Abstract We consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual time each job is described by an arbitrary positive function the position it holds on machine. However, itself may additionally depend or machine this was assigned to. Our aim to find schedule that minimizes objectives maximum completion total time. present full set pol...

We consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the first section. This problem is the generalization of the classical parallel machine scheduling problem, when the makespan is minimized; in that case each job contains only one task. On the other hand, the problem in consideration is still a special version of the workf...

The parallel machine scheduling problem is an important and difficult problem to be considered in the real-world situations. Traditionally, this problem consists of the scheduling of a set of independent jobs on parallel machines with the aim of minimizing the maximum job completion. In today's manufacturing systems, in which both early and tardy finishing of job processing are undesired, the o...

In this paper, we provide a new class of randomized approximation algorithms for parallel machine scheduling problems. The most general model we consider is scheduling unrelated machines with release dates (or even network scheduling) so as to minimize the average weighted completion time. We introduce an LP relaxation in time-indexed variables for this problem. The crucial idea to derive appro...

Traditionally,machine scheduling research is concernedwith the sequencing of tasks on one machine or on several parallel or different machines, subject to a set of constraints. Over the years, researchers have studied a huge variety of problems, developing numerous heuristics, approximation and exact algorithms, and complexity results. Some of these problems are interesting because of their int...

Machine scheduling admits two options to process jobs. In a preemptive mode processing may be interrupted and resumed later even on a different machine. In a nonpreemptive mode interruptions are not allowed. Usually, the possibility to preempt jobs leads to better performance values. However, also examples exist where preemptions do not improve the performance. This paper gives an overview of e...

In this paper, a Job shop scheduling problem with a parallel assembly stage and Lot Streaming (LS) is considered for the first time in both machining and assembly stages. Lot Streaming technique is a process of splitting jobs into smaller sub-jobs such that successive operations can be overlapped. Hence, to solve job shop scheduling problem with a parallel assembly stage and lot streaming, deci...

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove t...

in this paper, we considered solving approaches to flexible job shop problems. makespan is not a good evaluation criterion with overlapping in operations assumption. accordingly, in addition to makespan, we used total machine work loading time and critical machine work loading time as evaluation criteria. as overlapping in operations is a practical assumption in chemical, petrochemical, and gla...