spopt.locate.LSCPB¶

class spopt.locate.LSCPB(name: str, problem: LpProblem, solver: LpSolver)[source]¶

Implement the Location Set Covering Problem - Backup (LSCP-B) optimization model and solve it. The LSCP-B, as adapted from [CM18], can be formulated as:

\[\begin{split}\begin{array}{lllll} \displaystyle \textbf{Maximize} & \displaystyle \sum_{i \in I}{U_i} && & (1) \\ \displaystyle \textbf{Subject To} & \displaystyle \sum_{j \in J}{a_{ij}}{Y_j} \geq 1 + U_i && \forall i \in I & (2) \\ & \displaystyle \sum_{j \in J}{Y_j} = p && & (3) \\ & U_i \leq 1 && \forall i \in I & (4) \\ & Y_j \in \{0, 1\} && \forall j \in J & (5) \\ & && & \\ \displaystyle \textbf{Where} && i & = & \textrm{index of demand points/areas/objects in set } I \\ && j & = & \textrm{index of potential facility sites in set } J \\ && p & = & \textrm{objective value identified by using the } LSCP \\ && U_i & = & \begin{cases} 1, \textrm{if demand location is covered twice} \\ 0, \textrm{if demand location is covered once} \\ \end{cases} \\ && a_{ij} & = & \begin{cases} 1, \textrm{if facility location } j \textrm{ covers demand location } i \\ 0, \textrm{otherwise} \\ \end{cases} \\ && Y_j & = & \begin{cases} 1, \textrm{if a facility is sited at location } j \\ 0, \textrm{otherwise} \\ \end{cases} \end{array}\end{split}\]

Parameters:

namestr: The problem name.
problempulp.LpProblem: A pulp instance of an optimization model that contains constraints, variables, and an objective function.
solverpulp.LpSolver: A solver supported by pulp.

Attributes:

namestr: The problem name.
problempulp.LpProblem: A pulp instance of an optimization model that contains constraints, variables, and an objective function.
solverpulp.LpSolver: A solver supported by pulp.
lscp_obj_valuefloat: The objective value returned from a solved LSCP instance.
fac2clinumpy.array: A 2D array storing facility to client relationships where each row represents a facility and contains an array of client indices with which it is associated. An empty client array indicates the facility is associated with no clients.
cli2facnumpy.array: The inverse of fac2cli where client to facility relationships are shown.
aijnumpy.array: A cost matrix in the form of a 2D array between origins and destinations.

__init__(name: str, problem: LpProblem, solver: LpSolver)[source]¶

Initialize.

Parameters:

namestr: The desired name for the model.

Methods

`__init__`(name, problem, solver)	Initialize.
`check_status`()	Ensure a model is solved.
`client_facility_array`()	Create a 2D array storing client to facility relationships where each row represents a client and contains an array of facility indices with which it is associated.
`facility_client_array`()	Create a 2D array storing facility to client relationships where each row represents a facility and contains an array of client indices with which it is associated.
`from_cost_matrix`(cost_matrix, ...[, ...])	Create an `LSCPB` object based on a cost matrix.
`from_geodataframe`(gdf_demand, gdf_fac, ...)	Create an `LSCPB` object from `geopandas.GeoDataFrame` objects.
`get_percentage`()	Calculate the percentage of clients with backup.
`solve`([results])	Solve the `LSCPB` model.

facility_client_array() → None[source]¶

Create a 2D array storing facility to client relationships where each row represents a facility and contains an array of client indices with which it is associated. An empty client array indicates the facility is associated with no clients.

Returns:

None

classmethod from_cost_matrix(cost_matrix: array, service_radius: float, solver: LpSolver, predefined_facilities_arr: array = None, name: str = 'lscp-b')[source]¶

Create an LSCPB object based on a cost matrix.

Parameters:

cost_matrixnumpy.array: A cost matrix in the form of a 2D array between origins and destinations.
service_radiusfloat: Maximum acceptable service distance.
solverpulp.LpSolver: A solver supported by pulp.
predefined_facilities_arrnumpy.array (default None): A binary 1D array of service facilities that must appear in the solution. For example, consider 3 facilites ['A', 'B', 'C']. If facility 'B' must be in the model solution, then the passed in array should be [0, 1, 0].
namestr (default ‘lscp-b’): The problem name.

Returns:

spopt.locate.coverage.LSCPB

Examples

>>> from spopt.locate import LSCPB
>>> from spopt.locate.util import simulated_geo_points
>>> import geopandas
>>> import numpy
>>> import pulp
>>> import spaghetti

Create a regular lattice.

>>> lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)
>>> ntw = spaghetti.Network(in_data=lattice)
>>> streets = spaghetti.element_as_gdf(ntw, arcs=True)
>>> streets_buffered = geopandas.GeoDataFrame(
...     geopandas.GeoSeries(streets["geometry"].buffer(0.2).unary_union),
...     crs=streets.crs,
...     columns=["geometry"]
... )

Simulate points about the lattice.

>>> demand_points = simulated_geo_points(streets_buffered, needed=100, seed=5)
>>> facility_points = simulated_geo_points(streets_buffered, needed=5, seed=6)

Snap the points to the network of lattice edges.

