diff --git a/examples/python/vendor_scheduling_sat.py b/examples/python/vendor_scheduling_sat.py
new file mode 100644
index 0000000000..bef8ec389f
--- /dev/null
+++ b/examples/python/vendor_scheduling_sat.py
@@ -0,0 +1,139 @@
+# Copyright 2010-2017 Google
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+from ortools.sat.python import cp_model
+
+
+class SolutionPrinter(cp_model.CpSolverSolutionCallback):
+  """Print intermediate solutions."""
+
+  def __init__(self, num_vendors, num_hours, possible_schedules,
+               selected_schedules, hours_stat, min_vendors):
+    cp_model.CpSolverSolutionCallback.__init__(self)
+    self.__solution_count = 0
+    self.__num_vendors = num_vendors
+    self.__num_hours = num_hours
+    self.__possible_schedules = possible_schedules
+    self.__selected_schedules = selected_schedules
+    self.__hours_stat = hours_stat
+    self.__min_vendors = min_vendors
+
+  def OnSolutionCallback(self):
+    self.__solution_count += 1
+    print ('Solution %i: ', self.__solution_count)
+    print('  min vendors:', self.__min_vendors)
+    for i in range(self.__num_vendors):
+      print('  - vendor %i: ' % i,
+            self.__possible_schedules[self.Value(self.__selected_schedules[i])])
+    print()
+
+    for j in range(self.__num_hours):
+      print('  - # workers on day%2i: ' % j, end=' ')
+      print(self.Value(self.__hours_stat[j]), end=' ')
+      print()
+    print()
+
+  def SolutionCount(self):
+    return self.__solution_count
+
+
+def VendorScheduling():
+  # Create the model.
+  model = cp_model.CpModel()
+
+  #
+  # data
+  #
+  num_vendors = 9
+  num_hours = 10
+  num_work_types = 1
+
+  traffic = [100, 500, 100, 200, 320, 300, 200, 220, 300, 120]
+  max_traffic_per_vendor = 100
+
+  # Last columns are :
+  #   index_of_the_schedule, sum of worked hours (per work type).
+  # The index is useful for branching.
+  possible_schedules = [[1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 8],
+                        [1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 4],
+                        [0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 2, 5],
+                        [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 3, 4],
+                        [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 4, 3],
+                        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0]]
+
+  num_possible_schedules = len(possible_schedules)
+  selected_schedules = []
+  vendors_stat = []
+  hours_stat = []
+
+
+  # Auxiliary data
+  min_vendors = [t // max_traffic_per_vendor for t in traffic]
+  all_vendors = range(num_vendors)
+  all_hours = range(num_hours)
+
+  #
+  # declare variables
+  #
+  x = {}
+
+  for v in all_vendors:
+    tmp = []
+    for h in all_hours:
+      x[v, h] = model.NewIntVar(0, num_work_types, 'x[%i,%i]' % (v, h))
+      tmp.append(x[v, h])
+    selected_schedule = model.NewIntVar(0, num_possible_schedules - 1,
+                                        's[%i]' % v)
+    hours = model.NewIntVar(0, num_hours, 'h[%i]' % v)
+    selected_schedules.append(selected_schedule)
+    vendors_stat.append(hours)
+    tmp.append(selected_schedule)
+    tmp.append(hours)
+
+    model.AddAllowedAssignments(tmp, possible_schedules)
+
+  #
+  # Statistics and constraints for each hour
+  #
+  for h in all_hours:
+    workers = model.NewIntVar(0, 1000, 'workers[%i]' %h)
+    model.Add(workers == sum(x[v, h] for v in all_vendors))
+    hours_stat.append(workers)
+    model.Add(workers * max_traffic_per_vendor >= traffic[h])
+
+  #
+  # Redundant constraint: sort selected_schedules
+  #
+  for v in range(num_vendors - 1):
+    model.Add(selected_schedules[v] <= selected_schedules[v + 1])
+
+  # Solve model.
