diff --git a/notebooks/lscp_capacity.ipynb b/notebooks/lscp_capacity.ipynb
index b51206f9..ea9fe88e 100644
--- a/notebooks/lscp_capacity.ipynb
+++ b/notebooks/lscp_capacity.ipynb
@@ -60,8 +60,8 @@
    "execution_count": 1,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:53.041361Z",
-     "start_time": "2023-01-10T18:19:53.007862Z"
+     "end_time": "2023-01-10T23:04:25.556826Z",
+     "start_time": "2023-01-10T23:04:25.511104Z"
     }
    },
    "outputs": [
@@ -69,7 +69,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Last updated: 2023-01-10T13:19:53.030211-05:00\n",
+      "Last updated: 2023-01-10T18:04:25.545436-05:00\n",
       "\n",
       "Python implementation: CPython\n",
       "Python version       : 3.10.8\n",
@@ -97,8 +97,8 @@
    "execution_count": 2,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:55.712024Z",
-     "start_time": "2023-01-10T18:19:53.045515Z"
+     "end_time": "2023-01-10T23:04:27.903605Z",
+     "start_time": "2023-01-10T23:04:25.560503Z"
     }
    },
    "outputs": [
@@ -108,15 +108,15 @@
      "text": [
       "Watermark: 2.3.1\n",
       "\n",
-      "spaghetti : 1.6.10\n",
-      "numpy     : 1.23.5\n",
-      "geopandas : 0.12.2\n",
       "json      : 2.0.9\n",
+      "pandas    : 1.5.2\n",
       "shapely   : 2.0.0\n",
-      "spopt     : 0.4.1+200.g336f235.dirty\n",
-      "pulp      : 2.7.0\n",
+      "geopandas : 0.12.2\n",
+      "numpy     : 1.23.5\n",
       "matplotlib: 3.6.2\n",
-      "pandas    : 1.5.2\n",
+      "pulp      : 2.7.0\n",
+      "spopt     : 0.4.1+200.g336f235.dirty\n",
+      "spaghetti : 1.6.10\n",
       "\n"
      ]
     }
@@ -159,8 +159,8 @@
    "execution_count": 3,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:55.720970Z",
-     "start_time": "2023-01-10T18:19:55.716334Z"
+     "end_time": "2023-01-10T23:04:27.913721Z",
+     "start_time": "2023-01-10T23:04:27.909758Z"
     }
    },
    "outputs": [],
@@ -196,8 +196,8 @@
    "execution_count": 4,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:55.765767Z",
-     "start_time": "2023-01-10T18:19:55.723673Z"
+     "end_time": "2023-01-10T23:04:27.956375Z",
+     "start_time": "2023-01-10T23:04:27.916517Z"
     }
    },
    "outputs": [],
@@ -221,8 +221,8 @@
    "execution_count": 5,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:55.903447Z",
-     "start_time": "2023-01-10T18:19:55.768948Z"
+     "end_time": "2023-01-10T23:04:28.075025Z",
+     "start_time": "2023-01-10T23:04:27.958968Z"
     }
    },
    "outputs": [],
@@ -235,8 +235,8 @@
    "execution_count": 6,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:55.941977Z",
-     "start_time": "2023-01-10T18:19:55.906449Z"
+     "end_time": "2023-01-10T23:04:28.112687Z",
+     "start_time": "2023-01-10T23:04:28.078199Z"
     }
    },
    "outputs": [],
@@ -260,8 +260,8 @@
    "execution_count": 7,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:56.137766Z",
-     "start_time": "2023-01-10T18:19:55.945844Z"
+     "end_time": "2023-01-10T23:04:28.333204Z",
+     "start_time": "2023-01-10T23:04:28.115708Z"
     }
    },
    "outputs": [
@@ -299,8 +299,8 @@
    "execution_count": 8,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:56.160565Z",
-     "start_time": "2023-01-10T18:19:56.144139Z"
+     "end_time": "2023-01-10T23:04:28.350099Z",
+     "start_time": "2023-01-10T23:04:28.335755Z"
     }
    },
    "outputs": [],
@@ -325,8 +325,8 @@
    "execution_count": 9,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:56.642527Z",
-     "start_time": "2023-01-10T18:19:56.164585Z"
+     "end_time": "2023-01-10T23:04:28.837537Z",
+     "start_time": "2023-01-10T23:04:28.352994Z"
     }
    },
    "outputs": [
@@ -372,8 +372,8 @@
    "execution_count": 10,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:56.696496Z",
-     "start_time": "2023-01-10T18:19:56.645242Z"
+     "end_time": "2023-01-10T23:04:28.891494Z",
+     "start_time": "2023-01-10T23:04:28.840129Z"
     }
    },
    "outputs": [],
@@ -405,8 +405,8 @@
    "execution_count": 11,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.031388Z",
-     "start_time": "2023-01-10T18:19:56.699040Z"
+     "end_time": "2023-01-10T23:04:29.218510Z",
