diff --git a/include/ttmlir/Scheduler/PrecedenceScheduler.h b/include/ttmlir/Scheduler/PrecedenceScheduler.h
index ae4174695..c40c3be63 100644
--- a/include/ttmlir/Scheduler/PrecedenceScheduler.h
+++ b/include/ttmlir/Scheduler/PrecedenceScheduler.h
@@ -12,7 +12,7 @@ namespace mlir::tt::scheduler {
 class PrecedenceScheduler : public Scheduler {
 public:
   // Constructor taking an MLIR Operation (or a module)
-  PrecedenceScheduler(func::FuncOp *root) : Scheduler(root) {};
+  PrecedenceScheduler(func::FuncOp *root);
 
   // Copy constructor
   PrecedenceScheduler(const PrecedenceScheduler &scheduler)
@@ -34,6 +34,12 @@ class PrecedenceScheduler : public Scheduler {
   // Map of precedence
   llvm::DenseMap<mlir::Operation *, llvm::SmallVector<mlir::Operation *>>
       precedence;
+  // Output op of the function
+  mlir::Operation *outputOp;
+
+  // DFS schedule construction based on a precedence map
+  llvm::DenseSet<mlir::Operation *> visitedOps;
+  void constructSchedule(mlir::Operation *op);
 };
 
 } // namespace mlir::tt::scheduler
diff --git a/include/ttmlir/Scheduler/QueueScheduler.h b/include/ttmlir/Scheduler/QueueScheduler.h
index 44d351857..d3471d997 100644
--- a/include/ttmlir/Scheduler/QueueScheduler.h
+++ b/include/ttmlir/Scheduler/QueueScheduler.h
@@ -28,10 +28,6 @@ class QueueScheduler : public Scheduler {
 
   // Method to take a snapshot of the scheduler
   std::unique_ptr<Scheduler> snapshot() final;
-
-private:
-  // Method to check if an operation can be scheduled
-  bool canSchedule(mlir::Operation *op);
 };
 
 } // namespace mlir::tt::scheduler
diff --git a/include/ttmlir/Scheduler/Scheduler.h b/include/ttmlir/Scheduler/Scheduler.h
index ea88f875a..0fcde8a20 100644
--- a/include/ttmlir/Scheduler/Scheduler.h
+++ b/include/ttmlir/Scheduler/Scheduler.h
@@ -42,6 +42,9 @@ class Scheduler {
   // Method to check if there are unscheduled operations
   bool hasUnscheduledOps() const;
 
+  // Method to check if an operation can be scheduled
+  bool canSchedule(mlir::Operation *op);
+
 protected:
   // Map of dependencies
   llvm::DenseMap<mlir::Operation *, llvm::SmallVector<mlir::Operation *>>
@@ -49,7 +52,7 @@ class Scheduler {
 
   // Sets of unscheduled / schedulable / scheduled operations
   llvm::DenseSet<mlir::Operation *> unscheduledOps;
-  llvm::SmallVector<mlir::Operation *> schedulableOps;
+  llvm::DenseSet<mlir::Operation *> schedulableOps;
   llvm::DenseSet<mlir::Operation *> scheduledOps;
 
   // Operation schedule in order of execution
diff --git a/lib/Scheduler/PrecedenceScheduler.cpp b/lib/Scheduler/PrecedenceScheduler.cpp
index c18f1cdd3..c161ee7fd 100644
--- a/lib/Scheduler/PrecedenceScheduler.cpp
+++ b/lib/Scheduler/PrecedenceScheduler.cpp
@@ -6,18 +6,58 @@
 
 namespace mlir::tt::scheduler {
 
-void PrecedenceScheduler::scheduleOp(mlir::Operation *op) { return; }
+PrecedenceScheduler::PrecedenceScheduler(func::FuncOp *root) : Scheduler(root) {
+  root->walk([&](mlir::Operation *op) {
+    if (op->hasTrait<mlir::OpTrait::ReturnLike>()) {
+      outputOp = op;
+    }
+  });
+}
+
+void PrecedenceScheduler::scheduleOp(mlir::Operation *op) {
+  unscheduledOps.erase(op);
+  schedulableOps.erase(op);
+  scheduledOps.insert(op);
+
+  OpResult result = op->getResult(0);
+  for (mlir::Operation *use : result.getUsers()) {
+    precedence[use].push_back(op);
+
+    // Check the schedulability of the user op after scheduling the current op
+    //
+    if (canSchedule(use)) {
+      schedulableOps.insert(use);
+    }
+  }
+}
 
 llvm::SmallVector<mlir::Operation *> PrecedenceScheduler::getScheduleableOps() {
-  return {};
+  return llvm::SmallVector<mlir::Operation *>(schedulableOps.begin(),
+                                              schedulableOps.end());
 }
 
 llvm::SmallVector<mlir::Operation *> PrecedenceScheduler::getSchedule() {
-  return {};
+  constructSchedule(outputOp);
+  return schedule;
 }
 
 std::unique_ptr<Scheduler> PrecedenceScheduler::snapshot() {
   return std::make_unique<PrecedenceScheduler>(*this);
 }
 
