diff --git a/makefiles/Makefile.cpp.mk b/makefiles/Makefile.cpp.mk
index 56475dab85..c0355ba8b1 100755
--- a/makefiles/Makefile.cpp.mk
+++ b/makefiles/Makefile.cpp.mk
@@ -65,7 +65,7 @@ ortoolslibs: $(OR_TOOLS_LIBS)
 CVRPTW_LIBS   = $(LIB_DIR)/$(LIB_PREFIX)cvrptw_lib.$(LIB_SUFFIX)
 CVRPTW_DEPS = \
 	$(EX_DIR)/cpp/cvrptw_lib.h \
-	$(ROUTING_DEPS)
+	$(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 CVRPTW_LNK = $(PRE_LIB)cvrptw_lib$(POST_LIB) $(OR_TOOLS_LNK)
 cvrptwlibs: $(CVRPTW_LIBS)
 
@@ -156,7 +156,7 @@ ccexe: $(CC_BINARIES)
 CVRPTW_OBJS=\
 	$(OBJ_DIR)/cvrptw_lib.$O
 
-$(OBJ_DIR)/cvrptw_lib.$O: $(EX_DIR)/cpp/cvrptw_lib.cc $(EX_DIR)/cpp/cvrptw_lib.h $(ROUTING_DEPS)
+$(OBJ_DIR)/cvrptw_lib.$O: $(EX_DIR)/cpp/cvrptw_lib.cc $(EX_DIR)/cpp/cvrptw_lib.h 	$(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 	$(CCC) $(CFLAGS) -c $(EX_DIR)$Scpp/cvrptw_lib.cc $(OBJ_OUT)$(OBJ_DIR)$Scvrptw_lib.$O
 
 $(LIB_DIR)/$(LIB_PREFIX)cvrptw_lib.$(LIB_SUFFIX): $(CVRPTW_OBJS)
@@ -435,7 +435,7 @@ $(OBJ_DIR)/nqueens2.$O: $(EX_DIR)/cpp/nqueens2.cc $(CP_DEPS)
 $(BIN_DIR)/nqueens2$E: $(OR_TOOLS_LIBS) $(OBJ_DIR)/nqueens2.$O
 	$(CCC) $(CFLAGS) $(OBJ_DIR)/nqueens2.$O $(OR_TOOLS_LNK) $(OR_TOOLS_LD_FLAGS) $(EXE_OUT)$(BIN_DIR)$Snqueens2$E
 
-$(OBJ_DIR)/pdptw.$O: $(EX_DIR)/cpp/pdptw.cc $(ROUTING_DEPS)
+$(OBJ_DIR)/pdptw.$O: $(EX_DIR)/cpp/pdptw.cc $(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 	$(CCC) $(CFLAGS) -c $(EX_DIR)$Scpp/pdptw.cc $(OBJ_OUT)$(OBJ_DIR)$Spdptw.$O
 
 $(BIN_DIR)/pdptw$E: $(OR_TOOLS_LIBS) $(OBJ_DIR)/pdptw.$O
@@ -465,7 +465,7 @@ $(OBJ_DIR)/sports_scheduling.$O: $(EX_DIR)/cpp/sports_scheduling.cc $(CP_DEPS)
 $(BIN_DIR)/sports_scheduling$E: $(OR_TOOLS_LIBS) $(OBJ_DIR)/sports_scheduling.$O
 	$(CCC) $(CFLAGS) $(OBJ_DIR)/sports_scheduling.$O $(OR_TOOLS_LNK) $(OR_TOOLS_LD_FLAGS) $(EXE_OUT)$(BIN_DIR)$Ssports_scheduling$E
 
-$(OBJ_DIR)/tsp.$O: $(EX_DIR)/cpp/tsp.cc $(ROUTING_DEPS)
+$(OBJ_DIR)/tsp.$O: $(EX_DIR)/cpp/tsp.cc $(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 	$(CCC) $(CFLAGS) -c $(EX_DIR)$Scpp/tsp.cc $(OBJ_OUT)$(OBJ_DIR)$Stsp.$O
 
 $(BIN_DIR)/tsp$E: $(OR_TOOLS_LIBS) $(OBJ_DIR)/tsp.$O
diff --git a/makefiles/Makefile.gen.mk b/makefiles/Makefile.gen.mk
index 5f907ad86f..fd2a343618 100644
--- a/makefiles/Makefile.gen.mk
+++ b/makefiles/Makefile.gen.mk
@@ -1227,7 +1227,6 @@ $(OBJ_DIR)/graph/bellman_ford.$O: \
 $(OBJ_DIR)/graph/cliques.$O: \
     $(SRC_DIR)/graph/cliques.cc \
     $(SRC_DIR)/graph/cliques.h \
-    $(SRC_DIR)/base/callback.h \
     $(SRC_DIR)/base/hash.h
 	$(CCC) $(CFLAGS) -c $(SRC_DIR)/graph/cliques.cc $(OBJ_OUT)$(OBJ_DIR)$Sgraph$Scliques.$O
 