+     "start_time": "2023-01-10T23:04:28.893647Z"
     }
    },
    "outputs": [
@@ -449,8 +449,8 @@
    "execution_count": 12,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.104495Z",
-     "start_time": "2023-01-10T18:19:57.033703Z"
+     "end_time": "2023-01-10T23:04:29.292374Z",
+     "start_time": "2023-01-10T23:04:29.226199Z"
     }
    },
    "outputs": [
@@ -485,8 +485,8 @@
    "execution_count": 13,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.112475Z",
-     "start_time": "2023-01-10T18:19:57.107265Z"
+     "end_time": "2023-01-10T23:04:29.299210Z",
+     "start_time": "2023-01-10T23:04:29.294422Z"
     }
    },
    "outputs": [
@@ -527,8 +527,8 @@
    "execution_count": 14,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.124623Z",
-     "start_time": "2023-01-10T18:19:57.115202Z"
+     "end_time": "2023-01-10T23:04:29.311349Z",
+     "start_time": "2023-01-10T23:04:29.301327Z"
     }
    },
    "outputs": [
@@ -627,8 +627,8 @@
    "execution_count": 15,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.138015Z",
-     "start_time": "2023-01-10T18:19:57.126446Z"
+     "end_time": "2023-01-10T23:04:29.327964Z",
+     "start_time": "2023-01-10T23:04:29.312943Z"
     }
    },
    "outputs": [
@@ -724,8 +724,8 @@
    "execution_count": 16,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.146725Z",
-     "start_time": "2023-01-10T18:19:57.140539Z"
+     "end_time": "2023-01-10T23:04:29.334313Z",
+     "start_time": "2023-01-10T23:04:29.330619Z"
     }
    },
    "outputs": [],
@@ -751,15 +751,15 @@
    "execution_count": 17,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.193470Z",
-     "start_time": "2023-01-10T18:19:57.149054Z"
+     "end_time": "2023-01-10T23:04:29.667783Z",
+     "start_time": "2023-01-10T23:04:29.336901Z"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "<spopt.locate.coverage.LSCP at 0x15fb2b0d0>"
+       "<spopt.locate.coverage.LSCP at 0x15aafcd90>"
       ]
      },
      "execution_count": 17,
@@ -784,8 +784,8 @@
    "execution_count": 18,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.207249Z",
-     "start_time": "2023-01-10T18:19:57.196684Z"
+     "end_time": "2023-01-10T23:04:29.682819Z",
+     "start_time": "2023-01-10T23:04:29.670368Z"
     }
    },
    "outputs": [
@@ -878,8 +878,8 @@
    "execution_count": 19,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.255221Z",
-     "start_time": "2023-01-10T18:19:57.209332Z"
+     "end_time": "2023-01-10T23:04:29.730317Z",
+     "start_time": "2023-01-10T23:04:29.685128Z"
     }
    },
    "outputs": [],
@@ -908,8 +908,8 @@
    "execution_count": 20,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.302812Z",
-     "start_time": "2023-01-10T18:19:57.258781Z"
+     "end_time": "2023-01-10T23:04:29.777401Z",
+     "start_time": "2023-01-10T23:04:29.733472Z"
     }
    },
    "outputs": [],
@@ -938,8 +938,8 @@
    "execution_count": 21,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.350809Z",
-     "start_time": "2023-01-10T18:19:57.305776Z"
+     "end_time": "2023-01-10T23:04:29.822844Z",
+     "start_time": "2023-01-10T23:04:29.780531Z"
     }
    },
    "outputs": [],
@@ -968,8 +968,8 @@
    "execution_count": 22,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.401709Z",
-     "start_time": "2023-01-10T18:19:57.354465Z"
+     "end_time": "2023-01-10T23:04:29.873260Z",
+     "start_time": "2023-01-10T23:04:29.826601Z"
     }
    },
    "outputs": [],
@@ -998,8 +998,8 @@
    "execution_count": 23,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.454028Z",
-     "start_time": "2023-01-10T18:19:57.404811Z"
+     "end_time": "2023-01-10T23:04:29.923169Z",
+     "start_time": "2023-01-10T23:04:29.876581Z"
     }
    },
    "outputs": [],
@@ -1028,8 +1028,8 @@
    "execution_count": 24,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.464958Z",
-     "start_time": "2023-01-10T18:19:57.457511Z"
+     "end_time": "2023-01-10T23:04:29.933682Z",
+     "start_time": "2023-01-10T23:04:29.926791Z"
     }
    },
    "outputs": [
@@ -1087,8 +1087,8 @@
    "execution_count": 25,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.570952Z",
-     "start_time": "2023-01-10T18:19:57.466945Z"
