diff --git a/cmake/sources.cmake b/cmake/sources.cmake
index 89302f0e45f..9ad12a7a8cb 100644
--- a/cmake/sources.cmake
+++ b/cmake/sources.cmake
@@ -380,6 +380,7 @@ set(highs_sources
     mip/HighsImplications.cpp
     mip/HighsLpAggregator.cpp
     mip/HighsLpRelaxation.cpp
+    mip/HighsMachineSchedSeparator.cpp
     mip/HighsMipSolver.cpp
     mip/HighsMipSolverData.cpp
     mip/HighsMipWorker.cpp
@@ -510,6 +511,7 @@ set(highs_headers
     mip/HighsImplications.h
     mip/HighsLpAggregator.h
     mip/HighsLpRelaxation.h
+    mip/HighsMachineSchedSeparator.h
     mip/HighsMipSolver.h
     mip/HighsMipSolverData.h
     mip/HighsMipWorker.h
diff --git a/highs/meson.build b/highs/meson.build
index 897cf73f106..f593bca117f 100644
--- a/highs/meson.build
+++ b/highs/meson.build
@@ -268,6 +268,7 @@ _srcs = [
     'mip/HighsImplications.cpp',
     'mip/HighsLpAggregator.cpp',
     'mip/HighsLpRelaxation.cpp',
+    'mip/HighsMachineSchedSeparator.cpp',
     'mip/HighsMipSolver.cpp',
     'mip/HighsMipSolverData.cpp',
     'mip/HighsMipWorker.cpp',
diff --git a/highs/mip/HighsMachineSchedSeparator.cpp b/highs/mip/HighsMachineSchedSeparator.cpp
new file mode 100644
index 00000000000..bc93044b83d
--- /dev/null
+++ b/highs/mip/HighsMachineSchedSeparator.cpp
@@ -0,0 +1,298 @@
+/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+/*                                                                       */
+/*    This file is part of the HiGHS linear optimization suite           */
+/*                                                                       */
+/*    Available as open-source under the MIT License                     */
+/*                                                                       */
+/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+/**@file mip/HighsMachineSchedSeparator.cpp
+ */
+
+#include "mip/HighsMachineSchedSeparator.h"
+
+#include "../extern/pdqsort/pdqsort.h"
+#include "mip/HighsCutGeneration.h"
+#include "mip/HighsLpRelaxation.h"
+#include "mip/HighsMipSolverData.h"
+#include "mip/HighsTransformedLp.h"
+
+bool HighsMachineSchedSeparator::findSingleMachineScheduleClique(
+    std::vector<std::vector<double>>& vals,
+    std::vector<std::vector<HighsInt>>& inds, std::vector<double>& rhss,
+    const HighsDomain& globaldom, const HighsMipSolver& mipsolver) {
+  enum class ArcType {
+    kIfBinOne,
+    kIfBinZero,
+  };
+  HighsInt largestDegree = 0;
+  HighsInt largestDegreeCol = -1;
+  std::vector<HighsInt> degrees(mipsolver.numCol());
+  const HighsInt maxRows = std::min(HighsInt{50000}, 2 * mipsolver.numRow());
+  HighsHashTable<std::pair<HighsInt, HighsInt>,
+                 std::tuple<double, HighsInt, ArcType>>
+      adjacency(maxRows + 2);
+  HighsHashTable<std::pair<HighsInt, HighsInt>, std::vector<HighsInt>> arcToBin;
+  // 1 -> (i,j) y = 0, 2 -> (i,j) y = 1, 4 -> (j,i) y = 0, 8 -> (j,i) y = 1
+  HighsHashTable<std::tuple<HighsInt, HighsInt, HighsInt>, uint8_t> jobOrder;
+
+  auto addEntry = [&](HighsInt posCol, HighsInt negCol, HighsInt binCol,
+                      double p, ArcType t) {
+    // My_ji + s_i - s_j >= p_ji
+    // y_ji = val -> s_i >= s_j + p_ji - M * val
+    // Make an arc from negCol (j) to posCol (i)
+    if (p < 0) return;
+    const auto it = adjacency.find({negCol, posCol});
+    if (it != nullptr) {
+      if (std::get<0>(*it) < p) {
+        adjacency[{negCol, posCol}] = std::make_tuple(p, binCol, t);
+      }
+    } else {
+      degrees[posCol]++;
+      if (degrees[posCol] > largestDegree ||
+          (degrees[posCol] == largestDegree && posCol < largestDegreeCol)) {
+        largestDegreeCol = posCol;
+        largestDegree = degrees[posCol];
+      }
+      adjacency.insert(std::make_pair(negCol, posCol),
+                       std::make_tuple(p, binCol, t));
+    }
+    // Store binaries to later check if any two binaries
+    // imply the same ordering of two jobs.