>>> ntw.snapobservations(demand_points, "clients", attribute=True)
>>> clients_snapped = spaghetti.element_as_gdf(
...     ntw, pp_name="clients", snapped=True
... )
>>> ntw.snapobservations(facility_points, "facilities", attribute=True)
>>> facilities_snapped = spaghetti.element_as_gdf(
...     ntw, pp_name="facilities", snapped=True
... )

Calculate the cost matrix from origins to destinations.

>>> cost_matrix = ntw.allneighbordistances(
...     sourcepattern=ntw.pointpatterns["clients"],
...     destpattern=ntw.pointpatterns["facilities"]
... )

Create and solve an LSCPB instance from the cost matrix.

>>> lscpb_from_cost_matrix = LSCPB.from_cost_matrix(
...     cost_matrix, service_radius=8, solver=pulp.PULP_CBC_CMD(msg=False)
... )
>>> lscpb_from_cost_matrix = lscpb_from_cost_matrix.solve()

Get the facility lookup demand coverage array.

>>> for fac, cli in enumerate(lscpb_from_cost_matrix.fac2cli):
...     print(f"facility {fac} serving {len(cli)} clients")
facility 0 serving 0 clients
facility 1 serving 63 clients
facility 2 serving 85 clients
facility 3 serving 92 clients
facility 4 serving 0 clients

Get the percentage of clients covered by more than one facility.

>>> round(lscpb_from_cost_matrix.backup_perc, 3)
88.0

88% of clients are covered by more than 1 facility

classmethod from_geodataframe(gdf_demand: GeoDataFrame, gdf_fac: GeoDataFrame, demand_col: str, facility_col: str, service_radius: float, solver: LpSolver, predefined_facility_col: str = None, distance_metric: str = 'euclidean', name: str = 'lscp-b')[source]¶

Create an LSCPB object from geopandas.GeoDataFrame objects. Calculate the cost matrix between demand and facility locations before building the problem within the from_cost_matrix() method.

Parameters:

gdf_demandgeopandas.GeoDataFrame: Demand locations.
gdf_facgeopandas.GeoDataFrame: Facility locations.
demand_colstr: Demand sites geometry column name.
facility_colstr: Facility candidate sites geometry column name.
service_radiusfloat: Maximum acceptable service distance.
solverpulp.LpSolver: A solver supported by pulp.
predefined_facility_colstr (default None): Column name representing facilities are already defined. This a binary assignment per facility. For example, consider 3 facilites ['A', 'B', 'C']. If facility 'B' must be in the model solution, then the column should be [0, 1, 0].
distance_metricstr (default ‘euclidean’): A metric used for the distance calculations supported by scipy.spatial.distance.cdist.
namestr (default ‘lscp-b’): The name of the problem.

Returns:

spopt.locate.coverage.LSCPB

Examples

>>> from spopt.locate import LSCPB
>>> from spopt.locate.util import simulated_geo_points
>>> import geopandas
>>> import numpy
>>> import pulp
>>> import spaghetti

Create a regular lattice.

>>> lattice = spaghetti.regular_lattice((0, 0, 10, 10), 9, exterior=True)
>>> ntw = spaghetti.Network(in_data=lattice)
>>> streets = spaghetti.element_as_gdf(ntw, arcs=True)
>>> streets_buffered = geopandas.GeoDataFrame(
...     geopandas.GeoSeries(streets["geometry"].buffer(0.2).unary_union),
...     crs=streets.crs,
...     columns=["geometry"]
... )

Simulate points about the lattice.

>>> demand_points = simulated_geo_points(streets_buffered, needed=100, seed=5)
>>> facility_points = simulated_geo_points(streets_buffered, needed=5, seed=6)

Snap the points to the network of lattice edges and extract as GeoDataFrame objects.

>>> ntw.snapobservations(demand_points, "clients", attribute=True)
>>> clients_snapped = spaghetti.element_as_gdf(
...     ntw, pp_name="clients", snapped=True
... )
>>> ntw.snapobservations(facility_points, "facilities", attribute=True)
>>> facilities_snapped = spaghetti.element_as_gdf(
...     ntw, pp_name="facilities", snapped=True
... )

Create and solve an LSCPB instance from the GeoDataFrame objects.

>>> lscpb_from_geodataframe = LSCPB.from_geodataframe(
...     clients_snapped,
...     facilities_snapped,
...     "geometry",
...     "geometry",
...     service_radius=8,
...     solver=pulp.PULP_CBC_CMD(msg=False),
...     distance_metric="euclidean"
... )
>>> lscpb_from_geodataframe = lscpb_from_geodataframe.solve()

Get the facility lookup demand coverage array.

>>> for fac, cli in enumerate(lscpb_from_geodataframe.fac2cli):
...     print(f"facility {fac} serving {len(cli)} clients")
facility 0 serving 0 clients
facility 1 serving 0 clients
facility 2 serving 100 clients
facility 3 serving 0 clients
facility 4 serving 0 clients

Get the percentage of clients covered by more than one facility.

>>> round(lscpb_from_geodataframe.backup_perc, 3)
0.0

All clients are covered by 1 facility because only one facility is needed to solve the LSCP.

solve(results: bool = True)[source]¶

Solve the LSCPB model.

Parameters:

resultsbool (default True): If True it will create metainfo (which facilities cover which demand) and vice-versa, and the uncovered demand.

Returns:

spopt.locate.coverage.LSCPB