@@ -1264,7 +1263,6 @@ $(OBJ_DIR)/graph/min_cost_flow.$O: \
 $(OBJ_DIR)/graph/shortestpaths.$O: \
     $(SRC_DIR)/graph/shortestpaths.cc \
     $(SRC_DIR)/graph/shortestpaths.h \
-    $(SRC_DIR)/base/callback.h \
     $(SRC_DIR)/base/casts.h \
     $(SRC_DIR)/base/commandlineflags.h \
     $(SRC_DIR)/base/hash.h \
@@ -2280,19 +2278,6 @@ $(SRC_DIR)/linear_solver/glop_utils.h: \
     $(SRC_DIR)/linear_solver/linear_solver.h \
     $(SRC_DIR)/lp_data/lp_types.h
 
-$(SRC_DIR)/linear_solver/linear_expr.h:
-
-$(SRC_DIR)/linear_solver/linear_solver_ext.h: \
-    $(SRC_DIR)/linear_solver/linear_solver.h \
-    $(SRC_DIR)/base/commandlineflags.h \
-    $(SRC_DIR)/base/hash.h \
-    $(SRC_DIR)/base/integral_types.h \
-    $(SRC_DIR)/base/logging.h \
-    $(SRC_DIR)/base/macros.h \
-    $(SRC_DIR)/base/sparsetable.h \
-    $(SRC_DIR)/base/strutil.h \
-    $(SRC_DIR)/base/timer.h
-
 $(SRC_DIR)/linear_solver/linear_solver.h: \
     $(SRC_DIR)/linear_solver/linear_expr.h \
     $(GEN_DIR)/linear_solver/linear_solver.pb.h \
@@ -2605,21 +2590,16 @@ $(SRC_DIR)/constraint_solver/constraint_solveri.h: \
 $(SRC_DIR)/constraint_solver/hybrid.h: \
     $(SRC_DIR)/constraint_solver/constraint_solver.h
 
-$(SRC_DIR)/constraint_solver/routing_flags.h: \
-    $(GEN_DIR)/constraint_solver/routing_parameters.pb.h \
-    $(SRC_DIR)/base/commandlineflags.h
-
 $(SRC_DIR)/constraint_solver/routing.h: \
     $(SRC_DIR)/constraint_solver/constraint_solver.h \
     $(SRC_DIR)/constraint_solver/constraint_solveri.h \
     $(GEN_DIR)/constraint_solver/routing_parameters.pb.h \
-    $(SRC_DIR)/base/adjustable_priority_queue.h \
+    $(SRC_DIR)/constraint_solver/routing_types.h \
     $(SRC_DIR)/base/adjustable_priority_queue-inl.h \
+    $(SRC_DIR)/base/adjustable_priority_queue.h \
     $(SRC_DIR)/base/callback.h \
     $(SRC_DIR)/base/commandlineflags.h \
     $(SRC_DIR)/base/hash.h \
-    $(SRC_DIR)/base/integral_types.h \
-    $(SRC_DIR)/base/int_type.h \
     $(SRC_DIR)/base/int_type_indexed_vector.h \
     $(SRC_DIR)/base/logging.h \
     $(SRC_DIR)/base/macros.h \
@@ -2627,6 +2607,10 @@ $(SRC_DIR)/constraint_solver/routing.h: \
     $(SRC_DIR)/util/sorted_interval_list.h \
     $(SRC_DIR)/graph/graph.h
 
+$(SRC_DIR)/constraint_solver/routing_flags.h: \
+    $(GEN_DIR)/constraint_solver/routing_parameters.pb.h \
+    $(SRC_DIR)/base/commandlineflags.h
+
 $(SRC_DIR)/constraint_solver/routing_neighborhoods.h: \
     $(SRC_DIR)/constraint_solver/constraint_solver.h \
     $(SRC_DIR)/constraint_solver/constraint_solveri.h \
@@ -2707,16 +2691,6 @@ $(OBJ_DIR)/constraint_solver/collect_variables.$O: \
     $(SRC_DIR)/base/stl_util.h
 	$(CCC) $(CFLAGS) -c $(SRC_DIR)/constraint_solver/collect_variables.cc $(OBJ_OUT)$(OBJ_DIR)$Sconstraint_solver$Scollect_variables.$O
 
-$(OBJ_DIR)/constraint_solver/constraints.$O: \
-    $(SRC_DIR)/constraint_solver/constraints.cc \
-    $(SRC_DIR)/constraint_solver/constraint_solver.h \
-    $(SRC_DIR)/constraint_solver/constraint_solveri.h \
-    $(SRC_DIR)/base/integral_types.h \
-    $(SRC_DIR)/base/logging.h \
-    $(SRC_DIR)/util/saturated_arithmetic.h \
-    $(SRC_DIR)/util/string_array.h
-	$(CCC) $(CFLAGS) -c $(SRC_DIR)/constraint_solver/constraints.cc $(OBJ_OUT)$(OBJ_DIR)$Sconstraint_solver$Sconstraints.$O
-
 $(OBJ_DIR)/constraint_solver/constraint_solver.$O: \
     $(SRC_DIR)/constraint_solver/constraint_solver.cc \
     $(SRC_DIR)/constraint_solver/constraint_solver.h \
@@ -2736,6 +2710,17 @@ $(OBJ_DIR)/constraint_solver/constraint_solver.$O: \
     $(SRC_DIR)/util/tuple_set.h
 	$(CCC) $(CFLAGS) -c $(SRC_DIR)/constraint_solver/constraint_solver.cc $(OBJ_OUT)$(OBJ_DIR)$Sconstraint_solver$Sconstraint_solver.$O
 
+$(OBJ_DIR)/constraint_solver/constraints.$O: \
+    $(SRC_DIR)/constraint_solver/constraints.cc \
+    $(SRC_DIR)/constraint_solver/constraint_solver.h \
+    $(SRC_DIR)/constraint_solver/constraint_solveri.h \
+    $(SRC_DIR)/base/integral_types.h \
+    $(SRC_DIR)/base/join.h \
+    $(SRC_DIR)/base/logging.h \
+    $(SRC_DIR)/util/saturated_arithmetic.h \
+    $(SRC_DIR)/util/string_array.h
+	$(CCC) $(CFLAGS) -c $(SRC_DIR)/constraint_solver/constraints.cc $(OBJ_OUT)$(OBJ_DIR)$Sconstraint_solver$Sconstraints.$O
+
 $(OBJ_DIR)/constraint_solver/count_cst.$O: \
     $(SRC_DIR)/constraint_solver/count_cst.cc \
     $(SRC_DIR)/constraint_solver/constraint_solver.h \
@@ -2933,6 +2918,7 @@ $(OBJ_DIR)/constraint_solver/local_search.$O: \
     $(SRC_DIR)/base/commandlineflags.h \
     $(SRC_DIR)/base/hash.h \
     $(SRC_DIR)/base/integral_types.h \
+    $(SRC_DIR)/base/join.h \
     $(SRC_DIR)/base/logging.h \
     $(SRC_DIR)/base/macros.h \
     $(SRC_DIR)/base/map_util.h \
@@ -3002,11 +2988,13 @@ $(OBJ_DIR)/constraint_solver/routing.$O: \
     $(SRC_DIR)/constraint_solver/routing.cc \
     $(GEN_DIR)/constraint_solver/model.pb.h \
     $(SRC_DIR)/constraint_solver/routing.h \
+    $(SRC_DIR)/constraint_solver/routing_neighborhoods.h \
     $(SRC_DIR)/base/callback.h \
     $(SRC_DIR)/base/casts.h \
     $(SRC_DIR)/base/commandlineflags.h \
     $(SRC_DIR)/base/hash.h \
     $(SRC_DIR)/base/integral_types.h \
+    $(SRC_DIR)/base/join.h \
     $(SRC_DIR)/base/logging.h \
     $(SRC_DIR)/base/map_util.h \
     $(SRC_DIR)/base/stl_util.h \
diff --git a/makefiles/Makefile.java.mk b/makefiles/Makefile.java.mk
index 48bf00cdec..3fcab392c2 100755
--- a/makefiles/Makefile.java.mk
+++ b/makefiles/Makefile.java.mk
@@ -4,10 +4,10 @@
 
 JAVA_ORTOOLS_LIBS= $(LIB_DIR)/com.google.ortools.jar $(LIB_DIR)/$(LIB_PREFIX)jniortools.$(JNI_LIB_EXT)
 
-$(GEN_DIR)/constraint_solver/constraint_solver_java_wrap.cc: $(SRC_DIR)/constraint_solver/java/constraint_solver.swig $(SRC_DIR)/constraint_solver/java/routing.swig $(SRC_DIR)/base/base.swig $(SRC_DIR)/util/java/vector.swig $(SRC_DIR)/base/base.swig $(SRC_DIR)/util/java/proto.swig $(ROUTING_DEPS)
+$(GEN_DIR)/constraint_solver/constraint_solver_java_wrap.cc: $(SRC_DIR)/constraint_solver/java/constraint_solver.swig $(SRC_DIR)/constraint_solver/java/routing.swig $(SRC_DIR)/base/base.swig $(SRC_DIR)/util/java/vector.swig $(SRC_DIR)/base/base.swig $(SRC_DIR)/util/java/proto.swig $(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 	$(SWIG_BINARY) -I$(INC_DIR) -c++ -java -o $(GEN_DIR)$Sconstraint_solver$Sconstraint_solver_java_wrap.cc -package com.google.ortools.constraintsolver -module operations_research_constraint_solver -outdir $(GEN_DIR)$Scom$Sgoogle$Sortools$Sconstraintsolver $(SRC_DIR)$Sconstraint_solver$Sjava$Srouting.swig
 
-$(OBJ_DIR)/swig/constraint_solver_java_wrap.$O: $(GEN_DIR)/constraint_solver/constraint_solver_java_wrap.cc $(ROUTING_DEPS)
+$(OBJ_DIR)/swig/constraint_solver_java_wrap.$O: $(GEN_DIR)/constraint_solver/constraint_solver_java_wrap.cc $(CP_DEPS) $(SRC_DIR)/constraint_solver/routing.h
 	$(CCC) $(JNIFLAGS) $(JAVA_INC) -c $(GEN_DIR)$Sconstraint_solver$Sconstraint_solver_java_wrap.cc $(OBJ_OUT)$(OBJ_DIR)$Sswig$Sconstraint_solver_java_wrap.$O
 
 $(GEN_DIR)/algorithms/knapsack_solver_java_wrap.cc: $(SRC_DIR)/algorithms/java/knapsack_solver.swig $(SRC_DIR)/base/base.swig $(SRC_DIR)/util/java/vector.swig $(SRC_DIR)/algorithms/knapsack_solver.h
@@ -403,4 +403,4 @@ clean_java:
 	-$(DEL) $(OBJ_DIR)$Scom$Sgoogle$Sortools$Salgorithms$S*.class
 	-$(DEL) $(OBJ_DIR)$Scom$Sgoogle$Sortools$Slinearsolver$S*.class
 	-$(DEL) $(OBJ_DIR)$Scom$Sgoogle$Sortools$Ssamples$S*.class
-	-$(DEL) $(OBJ_DIR)$Sswig$S*java_wrap.$O
\ No newline at end of file
+	-$(DEL) $(OBJ_DIR)$Sswig$S*java_wrap.$O
diff --git a/makefiles/Makefile.port b/makefiles/Makefile.port
index 7c7828d6b1..cb15c8f656 100755
--- a/makefiles/Makefile.port
+++ b/makefiles/Makefile.port
@@ -90,7 +90,7 @@ endif
 # Windows specific part.
 ifeq ("$(SYSTEM)","win")
   # Detect 32/64bit
-  ifeq ("$(Platform)", "X64")
+  ifeq ("$(Platform)", "X64")  # Visual Studio 2015 64 bit
     PLATFORM = WIN64
     PTRLENGTH = 64
     CMAKE_SUFFIX = Win64
@@ -99,13 +99,23 @@ ifeq ("$(SYSTEM)","win")
     GLPK_PLATFORM = w64
     NETPLATFORM = x64
   else
-    PLATFORM = Win32
-    PTRLENGTH = 32
-    CMAKE_SUFFIX =
-    ARCH =
-    CBC_PLATFORM_PREFIX = Win32
-    GLPK_PLATFORM = w32
-    NETPLATFORM = x86
+     ifeq ("$(Platform)", "x64")  # Visual studio 2013 64 bit
+      PLATFORM = WIN64
+      PTRLENGTH = 64
+      CMAKE_SUFFIX = Win64
+      ARCH= /DARCH_K8
+      CBC_PLATFORM_PREFIX = x64
+      GLPK_PLATFORM = w64
+      NETPLATFORM = x64
+    else  # Visual Studio 32 bit (soon obsolete)
+      PLATFORM = Win32
+      PTRLENGTH = 32
+      CMAKE_SUFFIX =
+      ARCH =
+      CBC_PLATFORM_PREFIX = Win32
+      GLPK_PLATFORM = w32
+      NETPLATFORM = x86
+    endif
   endif
 
   # Detect visual studio version
diff --git a/makefiles/Makefile.third_party.unix.mk b/makefiles/Makefile.third_party.unix.mk
index 6c19213e81..0352ffed3c 100644
--- a/makefiles/Makefile.third_party.unix.mk
+++ b/makefiles/Makefile.third_party.unix.mk
@@ -1,7 +1,7 @@
 # SVN tags of dependencies to checkout.
 
