Parallel-machine batch scheduling to minimize the maximum lateness and the number of tardy jobs

[[abstract]]There is a set of jobs available to process in batches on a set of identical parallel machines. A sequence-independent setup time is incurred whenever a batch is formed on any machine. The jobs in the same batch are continuously processed after the setup. The processing length of a batch is the sum of the setup time and the processing times of the jobs it contains. Under the batch availability constraint, the completion time of a job is defined as the time when the batch it belongs to is totally completed. With each job, a due date is specified for its completion. In this paper, we first consider the problem to schedule as well as group the jobs so that the maximum lateness is minimized. The second problem is to minimize the number of tardy jobs. We first design dynamic programming algorithms for finding optimal solutions to the two problems. Then, we design several heuristics and conduct computational experiments to study their relative performance. (C) 2003 Elsevier B.V. All rights reserved.[[note]]SC

Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs

[[abstract]]In this paper, we study a scheduling problem of minimizing the total completion time on a single machine where the processing time of a job is a step function of its starting time and a due date that is common to all jobs. This problem has been shown to be NP-hard in the literature. To derive optimal solutions from a practical aspect, we develop a lower bound and two elimination rules to design branch-and-bound algorithms. Through computational experiments, we show that the proposed properties are effective in curtailing unnecessary explorations during the solution-finding process, and that the synergy of these properties can solve problems with up to 100 jobs in a few seconds. (C) 2003 Elsevier Ltd. All rights reserved.[[note]]SC

Makespan minimization in single-machine scheduling with step-deterioration of processing times

[[abstract]]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 N P-hard in the literature. In this paper, we first show this problem to be N P-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.[[note]]SC