                                'polyline': {
+                                    'points': 'ymtpGvvmBeAbAe@b@_@ZUN[To@f@e@^A?g ...',
+                                },
+                                'start_location': {
+                                    'lat': 44.8382126,
+                                    'lng': -0.5669969,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.1 km', 'value': 110},
+                                'duration': {'text': '1 min', 'value': 21},
+                                'end_location': {'lat': 44.841079, 'lng': -0.5691835},
+                                'html_instructions': 'Continue onto <b>Quai de la ...',
+                                'polyline': {'points': '_ztpG`anBUNQLULUJOHMFKDWN'},
+                                'start_location': {'lat': 44.840163, 'lng': -0.56865},
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.3 km', 'value': 262},
+                                'duration': {'text': '1 min', 'value': 44},
+                                'end_location': {'lat': 44.8433375, 'lng': -0.5701161},
+                                'html_instructions': 'Continue onto <b>Quai du ...',
+                                'polyline': {
+                                    'points': 'w_upGjdnBeBl@sBn@gA^[JIBc@Nk@Nk@L',
+                                },
+                                'start_location': {'lat': 44.841079, 'lng': -0.56915},
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.6 km', 'value': 550},
+                                'duration': {'text': '2 mins', 'value': 97},
+                                'end_location': {
+                                    'lat': 44.84822339999999,
+                                    'lng': -0.5705307,
+                                },
+                                'html_instructions': 'Continue onto <b>Quai ...',
+                                'polyline': {
+                                    'points': '{mupGfjnBYFI@IBaAPUD{AX}@NK@]Fe@H ...',
+                                },
+                                'start_location': {
+                                    'lat': 44.8433375,
+                                    'lng': -0.5701161,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.5 km', 'value': 508},
+                                'duration': {'text': '1 min', 'value': 87},
+                                'end_location': {'lat': 44.8523224, 'lng': -0.5678223},
+                                'html_instructions': 'Continue onto ...',
+                                'polyline': {
+                                    'points': 'klvpGxlnBWEUGWGSGMEOEOE[KMEQGIA] ...',
+                                },
+                                'start_location': {
+                                    'lat': 44.84822339999999,
+                                    'lng': -0.5705307,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '28 m', 'value': 28},
+                                'duration': {'text': '1 min', 'value': 45},
+                                'end_location': {
+                                    'lat': 44.85245620000001,
+                                    'lng': -0.5681259,
+                                },
+                                'html_instructions': 'Turn <b>left</b> onto <b> ...',
+                                'maneuver': 'turn-left',
+                                'polyline': {'points': '_fwpGz{mBGLADGPCFEN'},
+                                'start_location': {
+                                    'lat': 44.8523224,
+                                    'lng': -0.5678223,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.2 km', 'value': 176},
+                                'duration': {'text': '1 min', 'value': 31},
+                                'end_location': {'lat': 44.8536857, 'lng': -0.5667282},
+                                'html_instructions': 'Turn <b>right</b> onto <b> ...',
+                                'maneuver': 'turn-right',
+                                'polyline': {
+                                    'points': '{fwpGx}mB_@c@mAuAOQi@m@m@y@_@c@',
+                                },
+                                'start_location': {
+                                    'lat': 44.85245620000001,
+                                    'lng': -0.5681259,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.2 km', 'value': 172},
+                                'duration': {'text': '1 min', 'value': 28},
+                                'end_location': {'lat': 44.8547766, 'lng': -0.5682825},
+                                'html_instructions': 'Turn <b>left</b> onto <b> ... ',
+                                'maneuver': 'turn-left',
+                                'polyline': {'points': 'qnwpG`umBW`@UkDtF'},
+                                'start_location': {
+                                    'lat': 44.8536857,
+                                    'lng': -0.5667282,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '0.1 km', 'value': 101},
+                                'duration': {'text': '1 min', 'value': 17},
+                                'end_location': {'lat': 44.8554284, 'lng': -0.5673822},
+                                'html_instructions': 'Turn <b>right</b> onto ...',
