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Makespan minimization in single-machine scheduling with step-deterioration of processing times. (English) Zbl 1095.90038
Summary: This paper considers a single-machine scheduling problem of minimizing the maximum completion time for a set of independent jobs. The processing time of a job is a non-linear step function of its starting time and due date. The problem is already known to be $\cal {NP}$-hard in the literature. In this paper, we first show this problem to be $\cal {NP}$-hard in the ordinary sense by proposing a pseudo-polynomial time dynamic programming algorithm. Then, we develop two dominance rules and a lower bound to design a branch-and-bound algorithm for deriving optimal solutions. Numerical results indicate that the proposed properties can effectively reduce the time required for exploring the solution space.

90B35Scheduling theory, deterministic
90C39Dynamic programming
90C60Abstract computational complexity for mathematical programming problems
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