This paper considers a bi-objective model for a scheduling problem of unrelated parallel batch processing machines to minimize the makespan and maximum tardiness, simultaneously. Each job has a specific size and the data corresponding to its ready time, due date and processing time-dependent machine are uncertain and determined by trapezoidal fuzzy numbers. Each machine has a specific capacity,...

this paper addresses a production and outbound distribution scheduling problem in which a set of jobs have to be process on a single machine for delivery to customers or to other machines for further processing. we assume that there is a sufficient number of vehicles and the delivery costs is independent of batch size but it is dependent on each trip. in this paper, we present an artificial imm...

This paper addresses a production and outbound distribution scheduling problem in which a set of jobs have to be process on a single machine for delivery to customers or to other machines for further processing. We assume that there is a sufficient number of vehicles and the delivery costs is independent of batch size but it is dependent on each trip. In this paper, we present an Artificial Imm...

A batch machine is a machine that can process up to c jobs simultaneously as a batch, and the processing time of the batch is equal to the longest processing time of the jobs assigned to it. In this paper, we deal with the complexity of scheduling an unbounded batch machine, i.e., c = +∞. We prove that minimizing total tardiness is binary NP-hard, which has been an open problem in the literatur...

A batch machine is a machine that can process a number of jobs simultaneously as a batch, and the processing time of a batch is equal to the longest processing time of the jobs assigned to it. In this paper we present a polynomial time approximation scheme (PTAS) for scheduling a batch machine to minimize the total completion time with job release dates. Also, we present a fully polynomial time...

A batch processing machine can simultaneously process several jobs forming a batch. This paper considers the problem of scheduling jobs with non-identical capacity requirements, on a single-batch processing machine of a given capacity, to minimize the makespan. The processing time of a batch is equal to the largest processing time of any job in the batch. We present some dominance properties fo...

We consider the problem of scheduling n jobs with release dates on m identical parallel batch processing machines so as to minimize the maximum lateness. Each batch processing machine can process up to B (B < n) jobs simultaneously as a batch, and the processing time of a batch is the largest processing time among the jobs in the batch. Jobs processed in the same batch start and complete at the...

We consider the problem of minimizing the total late work ( n ∑ j=1 V j) on an unbounded batch processing machine, where V j = min{Tj, p j} and Tj = max{C j−d j,0}. The batch processing machine can process up to B (B≥ n) jobs simultaneously. The jobs that are processed together form a batch, and all jobs in a batch start and complete at the same time, respectively. For a batch of jobs, the proc...

We consider the problem of minimizing the makespan(Cmax) on m identical parallel batch processing machines. The batch processing machine can process 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. For a batch of jobs, the processing time of the batch is equal to the largest processing time among the job...