Minimizing the earliness-tardiness costs on a single machine

This paper deals with the problem of scheduling a given set of independent jobs on a single machine to minimize the sum of early and tardy costs without considering machine idle time. Jobs have distinct due dates and processing times with earliness and tardiness costs. The problem is proved to be NP-hard (K.R. Baker and G.D. Scudder, 1990). A mixed integer programming formulation for the problem is presented and a lower bound is obtained by the linear relaxation. A branch and bound algorithm is developed incorporating this lower bound and an upper bound proposed by George Lie (1997). Finally, computational experiments on problems with up to 25 jobs are discussed.