Added slack to CostOptimiser in the case of no feasible solution

.idea/Model.iml

@@ -7,7 +7,7 @@
       <sourceFolder url="file://$MODULE_DIR$/open_uprn" isTestSource="false" />
       <sourceFolder url="file://$MODULE_DIR$/recommendations" isTestSource="false" />
     </content>
-    <orderEntry type="jdk" jdkName="Python 3.10 (simulation_system_prediction)" jdkType="Python SDK" />
+    <orderEntry type="jdk" jdkName="Python 3.10 (backend)" jdkType="Python SDK" />
     <orderEntry type="sourceFolder" forTests="false" />
   </component>
 </module>

.idea/misc.xml

@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
-  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.10 (simulation_system_prediction)" project-jdk-type="Python SDK" />
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.10 (backend)" project-jdk-type="Python SDK" />
   <component name="PythonCompatibilityInspectionAdvertiser">
     <option name="version" value="3" />
   </component>

model_data/optimiser/CostOptimiser.py

@@ -1,4 +1,7 @@
-from mip import Model, xsum, minimize, BINARY
+from mip import Model, xsum, minimize, BINARY, OptimizationStatus
+from utils.logger import setup_logger
+
+logger = setup_logger()
 
 
 class CostOptimiser:
@@ -9,6 +12,7 @@ class CostOptimiser:
     def __init__(self, components, min_gain):
         self.components = components
         self.min_gain = min_gain
+        self.gain_constraint = None
         self.m = None
         self.variables = []
         self.solution = []
@@ -42,21 +46,51 @@ class CostOptimiser:
         # This constrain ensures that sum of gain_ig * x_ig >= min_gain, where gain_ig represents the gain for the ith
         # component
         # in group g, and x_ig is the binary decision variable for the ith component in group g
-        self.m += xsum(
+        gain_expression = xsum(
             item['gain'] * var for group, group_vars in zip(self.components, self.variables) for item, var in
             zip(group, group_vars)
         ) >= self.min_gain
 
+        self.gain_constraint = self.m.add_constr(gain_expression)
+
         # At most one item from each group
         # This constraint ensures that at most one item from each group is selected
         # This is expressed by summing up the decision variables for each group and ensuring that the sum is <= 1
         for group_vars in self.variables:
             self.m += xsum(var for var in group_vars) <= 1
 
+    def setup_slack(self):
+
+        # Remove the original gain constraint
+        self.m.remove(self.gain_constraint)
+        # Add slack variable
+        s = self.m.add_var(lb=0)
+
+        # Modify the constraint
+        self.m += xsum(
+            item['gain'] * var for group, group_vars in zip(self.components, self.variables) for item, var in
+            zip(group, group_vars)
+        ) + s >= self.min_gain
+
+        # Modify the objective to penalize the use of slack
+        penalty = 10000  # you can adjust this based on how much you want to penalize the use of slack
+        self.m.objective = minimize(
+            xsum(
+                component['cost'] * var for group, group_vars in zip(self.components, self.variables) for component, var
+                in
+                zip(group, group_vars)
+            ) + penalty * s
+        )
+
     def solve(self):
         # Solve the problem
         self.m.optimize()
 
+        if self.m.status == OptimizationStatus.INFEASIBLE:
+            logger.info("We have an infeasible model, setting up slack model")
+            self.setup_slack()
+            self.m.optimize()
+
         self.solution = [
             item for group, group_vars in zip(self.components, self.variables) for item, var in zip(group, group_vars)
             if