+     "end_time": "2023-01-10T23:04:30.044786Z",
+     "start_time": "2023-01-10T23:04:29.935872Z"
     }
    },
    "outputs": [],
@@ -1192,8 +1192,8 @@
    "execution_count": 26,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.583710Z",
-     "start_time": "2023-01-10T18:19:57.580222Z"
+     "end_time": "2023-01-10T23:04:30.050946Z",
+     "start_time": "2023-01-10T23:04:30.047184Z"
     }
    },
    "outputs": [],
@@ -1206,8 +1206,8 @@
    "execution_count": 27,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:57.999143Z",
-     "start_time": "2023-01-10T18:19:57.586461Z"
+     "end_time": "2023-01-10T23:04:30.474871Z",
+     "start_time": "2023-01-10T23:04:30.053102Z"
     }
    },
    "outputs": [
@@ -1247,8 +1247,8 @@
    "execution_count": 28,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:58.391013Z",
-     "start_time": "2023-01-10T18:19:58.001811Z"
+     "end_time": "2023-01-10T23:04:30.896633Z",
+     "start_time": "2023-01-10T23:04:30.477992Z"
     }
    },
    "outputs": [
@@ -1288,8 +1288,8 @@
    "execution_count": 29,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:58.863044Z",
-     "start_time": "2023-01-10T18:19:58.393714Z"
+     "end_time": "2023-01-10T23:04:31.422405Z",
+     "start_time": "2023-01-10T23:04:30.899081Z"
     }
    },
    "outputs": [
@@ -1329,8 +1329,8 @@
    "execution_count": 30,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:59.275307Z",
-     "start_time": "2023-01-10T18:19:58.865723Z"
+     "end_time": "2023-01-10T23:04:31.824194Z",
+     "start_time": "2023-01-10T23:04:31.425265Z"
     }
    },
    "outputs": [
@@ -1370,8 +1370,8 @@
    "execution_count": 31,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:19:59.660217Z",
-     "start_time": "2023-01-10T18:19:59.278736Z"
+     "end_time": "2023-01-10T23:04:32.228895Z",
+     "start_time": "2023-01-10T23:04:31.826665Z"
     }
    },
    "outputs": [
@@ -1411,8 +1411,8 @@
    "execution_count": 32,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:00.092469Z",
-     "start_time": "2023-01-10T18:19:59.662886Z"
+     "end_time": "2023-01-10T23:04:32.641725Z",
+     "start_time": "2023-01-10T23:04:32.231423Z"
     }
    },
    "outputs": [
@@ -1453,8 +1453,8 @@
    "execution_count": 33,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.467301Z",
-     "start_time": "2023-01-10T18:20:00.094647Z"
+     "end_time": "2023-01-10T23:04:34.693483Z",
+     "start_time": "2023-01-10T23:04:32.644278Z"
     }
    },
    "outputs": [
@@ -1501,8 +1501,8 @@
    "execution_count": 34,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.473687Z",
-     "start_time": "2023-01-10T18:20:02.469714Z"
+     "end_time": "2023-01-10T23:04:34.699660Z",
+     "start_time": "2023-01-10T23:04:34.696062Z"
     }
    },
    "outputs": [],
@@ -1529,8 +1529,8 @@
    "execution_count": 35,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.607861Z",
-     "start_time": "2023-01-10T18:20:02.476731Z"
+     "end_time": "2023-01-10T23:04:34.807693Z",
+     "start_time": "2023-01-10T23:04:34.702017Z"
     }
    },
    "outputs": [],
@@ -1563,8 +1563,8 @@
    "execution_count": 36,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.615185Z",
-     "start_time": "2023-01-10T18:20:02.611192Z"
+     "end_time": "2023-01-10T23:04:34.814997Z",
+     "start_time": "2023-01-10T23:04:34.810702Z"
     }
    },
    "outputs": [],
@@ -1585,8 +1585,8 @@
    "execution_count": 37,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.628194Z",
-     "start_time": "2023-01-10T18:20:02.617579Z"
+     "end_time": "2023-01-10T23:04:34.823001Z",
+     "start_time": "2023-01-10T23:04:34.817295Z"
     }
    },
    "outputs": [
@@ -1633,8 +1633,8 @@
    "execution_count": 38,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:02.641664Z",
-     "start_time": "2023-01-10T18:20:02.631018Z"
+     "end_time": "2023-01-10T23:04:34.834881Z",
+     "start_time": "2023-01-10T23:04:34.825818Z"
     }
    },
    "outputs": [
@@ -1779,8 +1779,8 @@
    "execution_count": 39,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:03.747326Z",
-     "start_time": "2023-01-10T18:20:02.644743Z"
+     "end_time": "2023-01-10T23:04:35.725743Z",
+     "start_time": "2023-01-10T23:04:34.843310Z"
     }
