This paper is concerned with the unit commitment problem in an electric power system with both thermal and pumped-storage hydroelectric units. This is a mixed integer programming problem and the Lagrangean relaxation method is used. We show that the relaxed problem decomposes into two kinds of subproblems : a shortest-path problem for each thermal unit and a minimum cost flow problem for each pumped-storage hydroelectric unit. A method of obtaining an incumbenet solution from the solution of a relaxed problem is presented. The Lagrangean multipliers are updated using both subgradient and incremental cost. The algorithm is applied to a real Korean power generation system and its computational results are reported and compaired with other works.