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In this paper, a single-machine scheduling model with a given common due date is considered. Job processing time is a linear decreasing function of its starting time. The objective function is to minimize the total weighted earliness award and tardiness penalty. Our aim is to find an optimal schedule so as to minimize the objective function. As the problem is NP-hard, some properties and polynomial time solvable cases of this problem are given. A dynamic programming algorithm for the general case of the problem is provided.

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This paper addresses a single-machine large-scale rescheduling problems with efficiency and stability subject to machine breakdown. Partial rescheduling (PR) strategy is used to cope with the computational complexity. Two kinds of objective functions of PR sub-problem, where the global dual objectives are reflected to an extent, are designed respectively for the procedural PR horizon and the terminal PR horizon. The PR problem is solved by a branch and bound algorithm. Lower bound and upper bound procedures as well as dominance rules are developed for the branch and bound algorithm. An extensive experimentation was conducted. The computational results show that the branch and bound can solve PR sub-problems with certain scales and the partial rescheduling procedure developed can greatly improve the stability of schedule with little sacrifice in efficiency and provide a reasonable trade-off between solution quality and computational cost.

In this paper, a single-machine scheduling model with a given common due date and simple linear processing times was considered. The objective is the total weighted tardiness penalty and earliness award. Some polynomial time solvable cases for this problem are given. A dynamic programming algorithm was provided and a branch and bound algorithm for general case of the problem was provided based on a rapid method for estimating the lower bound.