+  solver = cp_model.CpSolver()
+  solution_printer = SolutionPrinter(num_vendors, num_hours, possible_schedules,
+                                     selected_schedules, hours_stat,
+                                     min_vendors)
+  status = solver.SearchForAllSolutions(model, solution_printer)
+  print('Status = %s' % solver.StatusName(status))
+
+  print('Statistics')
+  print('  - conflicts : %i' % solver.NumConflicts())
+  print('  - branches  : %i' % solver.NumBranches())
+  print('  - wall time : %f s' % solver.WallTime())
+  print('  - number of solutions found: %i' % solution_printer.SolutionCount())
+
+
+VendorScheduling()
diff --git a/ortools/sat/cp_model_checker.cc b/ortools/sat/cp_model_checker.cc
index d588b41ff1..c6f98c6d96 100644
--- a/ortools/sat/cp_model_checker.cc
+++ b/ortools/sat/cp_model_checker.cc
@@ -358,6 +358,13 @@ class ConstraintChecker {
     for (int i = 0; i < num_variables; ++i) {
       sum += Value(ct.linear().vars(i)) * ct.linear().coeffs(i);
     }
+    if (!DomainInProtoContains(ct.linear(), sum)) {
+      for (int i = 0; i < num_variables; ++i) {
+        const int var = ct.linear().vars(i);
+        LOG(INFO) << "var#" << var << " = " << Value(var);
+      }
+      LOG(INFO) << ct.DebugString();
+    }
     return DomainInProtoContains(ct.linear(), sum);
   }
 
diff --git a/ortools/sat/cp_model_presolve.cc b/ortools/sat/cp_model_presolve.cc
index 1101e7bf5d..3cd92f2079 100644
--- a/ortools/sat/cp_model_presolve.cc
+++ b/ortools/sat/cp_model_presolve.cc
@@ -852,9 +852,6 @@ bool PresolveLinear(ConstraintProto* ct, PresolveContext* context) {
     rhs = AdditionOfSortedDisjointIntervals(
         rhs, {{-sum_of_fixed_terms, -sum_of_fixed_terms}});
   }
-  if (gcd > 1) {
-    rhs = InverseMultiplicationOfSortedDisjointIntervals(rhs, gcd);
-  }
   ct->mutable_linear()->clear_vars();
   ct->mutable_linear()->clear_coeffs();
   for (const auto entry : var_to_coeff) {
@@ -862,6 +859,14 @@ bool PresolveLinear(ConstraintProto* ct, PresolveContext* context) {
     ct->mutable_linear()->add_vars(entry.first);
     ct->mutable_linear()->add_coeffs(entry.second / gcd);
   }
+  if (gcd > 1) {
+    rhs = InverseMultiplicationOfSortedDisjointIntervals(rhs, gcd);
+    ct->mutable_linear()->clear_domain();
+    for (const auto& i : rhs) {
+      ct->mutable_linear()->add_domain(i.start);
+      ct->mutable_linear()->add_domain(i.end);
+    }
+  }
 
   // Empty constraint?
   if (ct->linear().vars().empty()) {
diff --git a/ortools/sat/integer_expr.h b/ortools/sat/integer_expr.h
index 1a9bac7936..edff77dd77 100644
--- a/ortools/sat/integer_expr.h
+++ b/ortools/sat/integer_expr.h
@@ -212,11 +212,13 @@ inline std::function<void(Model*)> WeightedSumLowerOrEqual(
   // Special cases.
   CHECK_GE(vars.size(), 1);
   if (vars.size() == 1) {
-    CHECK_NE(coefficients[0], 0);
-    if (coefficients[0] > 0) {
-      return LowerOrEqual(vars[0], upper_bound / coefficients[0]);
+    const int64 c = coefficients[0];
+    CHECK_NE(c, 0);
+    if (c > 0) {
+      return LowerOrEqual(vars[0], upper_bound / c);
     } else {
-      return GreaterOrEqual(vars[0], upper_bound / coefficients[0]);
+      const int64 ceil_c = (upper_bound + c + 1) / c;
+      return GreaterOrEqual(vars[0], ceil_c);
     }
   }
   if (vars.size() == 2 && (coefficients[0] == 1 || coefficients[0] == -1) &&