+                                'maneuver': 'turn-right',
+                                'polyline': {'points': 'kuwpGv~mBa@q@cA_B[a@'},
+                                'start_location': {
+                                    'lat': 44.8547766,
+                                    'lng': -0.5682825,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                            {
+                                'distance': {'text': '15 m', 'value': 15},
+                                'duration': {'text': '1 min', 'value': 3},
+                                'end_location': {
+                                    'lat': 44.85540839999999,
+                                    'lng': -0.5672105,
+                                },
+                                'html_instructions': 'Turn <b>right</b> onto <b> ...',
+                                'maneuver': 'turn-right',
+                                'polyline': {'points': 'mywpGbymBBC@C?E?C?E?EAC'},
+                                'start_location': {
+                                    'lat': 44.8554284,
+                                    'lng': -0.5673822,
+                                },
+                                'travel_mode': 'BICYCLING',
+                            },
+                        ],
+                        'traffic_speed_entry': [],
+                        'via_waypoint': [],
+                    },
+                ],
+                'overview_polyline': {
+                    'points': '}tspGxknBUoGi@LcDVe@_CW{Ba@sC[eA_@} ...',
+                },
+                'summary': 'Quai des Chartrons',
+                'warnings': ['Bicycling directions are in beta ...'],
+                'waypoint_order': [],
+            },
+        ]
+
+    @pytest.fixture
+    def _fake_google_api(self, api_response, monkeypatch):
+        """Patch out the call to the Google Maps Directions API."""
+
+        def directions(_self, *_args, **_kwargs):
+            return api_response
+
+        monkeypatch.setattr(googlemaps.Client, 'directions', directions)
+
+    @pytest.mark.usefixtures('_fake_google_api')
+    def test_sync_instances_with_google_maps(self, db_session, path):
+        """Call the method for a `Path` object without Google data."""
+        path.bicycle_distance = None
+        path.bicycle_duration = None
+        path._directions = None
+
+        path.sync_with_google_maps()
+
+        assert path.bicycle_distance == 2_999
+        assert path.bicycle_duration == 596
+        assert path._directions is not None
+
+    @pytest.mark.usefixtures('_fake_google_api')
+    def test_repeated_sync_instances_with_google_maps(self, db_session, path):
+        """Call the method for a `Path` object with Google data.
+
+        That call should immediately return without changing any data.
+
+        We use the `path`'s "Google" data from above.
+        """
+        old_distance = path.bicycle_distance
+        old_duration = path.bicycle_duration
+        old_directions = path._directions
+
+        path.sync_with_google_maps()
+
+        assert path.bicycle_distance is old_distance
+        assert path.bicycle_duration is old_duration
+        assert path._directions is old_directions
+
+
+class TestProperties:
+    """Test properties in `Path`."""
+
+    def test_waypoints_structure(self, path):
+        """Test `Path.waypoints` property."""
+        result = path.waypoints
+
+        assert isinstance(result, list)
+        assert isinstance(result[0], utils.Location)
+
+    def test_waypoints_content(self, path):
+        """Test `Path.waypoints` property."""
+        result = path.waypoints
+
+        # There are 5 inner points, excluding start and end,
+        # i.e., the `.first_address` and `second_address`.
+        assert len(result) == 5
+
+    def test_waypoints_is_cached(self, path):
+        """Test `Path.waypoints` property."""
+        result1 = path.waypoints
+        result2 = path.waypoints
+
+        assert result1 is result2
diff --git a/tests/db/test_addresses_pixels.py b/tests/db/test_addresses_pixels.py
index d5beadd..9f5f70e 100644
--- a/tests/db/test_addresses_pixels.py
+++ b/tests/db/test_addresses_pixels.py
@@ -24,7 +24,7 @@ def assoc(address, pixel):
 
 @pytest.mark.no_cover
 class TestSpecialMethods:
-    """Test special methods in `Pixel`."""
+    """Test special methods in `AddressPixelAssociation`."""
 
     def test_create_an_address_pixel_association(self, assoc):
         """Test instantiation of a new `AddressPixelAssociation` object."""
diff --git a/tests/db/utils/test_locations.py b/tests/db/utils/test_locations.py
index 8eb0263..0a3d3d2 100644
--- a/tests/db/utils/test_locations.py
+++ b/tests/db/utils/test_locations.py
@@ -122,6 +122,15 @@ class TestProperties:
 
         assert result == pytest.approx(float(address.longitude))
 
+    def test_lat_lng(self, location, address):
+        """Test `Location.lat_lng` property."""
+        result = location.lat_lng
+
+        assert result == (
+            pytest.approx(float(address.latitude)),
+            pytest.approx(float(address.longitude)),
+        )
+
     def test_easting(self, location):
         """Test `Location.easting` property."""
         result = location.easting