Single-machine scheduling for minimizing total cost with identical, asymmetrical earliness, and tardiness penalties

Costs of flowtime, earliness and tardiness should be incorporated in real production scheduling. This paper constructs a single-machine scheduling model with a common due date to minimize the total cost including an identical, asymmetric earliness-tardiness cost. Several dominance conditions necessary for an optimal schedule are derived. A branch and bound algorithm exploiting the conditions is proposed to find an optimal schedule for an unconstrained version of the scheduling problem. Numerical experiments are demonstrated to show the effectiveness of the proposed method.