diff --git a/src/andromede/expression/operators_expansion.py b/src/andromede/expression/operators_expansion.py
index f0f530b..03fa215 100644
--- a/src/andromede/expression/operators_expansion.py
+++ b/src/andromede/expression/operators_expansion.py
@@ -106,10 +106,10 @@ def scenario_operator(self, node: ScenarioOperatorNode) -> ExpressionNode:
             nodes.append(apply_scenario(operand, t))
         return sum_expressions(nodes) / self.scenarios_count
 
-    def pb_parameter(self, node: ProblemParameterNode) -> T:
+    def pb_parameter(self, node: ProblemParameterNode) -> ExpressionNode:
         raise ValueError("Should not reach")
 
-    def pb_variable(self, node: ProblemVariableNode) -> T:
+    def pb_variable(self, node: ProblemVariableNode) -> ExpressionNode:
         raise ValueError("Should not reach")
 
 
diff --git a/src/andromede/simulation/linear_expression.py b/src/andromede/simulation/linear_expression.py
index ebe0fbf..fd187aa 100644
--- a/src/andromede/simulation/linear_expression.py
+++ b/src/andromede/simulation/linear_expression.py
@@ -156,15 +156,6 @@ def _scenario_index_to_str(scenario_index: ScenarioIndex) -> str:
     return ""
 
 
-def _str_for_coeff(coeff: float) -> str:
-    if is_one(coeff):
-        return "+"
-    elif is_minus_one(coeff):
-        return "-"
-    else:
-        return "{:+g}".format(coeff)
-
-
 def _str_for_time_expansion(exp: TimeExpansion) -> str:
     if isinstance(exp, TimeShiftExpansion):
         return f".shift({exp.shift})"
diff --git a/src/andromede/simulation/linearize.py b/src/andromede/simulation/linearize.py
index 13b5372..454ce67 100644
--- a/src/andromede/simulation/linearize.py
+++ b/src/andromede/simulation/linearize.py
@@ -12,7 +12,7 @@
 
 from abc import ABC, abstractmethod
 from dataclasses import dataclass
-from typing import List, Optional
+from typing import Any, Dict, List, Optional, Union
 
 from andromede.expression import (
     AdditionNode,
@@ -34,6 +34,7 @@
     ParameterNode,
     PortFieldAggregatorNode,
     PortFieldNode,
+    ProblemParameterNode,
     ProblemVariableNode,
     ScenarioIndex,
     ScenarioOperatorNode,
@@ -89,7 +90,7 @@ class LinearExpressionData:
     constant: float
 
     def build(self) -> LinearExpression:
-        res_terms = {}
+        res_terms: Dict[TermKey, Any] = {}
         for t in self.terms:
             k = t.to_key()
             if k in res_terms:
@@ -120,7 +121,7 @@ def negation(self, node: NegationNode) -> LinearExpressionData:
     def addition(self, node: AdditionNode) -> LinearExpressionData:
         operands = [visit(o, self) for o in node.operands]
         terms = []
-        constant = 0
+        constant: float = 0
         for o in operands:
             constant += o.constant
             terms.extend(o.terms)
@@ -170,12 +171,18 @@ def _get_timestep(self, time_index: TimeIndex) -> int:
             return time_index.timestep
         if isinstance(time_index, NoTimeIndex):
             return self.timestep
+        else:
+            raise TypeError(f"Type {type(time_index)} is not a valid TimeIndex type.")
 
     def _get_scenario(self, scenario_index: ScenarioIndex) -> int:
         if isinstance(scenario_index, OneScenarioIndex):
             return scenario_index.scenario
         if isinstance(scenario_index, NoScenarioIndex):
             return self.scenario
+        else:
+            raise TypeError(
+                f"Type {type(scenario_index)} is not a valid TimeIndex type."
+            )
 
     def literal(self, node: LiteralNode) -> LinearExpressionData:
         return LinearExpressionData([], node.value)
@@ -215,7 +222,7 @@ def comp_parameter(self, node: ComponentParameterNode) -> LinearExpressionData:
             "Parameters need to be associated with their timestep/scenario before linearization."
         )
 
-    def pb_parameter(self, node: ProblemVariableNode) -> LinearExpressionData:
+    def pb_parameter(self, node: ProblemParameterNode) -> LinearExpressionData:
         # TODO SL: not the best place to do this.
         # in the future, we should evaluate coefficients of variables as time vectors once for all timesteps
         time_index = self._get_timestep(node.time_index)
diff --git a/src/andromede/simulation/optimization.py b/src/andromede/simulation/optimization.py
index 42562fd..eec666c 100644
--- a/src/andromede/simulation/optimization.py
+++ b/src/andromede/simulation/optimization.py
@@ -244,29 +244,8 @@ def get_variable(
             scenario,
             self.component.id,
             variable_name,
-            self.component.model.variables[variable_name].structure,
         )
 
-    def linearize_expression(
-        self,
-        block_timestep: int,
-        scenario: int,
-        expression: ExpressionNode,
-    ) -> LinearExpression:
-        parameters_valued_provider = _make_parameter_value_provider(
-            self.opt_context, block_timestep, scenario
-        )
-        evaluated_expr = resolve_parameters(expression, parameters_valued_provider)
-
-        value_provider = _make_value_provider(
-            self.opt_context, block_timestep, scenario, self.component
-        )
-        structure_provider = _make_data_structure_provider(
-            self.opt_context.network, self.component
-        )
-
-        return linearize_expression(evaluated_expr, structure_provider, value_provider)
-
 
 class BlockBorderManagement(Enum):
     """
@@ -338,7 +317,7 @@ def connection_fields_expressions(self) -> Dict[PortFieldKey, List[ExpressionNod
     def block_timestep_to_absolute_timestep(self, block_timestep: int) -> int:
         return self._block.timesteps[self.get_actual_block_timestep(block_timestep)]
 
-    def get_actual_block_timestep(self, block_timestep):
+    def get_actual_block_timestep(self, block_timestep: int) -> int:
         if self._border_management == BlockBorderManagement.CYCLE:
             return block_timestep % self.block_length()
         else: