more code samples for sat

examples/python/code_samples_sat.py

@@ -84,6 +84,67 @@ def RabbitsAndPheasants():
     print('%i rabbits and %i pheasants' % (solver.Value(r), solver.Value(p)))
 
 
+def BinpackingProblem():
+  """Solves a bin-packing problem."""
+  # Data.
+  bin_capacity = 100
+  slack_capacity = 20
+  num_bins = 10
+  all_bins = range(num_bins)
+
+  items = [(20, 12), (15, 12), (30, 8), (45, 5)]
+  num_items = len(items)
+  all_items = range(num_items)
+
+  # Model.
+  model = cp_model.CpModel()
+
+  # Main variables.
+  x = {}
+  for i in all_items:
+    num_copies = items[i][1]
+    for b in all_bins:
+      x[(i, b)] = model.NewIntVar(0, num_copies, 'x_%i_%i' % (i, b))
+
+  # Load variables.
+  load = [model.NewIntVar(0, bin_capacity, 'load_%i' % b) for b in all_bins]
+
+  # Slack variables.
+  slacks = [model.NewBoolVar('slack_%i' % b) for b in all_bins]
+
+  # Links load and x.
+  for b in all_bins:
+    model.Add(load[b] == sum(x[(i, b)] * items[i][0] for i in all_items))
+
+  # Place all items.
+  for i in all_items:
+    model.Add(sum(x[(i, b)] for b in all_bins) == items[i][1])
+
+  # Links load and slack through an equivalence relation.
+  safe_capacity = bin_capacity - slack_capacity
+  for b in all_bins:
+    # slack[b] => load[b] <= safe_capacity.
+    model.Add(load[b] <= safe_capacity).OnlyEnforceIf(slacks[b])
+    # not(slack[b]) => load[b] > safe_capacity.
+    model.Add(load[b] > safe_capacity).OnlyEnforceIf(slacks[b].Not())
+
+  # Maximize sum of slacks.
+  model.Maximize(sum(slacks))
+
+  print(model)
+
+  # Solves and prints out the solution.
+  solver = cp_model.CpSolver()
+  status = solver.Solve(model)
+  print('Solve status: %s' % solver.StatusName(status))
+  if status == cp_model.OPTIMAL:
+    print('Optimal objective value: %i' % solver.ObjectiveValue())
+  print('Statistics')
+  print('  - conflicts : %i' % solver.NumConflicts())
+  print('  - branches  : %i' % solver.NumBranches())
+  print('  - wall time : %f s' % solver.WallTime())
+
+
 def IntervalSample():
   model = cp_model.CpModel()
   horizon = 100
@@ -364,6 +425,8 @@ def main(_):
   ReifiedSample()
   print('--- RabbitsAndPheasants ---')
   RabbitsAndPheasants()
+  print('--- BinpackingProblem ---')
+  BinpackingProblem()
   print('--- IntervalSample ---')
   IntervalSample()
   print('--- MinimalCpSat ---')