In this paper, we consider the scheduling problem of minimizing total weighted completion time on uniform machines with unbounded batch. Each of the machine Ml (l = 1, ⋅ ⋅ ⋅ ,m) has a speed sl and can process up to B(≥ n) jobs simultaneously as a batch. The processing time of a batch denoted by P(B) is given by the processing time of the longest job in it, and the running time of the batch on m...

Scheduling is a key factor for manufacturing productivity. Effective scheduling can improve on-time delivery, reduce work-in-process inventory, cut lead time, and improve machine utilization. Motivated by the extensive use of batch machines in manufacturing industries, the scheduling of job shops with batch machines is studied in this paper. Unlike machines that can process one part at a time (...

We address the problem of scheduling jobs with non-identical sizes and distinct processing times on a single batch-processing machine, aiming at minimizing makespan. The extensive literature this NP-hard mostly focuses heuristics. Using an arc-flow based optimization approach, we construct novel formulation that represents it as determining flows in graphs. size increases machine capacity numbe...

This paper investigates the scheduling problem of minimizing makespan on parallel batch processing machines encountered in different manufacturing environments, such as the burn-in operation in the manufacture of semiconductors and the aging test operation in the manufacture of thin film transistor-liquid crystal displays (TFT-LCDs). Each job is characterized by a processing time, a release tim...

We consider the problem of scheduling n jobs onm identical parallel batching machines. Each job is characterized by a release time and a processing time. Each machine can process up to B (B < n ) jobs as a batch simultaneously. The processing time of a batch is equal to the largest processing time among all jobs in the batch. The objective is to minimize the maximum completion time (makespan). ...

We consider two semi-online scheduling problems on a single batch (processing) machine with jobs’ nondecreasing processing times and jobs’ nonincreasing processing times, respectively. Our objective is to minimize the makespan. A batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and a...

We consider the problem of on-line scheduling a set of n jobs on two parallel batch processing machines. Each machine can handle an infinite number of jobs as a batch simultaneously. The processing time of a batch is the time required for processing the longest job in the batch. Each job becomes available at its release date, which is not known in advance, and its processing time only becomes k...