+    HighsInt u = std::min(negCol, posCol);
+    HighsInt v = std::max(negCol, posCol);
+    if (jobOrder.find({u, v, binCol}) == nullptr) {
+      jobOrder[{u, v, binCol}] = 0;
+    }
+    if (negCol < posCol) {
+      arcToBin[{negCol, posCol}].emplace_back(binCol);
+      jobOrder[{negCol, posCol, binCol}] |= t == ArcType::kIfBinOne ? 2 : 1;
+    } else {
+      jobOrder[{posCol, negCol, binCol}] |= t == ArcType::kIfBinOne ? 8 : 4;
+    }
+  };
+
+  HighsInt numRows = 0;
+  for (HighsInt row = 0; row != mipsolver.numRow(); row++) {
+    const double rowLower = mipsolver.model_->row_lower_[row];
+    const double rowUpper = mipsolver.model_->row_upper_[row];
+    if (rowLower == rowUpper) continue;
+    const HighsInt start = mipsolver.mipdata_->ARstart_[row];
+    const HighsInt end = mipsolver.mipdata_->ARstart_[row + 1];
+    if (end - start != 3) continue;
+    bool machineSchedRow = true;
+    HighsInt posContCol = -1;
+    HighsInt negContCol = -1;
+    HighsInt binCol = -1;
+    double binCoef = 0;
+    for (HighsInt i = start; i != end; i++) {
+      HighsInt col = mipsolver.mipdata_->ARindex_[i];
+      if (globaldom.col_lower_[col] == -kHighsInf) {
+        machineSchedRow = false;
+        break;
+      }
+      if (globaldom.isBinary(col)) {
+        if (binCol != -1) {
+          machineSchedRow = false;
+          break;
+        }
+        binCol = col;
+        binCoef = mipsolver.mipdata_->ARvalue_[i];
+      } else if (mipsolver.mipdata_->ARvalue_[i] == -1) {
+        negContCol = col;
+      } else if (mipsolver.mipdata_->ARvalue_[i] == 1) {
+        posContCol = col;
+      } else {
+        machineSchedRow = false;
+        break;
+      }
+    }
+    if (!machineSchedRow || binCol == -1 || negContCol == -1 ||
+        posContCol == -1 || posContCol == negContCol)
+      continue;
+    // We want to put the row into form:
+    // Mx_ji + s_i - s_j >= p_ji, p_ji >= 0
+    // x_ji = 1 -> s_i >= s_j + p_ij - M
+    if (rowUpper != kHighsInf) {
+      // Given My_ij + s_i - s_j <= d
+      // The row becomes (after multiplying by -1):
+      // -My_ij + s_j - s_i >= -d
+      // Add implication s_j >= s_i + p_ij + M, p_ij + M > 0 when binCol = 1
+      // Add implication s_j >= s_i + p_ij, p, p_ij > 0 when binCol = 0
+      const double rhs_0 = -rowUpper;
+      const double rhs_1 = -rowUpper + binCoef;
+      if (rhs_0 > 0 || rhs_1 > 0) {
+        if (rhs_0 > rhs_1) {
+          addEntry(negContCol, posContCol, binCol, rhs_0, ArcType::kIfBinZero);
+        } else {
+          addEntry(negContCol, posContCol, binCol, rhs_1, ArcType::kIfBinOne);
+        }
+        numRows++;
+      }
+    }
+    if (rowLower != -kHighsInf) {
+      // Given Mx_ij + s_i - s_j >= d
+      // Add implication s_i >= s_j + pji - M, p_ji - M > 0 when binCol = 1
+      // Add implication s_i >= s_j + pji, p_ji > 0 when binCol = 0
+      const double rhs_0 = rowLower;
+      const double rhs_1 = rowLower - binCoef;
+      if (rhs_0 > 0 || rhs_1 > 0) {
+        if (rhs_0 > rhs_1) {
+          addEntry(posContCol, negContCol, binCol, rhs_0, ArcType::kIfBinZero);
+        } else {
+          addEntry(posContCol, negContCol, binCol, rhs_1, ArcType::kIfBinOne);
+        }
+        numRows++;
+      }
+    }
+    if (numRows >= maxRows) break;
+  }
+
+  // Extract binary variables that imply the same job ordering
+  if (!mipsolver.mipdata_->parallelLockActive()) {
+    std::vector<HighsCliqueTable::CliqueVar> clique(2);
