Prior to his retirement from the Faculty in September 1999, Professor Murphy had devoted the past several years to the development of courses in Labor Relations and Alternative Dispute Resolution at the law school. Recent changes in the curriculum were based upon Professor Murphy's professional experiences as an arbitrator and mediator, which began in 1976. In 1985 he was selected for admission to the National Academy of Arbitrators, and currently serves as an umpire in labor contract disputes across the nation. On an annual basis since 1985, at least four of Professor Murphy's written arbitration opinions have been selected for publication by Commerce Clearing House or the Bureau of National Affairs.
Professor Murphy now has a course in Public Sector Labor Law that requires students to represent the respective parties in a labor matter, and present the case to a professional mediator in an all-day Saturday session at the College of Law. He had a similar course in Arbitration in which the students represented clients and presented their respective cases to professional arbitrators drawn from the ranks of the National Academy of Arbitrators.
Professor Murphy was the only University faculty member in 1996 to receive the University of Cincinnati Distinguished Teaching Professorship, which is awarded to persons who represent the ideal of the teaching profession. In November 1997, he received the Crystal Owl Award from the American Arbitration Association, one of five such awards made annually to persons who advance arbitration as a method of resolving disputes. Since his retirement, Professor Murphy has become more actively involved as a labor arbitrator on a national basis, and as a lecturer on labor arbitration for practicing professionals.