Optimal constant due-date assignment and sequencing

This paper considers the sequencing of n jobs in a single-machine shop in which each job is assigned 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. We then derive the optimal constant flow allowance via considering the LP dual problem and show that it is independent of the job sequence. After the theoretical treatment, a numerical example is presented for discussion.