Warrior & Gulf Navigation Company (defendant) transported steel products by barge. The United Steelworkers of America (plaintiff) represented employees who maintained and repaired the barges. The parties’ collective-bargaining agreement (CBA) prohibited strikes and subjected disputes “as to the meaning and application of [its] provisions” to arbitration, except “matters which are strictly a function of management.” However, the provision also said that “[s]hould differences . . . or any kind of local trouble arise,” then the parties had to use the grievance-arbitration procedure. The union had tried for years to get a covenant that prohibited contracting out work, without success. Warrior contracted out the work and laid off most of the maintenance employees. The contracted companies used Warrior supervisors to lay out the work, hired some laid-off workers at reduced wages, and even assigned some back to Warrior’s barges. The union filed a grievance and sued to compel arbitration. The district court dismissed and the appellate court affirmed, reasoning that the management-functions clause excepted contracting out work from the grievance-arbitration requirement. The Supreme Court granted review.