 GFLAGS_TAG = 2.1.2
-PROTOBUF_TAG = 3.0.0
+PROTOBUF_TAG = 3.2.0
 CBC_TAG = 2.9.8
 SWIG_TAG = 3.0.12
 PCRE_TAG = 8.37
diff --git a/makefiles/Makefile.third_party.win.mk b/makefiles/Makefile.third_party.win.mk
index d8554fa22b..28b7150eec 100644
--- a/makefiles/Makefile.third_party.win.mk
+++ b/makefiles/Makefile.third_party.win.mk
@@ -1,6 +1,6 @@
 # tags of dependencies to checkout.
 GFLAGS_TAG = master
-PROTOBUF_TAG = 3.0.0
+PROTOBUF_TAG = 3.2.0
 CBC_TAG = 2.9.8
 ZLIB_TAG = 1.2.11
 ZLIB_ARCHIVE_TAG = 1211
diff --git a/src/base/hash.h b/src/base/hash.h
index fc4889bfef..de773a8500 100644
--- a/src/base/hash.h
+++ b/src/base/hash.h
@@ -389,8 +389,8 @@ namespace stdext {
 template <>
 inline size_t hash_value<std::pair<int64, int64>>(
     const std::pair<int64, int64>& a) {
-  PairIntHasher pairIntHasher;
-  return pairIntHasher(a);
+  PairInt64Hasher pairInt64Hasher;
+  return pairInt64Hasher(a);
 }
 }  //  namespace stdext
 #endif  // _MSC_VER
diff --git a/src/constraint_solver/constraint_solveri.h b/src/constraint_solver/constraint_solveri.h
index 8493efd19e..430fc52483 100644
--- a/src/constraint_solver/constraint_solveri.h
+++ b/src/constraint_solver/constraint_solveri.h
@@ -2079,8 +2079,12 @@ class CpModelLoader {
 
   // Returns stored integer expression.
   IntExpr* IntegerExpression(int index) const;
+  // Returns the number of stored integer expressions.
+  int NumIntegerExpressions() const { return expressions_.size(); }
   // Returns stored interval variable.
   IntervalVar* IntervalVariable(int index) const;
+  // Returns the number of stored interval variables.
+  int NumIntervalVariables() const { return intervals_.size(); }
 
 
 #if !defined(SWIG)
diff --git a/src/sat/integer.cc b/src/sat/integer.cc
index 2b06897a27..dd902a9916 100644
--- a/src/sat/integer.cc
+++ b/src/sat/integer.cc
@@ -1177,7 +1177,7 @@ std::function<LiteralIndex()> FirstUnassignedVarAtItsMinHeuristic(
             .Index();
       }
     }
-    return kNoLiteralIndex;
+    return LiteralIndex(kNoLiteralIndex);
   };
 }
 
@@ -1197,7 +1197,7 @@ std::function<LiteralIndex()> UnassignedVarWithLowestMinAtItsMinHeuristic(
         candidate_lb = lb;
       }
     }
-    if (candidate == kNoIntegerVariable) return kNoLiteralIndex;
+    if (candidate == kNoIntegerVariable) return LiteralIndex(kNoLiteralIndex);
     return integer_encoder
         ->GetOrCreateAssociatedLiteral(
             IntegerLiteral::LowerOrEqual(candidate, candidate_lb))
diff --git a/src/sat/integer.h b/src/sat/integer.h
index c1c0315366..84f2adb86f 100644
--- a/src/sat/integer.h
+++ b/src/sat/integer.h
@@ -918,7 +918,9 @@ class LiteralViews {
   explicit LiteralViews(Model* model) : model_(model) {}
 
   static LiteralViews* CreateInModel(Model* model) {
-    return new LiteralViews(model);
+    LiteralViews* const views = new LiteralViews(model);
+    model->TakeOwnership(views);
+    return views;
   }
 
   IntegerVariable GetIntegerView(const Literal lit) {
diff --git a/src/sat/intervals.h b/src/sat/intervals.h
index 8984e6128e..1b3a95e4c9 100644
--- a/src/sat/intervals.h
+++ b/src/sat/intervals.h
@@ -137,6 +137,7 @@ class SchedulingConstraintHelper {
   // Note that for tasks with variable durations, we don't necessarily have
   // duration-min between the the XXX-min and XXX-max value.
   IntegerValue DurationMin(int t) const;
+  IntegerValue DurationMax(int t) const;
   IntegerValue StartMin(int t) const;
   IntegerValue StartMax(int t) const;
   IntegerValue EndMin(int t) const;
@@ -240,6 +241,12 @@ inline IntegerValue SchedulingConstraintHelper::DurationMin(int t) const {
              : integer_trail_->LowerBound(duration_vars_[t]);
 }
 
+inline IntegerValue SchedulingConstraintHelper::DurationMax(int t) const {
+  return duration_vars_[t] == kNoIntegerVariable
+             ? fixed_durations_[t]
+             : integer_trail_->UpperBound(duration_vars_[t]);
+}
+
 inline IntegerValue SchedulingConstraintHelper::StartMin(int t) const {
   return integer_trail_->LowerBound(start_vars_[t]);
 }
@@ -340,6 +347,19 @@ inline std::function<IntegerVariable(const Model&)> SizeVar(
   };
 }
 