+    for (const auto& entry : arcToBin) {
+      std::pair<HighsInt, HighsInt> arc = entry.key();
+      HighsInt baseBinCol = -1;
+      bool baseForward = false;
+      for (const HighsInt& binCol : entry.value()) {
+        bool forward = false;
+        bool impliesOrder = false;
+        if ((jobOrder[{arc.first, arc.second, binCol}] & 9) == 9) {
+          impliesOrder = true;
+        } else if ((jobOrder[{arc.first, arc.second, binCol}] & 6) == 6) {
+          impliesOrder = true;
+          forward = true;
+        }
+        if (!impliesOrder || binCol == baseBinCol) continue;
+        if (baseBinCol == -1) {
+          baseBinCol = binCol;
+          baseForward = forward;
+          continue;
+        }
+        HighsCliqueTable::CliqueVar stayCliqueVar =
+            HighsCliqueTable::CliqueVar(baseBinCol, baseForward);
+        HighsCliqueTable::CliqueVar substCliqueVar =
+            HighsCliqueTable::CliqueVar(binCol, forward);
+        clique[0] = stayCliqueVar;
+        clique[1] = substCliqueVar.complement();
+        mipsolver.mipdata_->cliquetable.addClique(mipsolver, clique.data(), 2);
+        clique[0] = stayCliqueVar.complement();
+        clique[1] = substCliqueVar;
+        mipsolver.mipdata_->cliquetable.addClique(mipsolver, clique.data(), 2);
+        if (globaldom.infeasible()) return false;
+      }
+    }
+  }
+
+  // A clique of size 3 needs at least 6 arcs
+  if (numRows <= 5) return false;
+
+  // Greedily search neighbours of largest degree column for a double-sided
+  // clique (corresponds to a single machine schedule)
+  std::vector<HighsInt> potentialNeighbours;
+  potentialNeighbours.reserve(largestDegree);
+  for (const auto& entry : adjacency) {
+    auto arc = entry.key();
+    const HighsInt col = std::get<1>(arc);
+    if (col == largestDegreeCol) {
+      potentialNeighbours.emplace_back(std::get<0>(arc));
+    }
+  }
+  pdqsort(potentialNeighbours.begin(), potentialNeighbours.end(),
+          [&](const HighsInt c1, const HighsInt c2) {
+            return degrees[c1] > degrees[c2];
+          });
+
+  std::vector<HighsInt> neighbours;
+  neighbours.reserve(largestDegree + 1);
+  neighbours.emplace_back(largestDegreeCol);
+  double releaseDate = globaldom.col_lower_[largestDegreeCol];
+  std::vector<double> processingTimes;
+  processingTimes.resize(largestDegree + 1, kHighsInf);
+  // Iterate over potential neighbours and check validity
+  for (HighsInt col : potentialNeighbours) {
+    bool valid_neighbour = true;
+    for (HighsInt neighbour : neighbours) {
+      const auto fromArc = adjacency.find({col, neighbour});
+      const auto toArc = adjacency.find({neighbour, col});
+      // Need to verify that the to and fromArc exist and are opposites
+      if (toArc == nullptr || fromArc == nullptr ||
+          std::get<1>(*fromArc) != std::get<1>(*toArc) ||
+          std::get<2>(*fromArc) == std::get<2>(*toArc)) {
+        valid_neighbour = false;
+        break;
+      }
+    }
+    if (!valid_neighbour) continue;
+    const size_t newNeighbourIndex = neighbours.size();
+    // Extract the processing times from the arcs
+    for (size_t i = 0; i != neighbours.size(); ++i) {
+      HighsInt neighbour = neighbours[i];
+      const auto fromArc = adjacency.find({col, neighbour});
+      const auto toArc = adjacency.find({neighbour, col});
+      processingTimes[newNeighbourIndex] =
+          std::min(processingTimes[newNeighbourIndex], std::get<0>(*fromArc));
