This paper considers the n-job, single-machine sequencing problem with slack (SLK) due-dates. The objective is to determine the optimal value of the slack allowance k*and the optimal job sequence ρ*to minimize a cost function based on the slack allowance and the job earliness and tardiness values. A linear-programming formulation of the problem is proposed and the optimal slack allowance is derived through solving the LP dual problem. It is shown that for a problem in the general form the optimal job sequence cannot be determined, but under a special condition it can elegantly be established. After the theoretical treatment, a numerical example is given for discussion.
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