diff --git a/tests/test_planning.py b/tests/test_planning.py
index 640b6c64c..c395f0c15 100644
--- a/tests/test_planning.py
+++ b/tests/test_planning.py
@@ -257,9 +257,9 @@ def test_forward_plan():
     assert expr('Load(C2, P2, JFK)') in air_cargo_solution
     assert expr('Fly(P2, JFK, SFO)') in air_cargo_solution
     assert expr('Unload(C2, P2, SFO)') in air_cargo_solution
-    assert expr('Load(C1, P2, SFO)') in air_cargo_solution
-    assert expr('Fly(P2, SFO, JFK)') in air_cargo_solution
-    assert expr('Unload(C1, P2, JFK)') in air_cargo_solution
+    assert expr('Load(C1, P1, SFO)') in air_cargo_solution
+    assert expr('Fly(P1, SFO, JFK)') in air_cargo_solution
+    assert expr('Unload(C1, P1, JFK)') in air_cargo_solution
 
     sussman_anomaly_solution = astar_search(ForwardPlan(three_block_tower())).solution()
     sussman_anomaly_solution = list(map(lambda action: Expr(action.name, *action.args), sussman_anomaly_solution))
@@ -275,11 +275,12 @@ def test_forward_plan():
 
     shopping_problem_solution = astar_search(ForwardPlan(shopping_problem())).solution()
     shopping_problem_solution = list(map(lambda action: Expr(action.name, *action.args), shopping_problem_solution))
-    assert expr('Go(Home, SM)') in shopping_problem_solution
     assert expr('Buy(Banana, SM)') in shopping_problem_solution
     assert expr('Buy(Milk, SM)') in shopping_problem_solution
-    assert expr('Go(SM, HW)') in shopping_problem_solution
     assert expr('Buy(Drill, HW)') in shopping_problem_solution
+    # the plan must reach both stores; the exact route may vary by tie-breaking
+    assert expr('Go(Home, SM)') in shopping_problem_solution or expr('Go(HW, SM)') in shopping_problem_solution
+    assert expr('Go(Home, HW)') in shopping_problem_solution or expr('Go(SM, HW)') in shopping_problem_solution
 
 
 def test_backward_plan():
diff --git a/tests/test_utils.py b/tests/test_utils.py
index 6c2a50808..21cf9a437 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -299,5 +299,15 @@ def __eq__(self, other):
     assert len(queue) == 0
 
 
+def test_priority_queue_ties_with_non_comparable_items():
+    # Items with equal priority must never be compared with each other
+    # (these dicts are not orderable); ties keep insertion (FIFO) order.
+    queue = PriorityQueue(f=lambda d: d['cost'])
+    queue.append({'cost': 1, 'id': 'a'})
+    queue.append({'cost': 1, 'id': 'b'})
+    queue.append({'cost': 0, 'id': 'c'})
+    assert [queue.pop()['id'] for _ in range(3)] == ['c', 'a', 'b']
+
+
 if __name__ == '__main__':
     pytest.main()
diff --git a/utils.py b/utils.py
index 3158e3793..4ed9980f4 100644
--- a/utils.py
+++ b/utils.py
@@ -728,6 +728,9 @@ class PriorityQueue:
 
     def __init__(self, order='min', f=lambda x: x):
         self.heap = []
+        # monotonic tie-breaker so items with equal priority are never compared
+        # (which would fail for non-comparable items); ties keep insertion order
+        self.counter = 0
         if order == 'min':
             self.f = f
         elif order == 'max':  # now item with max f(x)
@@ -737,7 +740,8 @@ def __init__(self, order='min', f=lambda x: x):
 
     def append(self, item):
         """Insert item at its correct position."""
-        heapq.heappush(self.heap, (self.f(item), item))
+        heapq.heappush(self.heap, (self.f(item), self.counter, item))
+        self.counter += 1
 
     def extend(self, items):
         """Insert each item in items at its correct position."""
@@ -748,7 +752,7 @@ def pop(self):
         """Pop and return the item (with min or max f(x) value)
         depending on the order."""
         if self.heap:
-            return heapq.heappop(self.heap)[1]
+            return heapq.heappop(self.heap)[-1]
         else:
             raise Exception('Trying to pop from empty PriorityQueue.')
 
@@ -758,12 +762,12 @@ def __len__(self):
 
     def __contains__(self, key):
         """Return True if the key is in PriorityQueue."""
-        return any([item == key for _, item in self.heap])
+        return any(item == key for *_, item in self.heap)
 
     def __getitem__(self, key):
         """Returns the first value associated with key in PriorityQueue.
         Raises KeyError if key is not present."""
-        for value, item in self.heap:
+        for value, _, item in self.heap:
             if item == key:
                 return value
         raise KeyError(str(key) + " is not in the priority queue")
@@ -771,7 +775,7 @@ def __getitem__(self, key):
     def __delitem__(self, key):
         """Delete the first occurrence of key."""
         try:
-            del self.heap[[item == key for _, item in self.heap].index(True)]
+            del self.heap[[item == key for *_, item in self.heap].index(True)]
         except ValueError:
             raise KeyError(str(key) + " is not in the priority queue")
         heapq.heapify(self.heap)