    },
    "outputs": [
@@ -1832,8 +1832,8 @@
    "execution_count": 40,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:04.672051Z",
-     "start_time": "2023-01-10T18:20:03.750221Z"
+     "end_time": "2023-01-10T23:04:36.585753Z",
+     "start_time": "2023-01-10T23:04:35.728435Z"
     }
    },
    "outputs": [
@@ -1881,8 +1881,8 @@
    "execution_count": 41,
    "metadata": {
     "ExecuteTime": {
-     "end_time": "2023-01-10T18:20:05.818278Z",
-     "start_time": "2023-01-10T18:20:04.675097Z"
+     "end_time": "2023-01-10T23:04:37.624128Z",
+     "start_time": "2023-01-10T23:04:36.588495Z"
     }
    },
    "outputs": [
diff --git a/spopt/locate/base.py b/spopt/locate/base.py
index 33ec42e6..f2ea60bb 100644
--- a/spopt/locate/base.py
+++ b/spopt/locate/base.py
@@ -232,11 +232,13 @@ def add_client_integer_variable(
         setattr(obj, "cli_vars", cli_vars)
 
     @staticmethod
-    def add_client_assign_integer_variable(
+    def add_client_assign_variable(
         obj: T_FacModel,
         range_client: range,
         range_facility: range,
         var_name: str,
+        low_bound=0,
+        up_bound=1,
         lp_category=pulp.LpInteger,
     ) -> None:
         """Client assignment integer decision variables (used for allocation).
@@ -252,6 +254,10 @@ def add_client_assign_integer_variable(
             The range of facility points.
         var_name : str
             A formatted string for the  client assignment variable name.
+        low_bound : int (default 0)
+            The lower bound for variable values. Set to ``None`` for no lower bound.
+        up_bound : int (default 1)
+            The upper bound for variable values. Set to ``None`` for no upper bound.
         lp_category : pulp.LpVariable parameter
             The category this variable is in,
             ``pulp.LpInteger`` or ``pulp.LpContinuous``.
@@ -268,8 +274,8 @@ def add_client_assign_integer_variable(
                 [
                     pulp.LpVariable(
                         var_name.format(i=i, j=j),
-                        lowBound=0,
-                        upBound=1,
+                        lowBound=low_bound,
+                        upBound=up_bound,
                         cat=lp_category,
                     )
                     for j in range_facility
diff --git a/spopt/locate/coverage.py b/spopt/locate/coverage.py
index 2322d29c..20f9bd94 100644
--- a/spopt/locate/coverage.py
+++ b/spopt/locate/coverage.py
@@ -256,8 +256,13 @@ def from_cost_matrix(
                     f"({sum_demand} > {sum_capacity})."
                 )
 
-            FacilityModelBuilder.add_client_assign_integer_variable(
-                lscp, r_cli, r_fac, "z[{i}_{j}]", lp_category=pulp.LpContinuous
+            FacilityModelBuilder.add_client_assign_variable(
+                lscp,
+                r_cli,
+                r_fac,
+                "z[{i}_{j}]",
+                up_bound=None,
+                lp_category=pulp.LpContinuous,
             )
 
             FacilityModelBuilder.add_facility_capacity_constraint(
diff --git a/spopt/locate/p_center.py b/spopt/locate/p_center.py
index 32c9c13a..f4abbba6 100644
--- a/spopt/locate/p_center.py
+++ b/spopt/locate/p_center.py
@@ -193,7 +193,7 @@ def from_cost_matrix(
         p_center = PCenter(name, model, cost_matrix)
 
         FacilityModelBuilder.add_facility_integer_variable(p_center, r_fac, "y[{i}]")
-        FacilityModelBuilder.add_client_assign_integer_variable(
+        FacilityModelBuilder.add_client_assign_variable(
             p_center, r_cli, r_fac, "z[{i}_{j}]"
         )
         FacilityModelBuilder.add_weight_continuous_variable(p_center)
diff --git a/spopt/locate/p_median.py b/spopt/locate/p_median.py
index ca327f59..74d13976 100644
--- a/spopt/locate/p_median.py
+++ b/spopt/locate/p_median.py
@@ -242,7 +242,7 @@ def from_cost_matrix(
         p_median = PMedian(name, model, aij, weights_sum)
 
         FacilityModelBuilder.add_facility_integer_variable(p_median, r_fac, "y[{i}]")
-        FacilityModelBuilder.add_client_assign_integer_variable(
+        FacilityModelBuilder.add_client_assign_variable(
             p_median, r_cli, r_fac, "z[{i}_{j}]"
         )