Abstract
A condition is given to decompose a large scheduling problem into two or more scheduling problems of smaller size. The applicability of the decomposition approach to scheduling problems is illustrated through the single machine scheduling problem n/1/F_w|T_<max> = 0, minimizing the weighted flow time with zero maximum tardiness, and a branch and bound algorithm incorporating the decomposition principle is presented to obtain the optimal schedule. This algorithm is then extended to obtain the optimal schedule to the single machine scheduling problem n/1/F_w|T_<max'> minimizing the weighted flow time with minimum/maximum tardiness, by reducing n/1/F_w|T_<max> = 0.