+void PrecedenceScheduler::constructSchedule(mlir::Operation *op) {
+  // Schedule all the precedents of the current operation
+  //
+  for (mlir::Operation *precedent : precedence[op]) {
+    if (!visitedOps.count(precedent)) {
+      constructSchedule(precedent);
+    }
+  }
+
+  // Schedule the current operation
+  //
+  visitedOps.insert(op);
+  schedule.push_back(op);
+}
+
 } // namespace mlir::tt::scheduler
diff --git a/lib/Scheduler/QueueScheduler.cpp b/lib/Scheduler/QueueScheduler.cpp
index ad29e1499..68c0bba5b 100644
--- a/lib/Scheduler/QueueScheduler.cpp
+++ b/lib/Scheduler/QueueScheduler.cpp
@@ -31,14 +31,4 @@ std::unique_ptr<Scheduler> QueueScheduler::snapshot() {
   return std::make_unique<QueueScheduler>(*this);
 }
 
-bool QueueScheduler::canSchedule(mlir::Operation *op) {
-  for (mlir::Operation *dep : dependencies[op]) {
-    if (!scheduledOps.count(dep)) {
-      return false;
-    }
-  }
-
-  return true;
-}
-
 } // namespace mlir::tt::scheduler
diff --git a/lib/Scheduler/Scheduler.cpp b/lib/Scheduler/Scheduler.cpp
index ec0bad28b..451c2b2e3 100644
--- a/lib/Scheduler/Scheduler.cpp
+++ b/lib/Scheduler/Scheduler.cpp
@@ -52,6 +52,13 @@ Scheduler::Scheduler(func::FuncOp *func) {
       }
     }
   }
+
+  // Find the schedulable ops
+  for (const auto &entry : dependencies) {
+    if (entry.second.empty()) {
+      schedulableOps.insert(entry.first);
+    }
+  }
 }
 
 Scheduler::Scheduler(const Scheduler &scheduler)
@@ -62,4 +69,14 @@ Scheduler::Scheduler(const Scheduler &scheduler)
 
 bool Scheduler::hasUnscheduledOps() const { return !unscheduledOps.empty(); }
 
+bool Scheduler::canSchedule(mlir::Operation *op) {
+  for (mlir::Operation *dep : dependencies[op]) {
+    if (!scheduledOps.count(dep)) {
+      return false;
+    }
+  }
+
+  return true;
+}
+
 } // namespace mlir::tt::scheduler
diff --git a/test/unittests/TestScheduler/TestScheduler.cpp b/test/unittests/TestScheduler/TestScheduler.cpp
index 80a2f4954..29b3c16ad 100644
--- a/test/unittests/TestScheduler/TestScheduler.cpp
+++ b/test/unittests/TestScheduler/TestScheduler.cpp
@@ -18,6 +18,7 @@
 
 #include "ttmlir/Dialect/TT/IR/TT.h"
 #include "ttmlir/Dialect/TTIR/IR/TTIR.h"
+#include "ttmlir/Scheduler/PrecedenceScheduler.h"
 #include "ttmlir/Scheduler/QueueScheduler.h"
 
 #include "ttmlir/Dialect/TT/IR/TTOpsTypes.h"
@@ -244,3 +245,25 @@ TEST_F(SchedulerBase, VerifyFork) {
   scheduler.scheduleOp(scheduleableOps[0]);
   ASSERT_FALSE(scheduler.hasUnscheduledOps());
 }
+
+// This tests the precedenceScheduler with a single operation
+TEST_F(SchedulerBase, SingleOpPrecedenceScheduler) {
+  mlir::Value dest = createEmptyTensor();
+  mlir::Value lhs = func.getBody().getBlocks().front().getArgument(0);
+  mlir::Value rhs = func.getBody().getBlocks().front().getArgument(1);
+
+  mlir::ArrayAttr attrs = builder.getArrayAttr(createOperandConstraints());
+
+  // First operation has arg1 and arg2 and %0 as dps operand
+  ttir::TTIROp op = builder.create<ttir::AddOp>(builder.getUnknownLoc(), lhs,
+                                                rhs, dest, attrs);
+
+  mlir::tt::scheduler::PrecedenceScheduler scheduler(&func);
+  ASSERT_TRUE(scheduler.hasUnscheduledOps());
+  llvm::SmallVector<mlir::Operation *> scheduleableOps =
+      scheduler.getScheduleableOps();
+  ASSERT_EQ(scheduleableOps.size(), 1);
+  scheduler.scheduleOp(scheduleableOps[0]);
+  ASSERT_FALSE(scheduler.hasUnscheduledOps());
+  ASSERT_EQ(scheduleableOps[0], op.getOperation());
+}