=begin
   Assign workers to shifts; each worker may or may not be available on a
   particular day. If the problem cannot be solved, use IIS to find a set of
   conflicting constraints. Note that there may be additional conflicts
   besides what is reported via IIS.
=end

describe 'Workforce1' do
  it 'works' do
    # Sample data
    # Sets of days and workers
    Shifts =
      [ "Mon1", "Tue2", "Wed3", "Thu4", "Fri5", "Sat6",
        "Sun7", "Mon8", "Tue9", "Wed10", "Thu11", "Fri12", "Sat13",
        "Sun14" ]
    Workers =
      [ "Amy", "Bob", "Cathy", "Dan", "Ed", "Fred", "Gu" ]

    # Number of workers required for each shift
    shiftRequirements =
      [ 3, 2, 4, 4, 5, 6, 5, 2, 2, 3, 4, 6, 7, 5 ]

    # Amount each worker is paid to work one shift
    pay = [ 10, 12, 10, 8, 8, 9, 11 ]

    # Worker availability: 0 if the worker is unavailable for a shift
    availability =
      [ [ 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 ],
        [ 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0 ],
        [ 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 ],
        [ 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1 ],
        [ 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1 ],
        [ 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1 ],
        [ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ]

    # Model
    env = Gurobi::Env.new
    model = Gurobi::Model.new(env)
    model.set_string(Gurobi::StringAttr::MODEL_NAME, "assignment")

    # Assignment variables: x[w][s] == 1 if worker w is assigned
    # to shift s. Since an assignment model always produces integer
    # solutions, we use continuous variables and solve as an LP.
    xCt = 0
    x   = []
    Workers.size.times do |w|
      x[w] = model.addVars(Shifts.size)
      xCt += 1
      model.update
      Shifts.size.times do |s|
        x[w][s].set_double(Gurobi::DoubleAttr::UB, availability[w][s])
        x[w][s].set_double(Gurobi::DoubleAttr::OBJ, pay[w])
        x[w][s].set_string(Gurobi::StringAttr::VAR_NAME,
            Workers[w] + "." + Shifts[s])
      end
    end

    # The objective is to minimize the total pay costs
    model.set_int(Gurobi::IntAttr::MODEL_SENSE, 1)

    # Update model to integrate new variables
    model.update

    # Constraint: assign exactly shiftRequirements[s] workers
    # to each shift s
    Shifts.size.times do |s|
      lhs = Gurobi::LinExpr.new(0.0)
      Workers.size.times do |w|
        lhs += x[w][s]
      end
      model.addConstr(lhs == shiftRequirements[s], Shifts[s])
    end

    # Optimize
    model.optimize
    status = model.get_int(Gurobi::IntAttr::STATUS)
    if status == Gurobi::UNBOUNDED
      print "The model cannot be solved ",
          "because it is unbounded\n"
      return 1
    end
    if status == Gurobi::OPTIMAL
      print "The optimal objective is ",
          model.get_double(Gurobi::DoubleAttr::OBJ_VAL), "\n"
      return 0
    end
    if status != Gurobi::INF_OR_UNBD && status != Gurobi::INFEASIBLE
      print "Optimization was stopped with status ", status, "\n"
      return 1
    end

    # do IIS
    print "The model is infeasible; computing IIS\n"
    model.computeIIS
    print "\nThe following constraint(s) ",
        "cannot be satisfied:\n"
    c = model.getConstrs
    c.size.times do |i|
      if c[i].get_int(Gurobi::IntAttr::IIS_CONSTR) == 1
        print c[i].get_string(Gurobi::StringAttr::CONSTR_NAME), "\n"
      end
    end
    c.map{|_c| _c.get_string(Gurobi::StringAttr::CONSTR_NAME)}.include?('Fri12').should be_true
  end
end