+      processingTimes[i] = std::min(processingTimes[i], std::get<0>(*toArc));
+    }
+    releaseDate = std::min(globaldom.col_lower_[col], releaseDate);
+    neighbours.emplace_back(col);
+  }
+  if (neighbours.size() < 3) return false;
+
+  // Now populate the actual inequalities
+  vals.resize(neighbours.size(), std::vector<double>(neighbours.size()));
+  inds.resize(neighbours.size(), std::vector<HighsInt>(neighbours.size()));
+  rhss.resize(neighbours.size());
+  for (size_t i = 0; i != neighbours.size(); ++i) {
+    rhss[i] -= releaseDate;
+    HighsInt col = neighbours[i];
+    for (size_t j = 0; j != neighbours.size(); ++j) {
+      size_t jj = j >= i ? j + 1 : j;
+      if (jj >= neighbours.size()) continue;
+      HighsInt neighbour = neighbours[jj];
+      const auto toArc = adjacency.find({neighbour, col});
+      assert(toArc != nullptr);
+      inds[i][j] = std::get<1>(*toArc);
+      vals[i][j] = processingTimes[jj];
+      if (std::get<2>(*toArc) == ArcType::kIfBinZero) {
+        rhss[i] -= vals[i][j];
+        vals[i][j] *= -1;
+      }
+    }
+    // Put the job start time on the LHS
+    inds[i].back() = col;
+    vals[i].back() = -1;
+  }
+
+  return true;
+}
+
+void HighsMachineSchedSeparator::separateLpSolution(
+    HighsLpRelaxation& lpRelaxation, HighsLpAggregator& lpAggregator,
+    HighsTransformedLp& transLp, HighsCutPool& cutpool) {
+  // Only separate once
+  if (separated) return;
+  const HighsMipSolver& mip = lpRelaxation.getMipSolver();
+  std::vector<std::vector<double>> vals;
+  std::vector<std::vector<HighsInt>> inds;
+  std::vector<double> rhss;
+  has_single_machine_schedule = findSingleMachineScheduleClique(
+      vals, inds, rhss, transLp.getGlobaldom(), mip);
+  if (!has_single_machine_schedule) {
+    separated = true;
+    return;
+  }
+
+  // Load the cuts
+  const std::vector<double>& lpSolution = lpRelaxation.getSolution().col_value;
+  for (size_t i = 0; i != inds.size(); ++i) {
+    double viol = -rhss[i];
+    for (size_t j = 0; j != inds[i].size(); j++) {
+      viol += lpSolution[inds[i][j]] * vals[i][j];
+    }
+    if (viol >= 10 * mip.mipdata_->feastol)
+      cutpool.addCut(mip, inds[i].data(), vals[i].data(),
+                     static_cast<HighsInt>(inds[i].size()), rhss[i]);
+  }
+  separated = true;
+}
diff --git a/highs/mip/HighsMachineSchedSeparator.h b/highs/mip/HighsMachineSchedSeparator.h
new file mode 100644
index 00000000000..c47494a43b3
--- /dev/null
+++ b/highs/mip/HighsMachineSchedSeparator.h
@@ -0,0 +1,60 @@
+/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+/*                                                                       */
+/*    This file is part of the HiGHS linear optimization suite           */
+/*                                                                       */
+/*    Available as open-source under the MIT License                     */
+/*                                                                       */
+/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
+/**@file mip/HighsMachineSchedSeparator.h
+ * @brief Class for separating release-date cuts, see Section 4.1 in
+ * Recognition and Exploitation of Single-Machine Scheduling Subproblems in
+ * Mixed Integer Programs, Reinout Lambertus Henricus Wijfjes, Msc Thesis, 2022,
+ * or Cutting Plane Algorithm for the Single Machine Scheduling Problem
+ * with Release Times, G. L. Nemhauser and M. W. P. Savelsbergh, 1992.
