Optimal constant due-date determination and sequencing of n jobs on a single machine

This paper considers due-date determination and sequencing of n jobs on a single-machine where each job is given a constant flow allowance. The objective is to determine the optimal value of the flow allowance and the optimal job sequence to minimize a cost function based on the flow allowance and the job earliness and tardiness values. We first propose a linear programming (LP) formulation of the problem and then derive the optimal constant flow allowance via considering the LP dual problem. We show that the optimal constant due-date value is independent of job sequence. After the theoretical treatment, a numerical example is presented for discussion.