This work deals with the parallel machines scheduling problem which consists in the assignment of n jobs on m parallel machines. The most general variant of this problem is when the processing time depends on the machine to which each job is assigned to. This case is known as the unrelated parallel machines problem. Similarly to most of the literature, this paper deals with the minimization of ...

In this paper we consider the problem of scheduling jobs on parallel identical machines, where the processing times of jobs are uncertain: only interval bounds of processing times are known. The optimality criterion of a schedule is the total completion time. In order to cope with the uncertainty we consider the maximum regret objective and we seek a schedule which performs well under all possi...

The unrelated parallel machine scheduling (PMS) problem is essential for the manufacturing industry. Scheduling will save company resources, especially time management. By solving problems quickly and precisely, can get more profit. On that note, this paper focused on PMS problems, which did not consider inherent uncertainty in processing set up by minimizing makespan tardiness. This aimed to m...

A classical scheduling problem is to find schedules that minimize average weighted completion time of jobs with release dates. When multiple machines are available, the machine environments may range from identical machines (the processing time required by a job is invariant across the machines) at one end, to unrelated machines (the processing time required by a job on any machine is an arbitr...

This paper studies the customer order scheduling problem in context of additive manufacturing. The study discusses an integrated involving nesting parts as well batches nested onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from literature, that integrates different materials and sequence-dependent setup times. Additionally, a met...

A very well-known machine model in scheduling allows the machines to be unrelated, modelling jobs that might have different characteristics on each machine. Due to its generality, many optimization problems of this form are very difficult to tackle and typically APX-hard. However, in many applications the number of different types of machines, such as processor cores, GPUs, etc. is very limited...

We derive the first performance guarantees for a combinatorial online algorithm that schedules stochastic, nonpreemptive jobs on unrelated machines to minimize the expectation of the total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required sophisticated linear or convex programming relaxations for the assign...