Research on Multiple Slack Due-Date Assignments Scheduling with Position-Dependent Weights

This paper considers a single-machine scheduling problem where jobs have multiple slack due-date assignments, i.e., some jobs have a common flow allowance and all jobs have m (m > 0 is a given constant) common flow allowances. The objective is to determine the multiple common flow allowances and optimal job sequence that minimizes the weighted sum of earliness-tardiness penalty and slack due-date assignment cost, where the weights only depend on their positions in a sequence, i.e., the position-dependent weights. Optimal properties are given for this problem, and then the problem is shown to be polynomially solvable when the number of multiple slack due-date assignments is a given constant. The model with multiple slack due-date assignments can also be extended to position (time)-dependent scheduling.