Parallel Batch Processing Machines Research Articles

Optimal on-line algorithms for scheduling on parallel batch processing machines

We consider the problem of scheduling jobs on-line on parallel batch processing machines with dynamic job arrivals to minimize makespan. We are given m identical batch processing machines, each of which can handle up to B (the capacity of a machine) 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 a constant, which is independent of the number and identity of the jobs. Each job becomes available at its arrival time, which is unknown in advance. First we deal with the unbounded case where the capacity of the batch processing machines is infinite, and derive an optimal on-line algorithm with competitive ratio 1+ g m , where g m >0 is determined by (1+ g m ) m +1 = g m +2. We then consider the bounded case where the capacity B of the batch processing machines is bounded. We provide an on-line algorithm with competitive ratio (\\sqrt{5}+1)/2 (the golden ratio) and prove that the result is the best possible for all m .

On‐line algorithms for minimizing makespan on batch processing machines

We consider problem of scheduling jobs on-line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on-line algorithms with worst-case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst-case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on-line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001

On‐line algorithms for minimizing makespan on batch processing machines

AbstractWe consider problem of scheduling jobs on‐line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on‐line algorithms with worst‐case ratio $(\sqrt{5}+1)/2$ (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst‐case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on‐line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001

Scheduling batch processing machines with incompatible job families

The problem of scheduling a single batch processing machine with incompatible job families was studied, where jobs of different families cannot be processed together in the same batch. First static problems where all jobs are available simultaneously were considered and showed that for a regular performance measure there will be no unnecessary partial batches. This allowed us to develop efficient optimal algorithms to minimize makespan (Cmax), maximum lateness (Lmax) and total weighted completion time and apply some of these results to problems with parallel identical batch processing machines. Then problems withdynamic job arrivals were considered and an efficient optimal algorithm for minimizing Cmax and several heuristics to minimize Lmax were provided. Computational experiments showed that the heuristics developed for the latter problem consistently improve on dispatching solutions in very reasonable CPU times.

Minimizing total completion time on batch processing machines

Abstract We study the problem of minimizing total completion time on single and parallel batch processing machines. A batch processing machine is one which can process up to B jobs simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. This problem is motivated by burn-in operations in the final testing stage of semiconductor manufacturing and is expected to occur in other production environments. We provide an exact solution procedure for the single-machine problem and heuristic algorithms for both single and parallel machine problems. While the exact algorithms have limited applicability due to high computational requirements, extensive experiments show that the heuristics are capable of consistently obtaining near-optimal solutions in very reasonable CPU times.

Efficient Algorithms for Scheduling Semiconductor Burn-In Operations

In this paper, we study the problem of scheduling semiconductor burn-in operations, where burn-in ovens are modeled as batch processing machines. A batch processing machine is one that can process up to B jobs simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. We present efficient dynamic programming-based algorithms for minimizing a number of different performance measures on a single batch processing machine. We also present heuristics for a number of problems concerning parallel identical batch processing machines and we provide worst case error bounds.

Bounds on Multiprocessing Timing Anomalies

Bounds on Multiprocessing Timing Anomalies