+inline std::function<bool(const Model&)> IsOptional(IntervalVariable v) {
+  return [=](const Model& model) {
+    return model.Get<IntervalsRepository>()->IsOptional(v);
+  };
+}
+
+inline std::function<Literal(const Model&)> IsPresentLiteral(
+    IntervalVariable v) {
+  return [=](const Model& model) {
+    return model.Get<IntervalsRepository>()->IsPresentLiteral(v);
+  };
+}
+
 inline std::function<IntervalVariable(Model*)> NewInterval(int64 min_start,
                                                            int64 max_end,
                                                            int64 size) {
diff --git a/src/sat/linear_programming_constraint.cc b/src/sat/linear_programming_constraint.cc
index 48b72501f4..5a9cfd1e35 100644
--- a/src/sat/linear_programming_constraint.cc
+++ b/src/sat/linear_programming_constraint.cc
@@ -25,6 +25,8 @@ DEFINE_bool(lp_constraint_use_dual_ray, true,
 namespace operations_research {
 namespace sat {
 
+const double LinearProgrammingConstraint::kEpsilon = 1e-6;
+
 LinearProgrammingConstraint::LinearProgrammingConstraint(
     IntegerTrail* integer_trail)
     : integer_trail_(integer_trail) {
diff --git a/src/sat/linear_programming_constraint.h b/src/sat/linear_programming_constraint.h
index 8b372c5828..0ae774fd56 100644
--- a/src/sat/linear_programming_constraint.h
+++ b/src/sat/linear_programming_constraint.h
@@ -127,7 +127,7 @@ class LinearProgrammingConstraint : public PropagatorInterface {
   glop::Fractional GetVariableValueAtCpScale(glop::ColIndex var);
 
   // TODO(user): use solver's precision epsilon.
-  constexpr static double kEpsilon = 1e-6;
+  static const double kEpsilon;
 
   // Underlying LP solver API.
   glop::LinearProgram lp_data_;
diff --git a/src/sat/timetable.cc b/src/sat/timetable.cc
index 3295e95168..7cb74e8636 100644
--- a/src/sat/timetable.cc
+++ b/src/sat/timetable.cc
@@ -35,9 +35,16 @@ TimeTablingPerTask::TimeTablingPerTask(
   // the profile is shaped like the Hanoi tower. The additional space is for
   // both extremities and the sentinels.
   profile_.reserve(2 * num_tasks_ + 4);
-  in_profile_.resize(num_tasks_);
   scp_.reserve(num_tasks_);
   ecp_.reserve(num_tasks_);
+  is_in_profile_.resize(num_tasks_);
+  in_profile_.reserve(num_tasks_);
+  // Reversible set of tasks to consider for propagation.
+  num_tasks_to_sweep_ = num_tasks_;
+  tasks_to_sweep_.resize(num_tasks_);
+  for (int t = 0; t < num_tasks_; ++t) {
+    tasks_to_sweep_[t] = t;
+  }
 }
 
 void TimeTablingPerTask::RegisterWith(GenericLiteralWatcher* watcher) {
@@ -47,6 +54,8 @@ void TimeTablingPerTask::RegisterWith(GenericLiteralWatcher* watcher) {
   for (int t = 0; t < num_tasks_; t++) {
     watcher->WatchLowerBound(demand_vars_[t], id);
   }
+  // Reversible number of tasks to consider for propagation.
+  watcher->RegisterReversibleInt(id, &num_tasks_to_sweep_);
 }
 
 bool TimeTablingPerTask::Propagate() {
@@ -75,19 +84,23 @@ bool TimeTablingPerTask::BuildProfile() {
 
   scp_.clear();
   ecp_.clear();
+  in_profile_.clear();
 
   // Build start of compulsory part events.
   for (int i = num_tasks_ - 1; i >= 0; --i) {
     const auto task_time = by_decreasing_start_max[i];
     const int t = task_time.task_index;
-    in_profile_[t] =
+    is_in_profile_[t] =
         helper_->IsPresent(t) && task_time.time < helper_->EndMin(t);
-    if (in_profile_[t]) scp_.push_back(task_time);
+    if (is_in_profile_[t]) {
+      in_profile_.push_back(t);
+      scp_.push_back(task_time);
+    }
   }
 
