Online scheduling on two parallel-batching machines with limited restarts to minimize the makespan

Fu, Ruyan; Cheng, T.C.E.; Ng, C. T.; Yuan, Jinjiang

doi:10.1016/j.ipl.2010.04.008

Cited by 9 publications

(2 citation statements)

References 15 publications

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“…For the corresponding problem using limited restart, Fu et al [6] gave an online algorithm with a competitive ratio of 3/2 and proved that it is best possible. For the problem of minimizing makespan on two unbounded parallel batch machines with limited restart, Fu et al [20] provided a best possible online algorithm which is ( √ 3+1)/2-competitive under the secondrestart assumption. Recently, Liu and Yuan [21] presented best possible online algorithms for minimizing makespan of equal length jobs on a bounded parallel batch machine with limited restart or restart.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

Liu

Wan

Yan

et al. 2015

Mathematical Problems in Engineering

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We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacitybto minimize the time by which all jobs have been delivered with limited restart. Here, “restart” means that a running batch may be interrupted, losing all the work done on it, and jobs in the interrupted batch are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that a running batch which contains some restarted jobs cannot be restarted again. Whenb=2, we propose a best possible online algorithmH(b=2)with a competitive ratio of1+α, whereαis the positive solution of2α(1+α)=1. Whenb≥3, we present a best possible online algorithmH(b≥3)with a competitive ratio of1+β, whereβis the positive solution ofβ(1+β)2=1.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

Liu

Wan

Yan

et al. 2015

Mathematical Problems in Engineering

Self Cite

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“…Constraints (6) and (7) assure that each non empty batch is processed in just one position of the first and of the second furnace respectively. Constraints (8) and (9) define the completion time of the last processed batch on the two furnaces. Constraints (10) impose that each batch is processed just on one of the two furnaces.…”

Section: Literature Reviewmentioning

confidence: 99%

A MILP formulation for a batch scheduling problem on parallel machines in the aircraft industry

Boccia

Bruno²,

Sterle³

2013

2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO)

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In the aircraft industry structural components, referred to as part numbers (PN), have to be subject to an heat treatment in capacitated burn-in furnaces for a pre-defined period (exposure time) in order to provide them with specific physic and chemical features (e.g. hardness, corrosion resistance, conductivity). Two or more part numbers can be grouped in a batch and treated simultaneously in the same furnace if it is possible to individuate a common exposure time. In order to minimize the total completion time (makespan) of the process it needs to determine the appropriate grouping of the part numbers into batches (batching problem) to be processed by each furnace (scheduling problem). The problem can be modeled as a batch scheduling problem on parallel machines where the batching and the scheduling problem are considered at the same time. Starting from a real case study, we present an original integer linear programming formulation in the case of two capacitated parallel machines and we provide the results obtained on two real instances coming from the aircraft industry

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Online and Semi-online Scheduling

Tan

Zhang

2013

Handbook of Combinatorial Optimization

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Online scheduling on two parallel-batching machines with limited restarts to minimize the makespan

Cited by 9 publications

References 15 publications

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

A MILP formulation for a batch scheduling problem on parallel machines in the aircraft industry

Online and Semi-online Scheduling

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