+ *
+ * Given a set of jobs N with start times s_j, processing times p_ij,
+ * release times r_j, and binary dependency variables y_ij,
+ * where y = 1 -> s_i - s_j < p_ij.
+ * To simplify the problem: We set p_j = min{p_ji : i \in N / j}
+ * A valid inequality is then:
+ * s_j >= min{r_{i} : i \in N} + \sum_{i \in N / j} p_i y_ij
+ *
+ */
+
+#ifndef MIP_HIGHS_MACHINE_SCHED_SEPARATOR_H_
+#define MIP_HIGHS_MACHINE_SCHED_SEPARATOR_H_
+
+#include "mip/HighsMipSolver.h"
+#include "mip/HighsMipSolverData.h"
+#include "mip/HighsSeparator.h"
+#include "util/HighsRandom.h"
+
+/// Helper class to compute single-row relaxations from the current LP
+/// relaxation by substituting bounds and aggregating rows
+class HighsMachineSchedSeparator : public HighsSeparator {
+ private:
+  HighsRandom randgen;
+  bool has_single_machine_schedule = false;
+  bool separated = false;
+
+  bool findSingleMachineScheduleClique(std::vector<std::vector<double>>& vals,
+                                       std::vector<std::vector<HighsInt>>& inds,
+                                       std::vector<double>& rhss,
+                                       const HighsDomain& globaldom,
+                                       const HighsMipSolver& mipsolver);
+
+ public:
+  void separateLpSolution(HighsLpRelaxation& lpRelaxation,
+                          HighsLpAggregator& lpAggregator,
+                          HighsTransformedLp& transLp,
+                          HighsCutPool& cutpool) override;
+
+  HighsMachineSchedSeparator(const HighsMipSolver& mipsolver)
+      : HighsSeparator(mipsolver, kMachineSchedSepaString) {
+    randgen.initialise(mipsolver.options_mip_->random_seed);
+    has_single_machine_schedule = false;
+    separated = false;
+  }
+};
+
+#endif
diff --git a/highs/mip/HighsSeparation.cpp b/highs/mip/HighsSeparation.cpp
index a2c144c28fd..87e72b6dde8 100644
--- a/highs/mip/HighsSeparation.cpp
+++ b/highs/mip/HighsSeparation.cpp
@@ -16,6 +16,7 @@
 #include "mip/HighsImplications.h"
 #include "mip/HighsLpAggregator.h"
 #include "mip/HighsLpRelaxation.h"
+#include "mip/HighsMachineSchedSeparator.h"
 #include "mip/HighsMipSolverData.h"
 #include "mip/HighsModkSeparator.h"
 #include "mip/HighsPathSeparator.h"
@@ -38,6 +39,7 @@ HighsSeparation::HighsSeparation(HighsMipWorker& mipworker)
   separators.emplace_back(new HighsTableauSeparator(mipsolver));
   separators.emplace_back(new HighsPathSeparator(mipsolver));
   separators.emplace_back(new HighsModkSeparator(mipsolver));
+  separators.emplace_back(new HighsMachineSchedSeparator(mipsolver));
 }
 
 HighsInt HighsSeparation::separationRound(HighsDomain& propdomain,
diff --git a/highs/mip/HighsSeparator.h b/highs/mip/HighsSeparator.h
index 75fb1a41e07..2eb5d60cdcd 100644
--- a/highs/mip/HighsSeparator.h
+++ b/highs/mip/HighsSeparator.h
