Lower bounds for earliness-tardiness minimization on a single machine

In this paper, we propose tow lower bounds for the problem of scheduling N-independent jobs on a single machine to minimize the sum of early and tardy costs. Jobs have distinct due dates and processing times with earliness and tardiness costs. The problem is proved to be NP-hard. A simple local search algorithm is presented in order to derive an upper bound for the problem and tested the proposed lower bounds in a branch and bound algorithm. Computational experiments show that in several cases, where the lower bounds of the literature are weak, our lower bounds are more efficient.