diff --git a/src/optimizer/optimizer.py b/src/optimizer/optimizer.py
index fa7eeb17c..4ac1b98ff 100644
--- a/src/optimizer/optimizer.py
+++ b/src/optimizer/optimizer.py
@@ -141,7 +141,10 @@ def _setup_variables(self):
         self.variables['s'] = {}
         for i, bat in enumerate(self.batteries):
             self.variables['s'][i] = [
-                pulp.LpVariable(f"s_{i}_{t}", lowBound=0, upBound=bat.s_capacity)
+                pulp.LpVariable(
+                    f"s_{i}_{t}",
+                    lowBound=bat.s_min if bat.s_min <= bat.s_initial <= bat.s_max else 0,
+                    upBound=bat.s_max if bat.s_min <= bat.s_initial <= bat.s_max else bat.s_capacity)
                 for t in self.time_steps
             ]
 
@@ -323,7 +326,10 @@ def _setup_target_function(self):
                 objective += self.variables['c'][i][t] * self.min_import_price * 5e-5 * (self.T - t) * bat.c_priority
                 objective += self.variables['d'][i][t] * self.min_import_price * 5e-5 * (self.T - t) * bat.c_priority
 
-        self.problem += objective
+        # scale the solver-facing objective so CBC's absolute tolerances
+        # (integrality 1e-6, cutoff increment 1e-5) can separate near-ties;
+        # reported values are recomputed from variables and stay unscaled
+        self.problem += objective * 1e4
 
     def _add_energy_balance_constraints(self):
         """
@@ -430,6 +436,8 @@ def _add_battery_constraints(self):
         # greater than the maximum SOC or lesser than min SOC, maximum discharging is forced until the max.
         # SOC is reached or max. charing will be forced until min SOC is reached.
         for i, bat in enumerate(self.batteries):
+            if bat.s_min <= bat.s_initial <= bat.s_max:
+                continue  # SOC kept in range by hard variable bounds
             for t in range(0, self.T):
                 self.problem += (self.variables['s_max_pen'][i][t] >= self.variables['s'][i][t] - bat.s_max)
                 self.problem += (self.variables['s_min_pen'][i][t] >= bat.s_min - self.variables['s'][i][t])
diff --git a/test_cases/013-grid-export-limit-hit.json b/test_cases/013-grid-export-limit-hit.json
index 53863f505..4a3d34bcf 100644
--- a/test_cases/013-grid-export-limit-hit.json
+++ b/test_cases/013-grid-export-limit-hit.json
@@ -199,7 +199,7 @@
     },
     "expected_response": {
         "status": "Optimal",
-        "objective_value": 17.5372629588039,
+        "objective_value": 17.531374666979104,
         "limit_violations": {
             "grid_import_limit_exceeded": false,
             "grid_export_limit_hit": true
diff --git a/test_cases/019-unexpected-charge-spikes.json b/test_cases/019-unexpected-charge-spikes.json
index b61ffda0a..5d00cc867 100644
--- a/test_cases/019-unexpected-charge-spikes.json
+++ b/test_cases/019-unexpected-charge-spikes.json
@@ -274,7 +274,7 @@
     },
     "expected_response": {
         "status": "Optimal",
-        "objective_value": 1.2481766551776774,
+        "objective_value": 1.2393735754976773,
         "limit_violations": {
             "grid_import_limit_exceeded": false,
             "grid_export_limit_hit": false