   // Build end of compulsory part events.
   for (int i = 0; i < num_tasks_; ++i) {
-    if (in_profile_[by_increasing_end_min[i].task_index]) {
+    if (is_in_profile_[by_increasing_end_min[i].task_index]) {
       ecp_.push_back(by_increasing_end_min[i]);
     }
   }
@@ -189,17 +202,38 @@ void TimeTablingPerTask::ReverseProfile() {
 bool TimeTablingPerTask::SweepAllTasks() {
   // Tasks with a lower or equal demand will not be pushed.
   const IntegerValue min_demand = CapacityMax() - profile_max_height_;
-  for (int t = 0; t < num_tasks_; ++t) {
-    // Note: We still push the optional task that may be present. It is OK to
-    // propagate the bounds of such tasks. They should become unperformed if
-    // the bounds are no longer consistent.
-    if (DemandMin(t) <= min_demand || helper_->DurationMin(t) == 0) continue;
-    if (helper_->IsAbsent(t)) continue;
 
-    if (helper_->StartMin(t) != helper_->StartMax(t) && !SweepTask(t)) {
-      return false;
+  for (int i = num_tasks_to_sweep_ - 1; i >= 0; --i) {
+    const int t = tasks_to_sweep_[i];
+    const bool fixed_start = helper_->StartMin(t) == helper_->StartMax(t);
+    const bool fixed_end = helper_->EndMin(t) == helper_->EndMax(t);
+    // A task does not have to be considered for propagation in the rest of the
+    // sub-tree if it respects one of these conditions:
+    // - its start and end variables are fixed;
+    // - it has a maximum duration of 0;
+    // - it has a maximum demand of 0;
+    // - it is absent.
+    if ((fixed_start && fixed_end) || helper_->DurationMax(t) == 0 ||
+        DemandMax(t) == 0 || helper_->IsAbsent(t)) {
+      // Remove the task from the set of tasks to sweep.
+      num_tasks_to_sweep_--;
+      tasks_to_sweep_[i] = tasks_to_sweep_[num_tasks_to_sweep_];
+      tasks_to_sweep_[num_tasks_to_sweep_] = t;
+      continue;
     }
+    // A task does not have to be considered for propagation in this particular
+    // iteration if it respects one of these conditions:
+    // - its start variable is fixed;
+    // - its minimum demand cannot lead to a resource overload;
+    // - its minimum duration is 0.
+    if (fixed_start || DemandMin(t) <= min_demand ||
+        helper_->DurationMin(t) == 0) {
+      continue;
+    }
+
+    if (!SweepTask(t)) return false;
   }
+
   return true;
 }
 
@@ -249,7 +283,7 @@ bool TimeTablingPerTask::SweepTask(int task_id) {
     new_start_min = profile_[rec_id].end;
     if (start_max < new_start_min) {
       new_start_min = start_max;
-      overload = !in_profile_[task_id];
+      overload = !is_in_profile_[task_id];
     }
     new_end_min = std::max(new_end_min, new_start_min + duration_min);
 
@@ -294,13 +328,12 @@ bool TimeTablingPerTask::UpdateStartingTime(int task_id, IntegerValue left,
 
 void TimeTablingPerTask::AddProfileReason(IntegerValue left,
                                           IntegerValue right) {
-  for (int t = 0; t < num_tasks_; ++t) {
+  for (const int t : in_profile_) {
     const IntegerValue start_max = helper_->StartMax(t);
     const IntegerValue end_min = helper_->EndMin(t);
 
-    // Do not consider the task if it does not overlap [left, right), if it is
-    // absent, or if it does not have a mandatory part.
-    if (end_min <= left || right <= start_max || !in_profile_[t]) continue;
+    // Do not consider the task if it does not overlap [left, right).
+    if (end_min <= left || right <= start_max) continue;
 
     helper_->AddPresenceReason(t);
     helper_->AddStartMaxReason(t, std::max(left, start_max));
diff --git a/src/sat/timetable.h b/src/sat/timetable.h
index 7c6abab82e..a25cf8d612 100644
--- a/src/sat/timetable.h
+++ b/src/sat/timetable.h
@@ -88,6 +88,10 @@ class TimeTablingPerTask : public PropagatorInterface {
     return integer_trail_->LowerBound(demand_vars_[task_id]);
   }
 
+  IntegerValue DemandMax(int task_id) const {
+    return integer_trail_->UpperBound(demand_vars_[task_id]);
+  }
+
   // Number of tasks.
   const int num_tasks_;
 
@@ -110,12 +114,21 @@ class TimeTablingPerTask : public PropagatorInterface {
 
   // True if the corresponding task is part of the profile, i.e., it has a
   // mandatory part and is not optional.
-  std::vector<bool> in_profile_;
+  std::vector<bool> is_in_profile_;
+
+  // Tasks that are part of the profile. In other words, this vector contains
+  // all the tasks for which is_in_profile_ is true.
+  std::vector<int> in_profile_;
 
   // True if the last call of the propagator has filtered the domain of a task
   // and changed the shape of the profile.
   bool profile_changed_;
 
