Showing papers by "Peter Brucker published in 1998"

Scheduling a batching machine

Abstract: We address the problem of scheduling n jobs on a batching machine to minimize regular scheduling criteria that are non-decreasing in the job completion times A batching machine is a machine that can handle up to b jobs simultaneously The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time The processing time of a batch is equal to the largest processing time of any job in the batch We analyse two variants: the unbounded model, where b⩾n; and the bounded model, where b1; for the case with m different processing times, we give a dynamic programming algorithm that requires O(b2m22m) time Moreover, we prove that due date based scheduling criteria give rise to NP-hard problems Finally, we show that an arbitrary regular cost function can be minimized in polynomial time for a fixed number of batches © 1998 John Wiley & Sons, Ltd

Tabu-search for the multi-mode job-shop problem

Abstract: In a multi-processor-tasks job-shop problem (MPTJSP) there is a machine set associated with each operation. All machines are needed for the whole processing period to process the operation. The objective is to find a schedule which minimizes the makespan. In a multi-mode job-shop problem (MMJSP) there is a set of machine sets associated with each operation. One has to assign a machine set to each operation and to solve the resulting MPTJSP such that the resulting makespan is minimized. For the MMJSP a tabu-search algorithm is presented. Computational results are reported.

Batch scheduling with deadlines on parallel machines

Abstract: The problem of scheduling G groups of jobs on m parallel machines is considered Each group consists of several identical jobs We have to find splittings of groups into batches (ie sets of jobs to be processed contiguously) and to schedule the batches on the machines It is possible for different batches of the same group to be processed concurrently on different machines However, at any time, a batch can be processed on at most one machine A sequence-independent machine set-up time is required immediately before a batch of a group is processed A deadline is associated with each group The objective is to find a schedule which is feasible with respect to deadlines The problem is shown to be NP-hard even for the case of two identical machines, unit processing times, unit set-up times and a common deadline It is strongly NP-hard if machines are uniform, the number of jobs in each group is equal and processing times, set-up times and deadlines are unit Special cases which are polynomially solvable are discussed For the general problem, a family {DPɛ} of approximation algorithms is constructed A new dynamic rounding technique is used to develop DP ɛ For any ɛ > 0, DP ɛ delivers a schedule in which the completion time of each group is at most (1 + ɛ) times the value of its deadline if there exists a schedule which is feasible with respect to the deadlines The time complexity of DP ɛ is O(G 2m+1/ɛ2m)

Scheduling: Theory and Applications

Abstract: This paper has two parts. In the first part (Section 2 to 5), we discuss complexity issues for deterministic scheduling problems and their implications. These issues reflect the current trend in the scheduling literature. The second part (Section 6), is devoted to a practical case study.