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This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems. [ABSTRACT FROM AUTHOR]

Abstract  We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the problem of scheduling a single machine to minimize the number of late jobs in the presence of sequence-independent family set-up times. The jobs are partitioned into families, and a set-up time is required at the start of each batch, where a batch is a maximal set of jobs in the same family that are processed consecutively. We design branch and bound algorithms that have several alternative features. Lower bounds can be derived by relaxing either the set-up times or the due dates. A first branching scheme uses a forward branching rule with a depth-first search strategy. Dominance criteria, which determine the order of the early jobs within each family and the order of the batches containing early jobs, can be fully exploited in this scheme. A second scheme uses a ternary branching rule in which the next job is fixed to be early and starting a batch, to be early and not starting a batch, or to be late. The different features are compared on a large set of test problems, where the number of jobs ranges from 30 to 50 and the number of families ranges from 4 to 10. [ABSTRACT FROM AUTHOR]