+  // Reversible set of tasks to consider for propagation. The set contains the
+  // tasks in the [0, num_tasks_to_sweep_) prefix of tasks_to_sweep_.
+  std::vector<int> tasks_to_sweep_;
+  int num_tasks_to_sweep_;
+
   DISALLOW_COPY_AND_ASSIGN(TimeTablingPerTask);
 };
 
diff --git a/src/util/piecewise_linear_function.cc b/src/util/piecewise_linear_function.cc
index 939b981c69..6fc9a4dc79 100644
--- a/src/util/piecewise_linear_function.cc
+++ b/src/util/piecewise_linear_function.cc
@@ -351,53 +351,58 @@ PiecewiseLinearFunction* PiecewiseLinearFunction::CreateFullDomainFunction(
 
 PiecewiseLinearFunction* PiecewiseLinearFunction::CreateOneSegmentFunction(
     int64 point_x, int64 point_y, int64 slope, int64 other_point_x) {
-  return new PiecewiseLinearFunction(
-      {PiecewiseSegment(point_x, point_y, slope, other_point_x)});
+  std::vector<PiecewiseSegment> segments =
+    {PiecewiseSegment(point_x, point_y, slope, other_point_x)};
+  return new PiecewiseLinearFunction(segments);
 }
 
 PiecewiseLinearFunction* PiecewiseLinearFunction::CreateRightRayFunction(
     int64 point_x, int64 point_y, int64 slope) {
-  return new PiecewiseLinearFunction(
-      {PiecewiseSegment(point_x, point_y, slope, kint64max)});
+  std::vector<PiecewiseSegment> segments =
+      {PiecewiseSegment(point_x, point_y, slope, kint64max)};
+  return new PiecewiseLinearFunction(std::move(segments));
 }
 
 PiecewiseLinearFunction* PiecewiseLinearFunction::CreateLeftRayFunction(
     int64 point_x, int64 point_y, int64 slope) {
-  return new PiecewiseLinearFunction(
-      {PiecewiseSegment(point_x, point_y, slope, kint64min)});
+  std::vector<PiecewiseSegment> segments =
+      {PiecewiseSegment(point_x, point_y, slope, kint64min)};
+  return new PiecewiseLinearFunction(std::move(segments));
+
 }
 
 PiecewiseLinearFunction* PiecewiseLinearFunction::CreateFixedChargeFunction(
     int64 slope, int64 value) {
-  std::vector<PiecewiseSegment> segments;
+  std::vector<PiecewiseSegment> segments =
+      {PiecewiseSegment(0, 0, 0, kint64min),
+       PiecewiseSegment(0, value, slope, kint64max)};
   CHECK_GE(slope, 0);
   CHECK_GE(value, 0);
-  return new PiecewiseLinearFunction(
-      {PiecewiseSegment(0, 0, 0, kint64min),
-       PiecewiseSegment(0, value, slope, kint64max)});
+  return new PiecewiseLinearFunction(std::move(segments));
 }
 
 PiecewiseLinearFunction* PiecewiseLinearFunction::CreateEarlyTardyFunction(
     int64 reference, int64 earliness_slope, int64 tardiness_slope) {
-  std::vector<PiecewiseSegment> segments;
+  std::vector<PiecewiseSegment> segments =
+      {PiecewiseSegment(reference, 0, -earliness_slope, kint64min),
+       PiecewiseSegment(reference, 0, tardiness_slope, kint64max)};
   CHECK_GE(earliness_slope, 0);
   CHECK_GE(tardiness_slope, 0);
-  return new PiecewiseLinearFunction(
-      {PiecewiseSegment(reference, 0, -earliness_slope, kint64min),
-       PiecewiseSegment(reference, 0, tardiness_slope, kint64max)});
+  return new PiecewiseLinearFunction(std::move(segments));
 }
 
 PiecewiseLinearFunction*
 PiecewiseLinearFunction::CreateEarlyTardyFunctionWithSlack(
     int64 early_slack, int64 late_slack, int64 earliness_slope,
     int64 tardiness_slope) {
-  std::vector<PiecewiseSegment> segments;
-  CHECK_GE(earliness_slope, 0);
-  CHECK_GE(tardiness_slope, 0);
-  return new PiecewiseLinearFunction(
+  std::vector<PiecewiseSegment> segments =
       {PiecewiseSegment(early_slack, 0, -earliness_slope, kint64min),
        PiecewiseSegment(early_slack, 0, 0, late_slack),
-       PiecewiseSegment(late_slack, 0, tardiness_slope, kint64max)});
+       PiecewiseSegment(late_slack, 0, tardiness_slope, kint64max)};
+
+  CHECK_GE(earliness_slope, 0);
+  CHECK_GE(tardiness_slope, 0);
+  return new PiecewiseLinearFunction(std::move(segments));
 }
 
 bool PiecewiseLinearFunction::InDomain(int64 x) const {