@@ -22,6 +22,8 @@ const std::string kCliqueSepaString = "Separation: Clique";
 const std::string kTableauSepaString = "Separation: Tableau";
 const std::string kPathAggrSepaString = "Separation: Path aggregation";
 const std::string kModKSepaString = "Separation: Mod-k";
+const std::string kMachineSchedSepaString =
+    "Separation: Single Machine Scheduling";
 
 class HighsLpRelaxation;
 class HighsTransformedLp;
diff --git a/highs/mip/MipTimer.h b/highs/mip/MipTimer.h
index 33a195b411c..68bb782a93f 100644
--- a/highs/mip/MipTimer.h
+++ b/highs/mip/MipTimer.h
@@ -96,6 +96,7 @@ enum iClockMip : int {
   kMipClockTableauSepa,
   kMipClockPathAggrSepa,
   kMipClockModKSepa,
+  kMipClockMachineSchedSepa,
 
   // LP solves
   kMipClockDuSimplexBasisSolveLp,
@@ -326,6 +327,8 @@ class MipTimer {
         timer_pointer->clock_def(kPathAggrSepaString.c_str());
     clock[kMipClockModKSepa] =
         timer_pointer->clock_def(kModKSepaString.c_str());
+    clock[kMipClockMachineSchedSepa] =
+        timer_pointer->clock_def(kMachineSchedSepaString.c_str());
     */
     // Presolve - Should correspond to kMipClockRunPresolve
     clock[kMipClockProbingPresolve] =
@@ -581,7 +584,7 @@ class MipTimer {
   void reportMipSeparationClock(const HighsTimerClock& mip_timer_clock) {
     const std::vector<HighsInt> mip_clock_list{
         kMipClockImplboundSepa, kMipClockCliqueSepa, kMipClockTableauSepa,
-        kMipClockPathAggrSepa, kMipClockModKSepa};
+        kMipClockPathAggrSepa,  kMipClockModKSepa,   kMipClockMachineSchedSepa};
     reportMipClockList("MipSeparation", mip_clock_list, mip_timer_clock,
                        kMipClockTotal);  //, tolerance_percent_report);
   };
diff --git a/highs/presolve/HPresolve.cpp b/highs/presolve/HPresolve.cpp
index fe418c03492..a2f32d4addf 100644
--- a/highs/presolve/HPresolve.cpp
+++ b/highs/presolve/HPresolve.cpp
@@ -4472,12 +4472,13 @@ HPresolve::Result HPresolve::colPresolve(HighsPostsolveStack& postsolve_stack,
     // check if variable is implied integer
     HPRESOLVE_CHECKED_CALL(static_cast<Result>(convertImpliedInteger(col)));
 
-    // shift integral variables to have a lower bound of zero
+    // shift "binary" variables to have a lower bound of zero
     if (model->integrality_[col] != HighsVarType::kContinuous &&
         model->col_lower_[col] != 0.0 &&
         (model->col_lower_[col] != -kHighsInf ||
          model->col_upper_[col] != kHighsInf) &&
-        model->col_upper_[col] - model->col_lower_[col] > 0.5) {
+        model->col_upper_[col] - model->col_lower_[col] > 0.5 &&
+        model->col_upper_[col] - model->col_lower_[col] < 1.5) {
       // substitute with the bound that is smaller in magnitude and only
       // substitute if bound is not large for an integer
       if (std::abs(model->col_upper_[col]) > std::abs(model->col_lower_[col])) {