Split scheduling with uniform setup times

Schalekamp, Frans; Sitters, René; Ster, Suzanne van der; Stougie, Leen; Verdugo, Victor; Zuylen, Anke van

doi:10.1007/s10951-014-0370-4

Cited by 13 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They achieve a (1+φ)-approximation where φ denotes the golden ratio, using a newly designed linear programming formulation. Moreover, there are recent results concerning machine scheduling in the splittable model considering the sum of (weighted) completion times as the objective function, e.g., [9,32]. For the preemptive model, a PTAS for the special case that all jobs have the same setup time has been developed by Schuurman and Woeginger [33].…”

Section: Related Workmentioning

confidence: 99%

Empowering the configuration-IP: new PTAS results for scheduling with setup times

et al. 2021

View full text Add to dashboard Cite

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time $$f(1/\varepsilon )\cdot \mathrm {poly}(|I|)$$ f ( 1 / ε ) · poly ( | I | ) . Previously, only constant factor approximations of 5/3 and $$4/3 + \varepsilon $$ 4 / 3 + ε , respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.

show abstract

Section: Related Workmentioning

confidence: 99%

Empowering the configuration-IP: new PTAS results for scheduling with setup times

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Moreover, there are recent results concerning machine scheduling in the splittable model considering the sum of the (weighted) completion times as the objective function, e.g. [24,8]. For the preemptive model, a PTAS for the special case that all jobs have the same setup time has been developed by Schuurman and Woeginger [25].…”

Section: Related Workmentioning

confidence: 99%

Empowering the Configuration-IP $-$ New PTAS Results for Scheduling with Setups Times

Jansen,

Klein,

Maack

et al. 2018

Preprint

View full text Add to dashboard Cite

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a configuration describes a possible placement on one of the target locations, and the IP is used to chose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and therefore be solved efficiently. As an application, we consider scheduling problems with setup times, in which a set of jobs has to be scheduled on a set of identical machines, with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f (1/ε) × poly(|I|) with a single exponential term in f for the first and a double exponential one for the second case. Previously, only constant factor approximations of 5/3 and 4/3 + ε respectively were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine. ACM Subject ClassificationTheory of computation → Scheduling algorithms, Theory of computation → Discrete optimization Keywords and phrases Parallel Machines, Setup Time, EPTAS, n-fold integer programming Acknowledgements We thank Syamantak Das for helpful discussions on the problem.

show abstract

“…Equation ( 10) defines variable 𝑥 𝑖𝑙𝑗 must be one if variable 𝑤 𝑖𝑙𝑗 is greater than zero. Definition of total processing time of a machine 𝑗, 𝑗 ∈ 𝑀 consists of total processing time of jobs that is scheduled in that machine in (12). Make span is defined as the latest total processing time of any machine 𝑗, 𝑗 ∈ 𝑀 in (13).…”

Section: Milp Model With Job-splitting Propertymentioning

confidence: 99%

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear Programming

Oktafiani

Ardiansyah²

2023

IJIES

View full text Add to dashboard Cite

The scheduling of parallel machines with and without a job-splitting property, deterministic demand, and sequence-independent setup time with the goal of minimizing makespan is examined in this work. For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random (job) sections. When a job starts to be processed on a machine, an operator has to setup the machine for an hour. By creating two Mixed Integer Linear Programming models, this work proposes a mathematical programming strategy (MILP). A MILP model takes the job-splitting property into account. Another model, however, does not include the job-splitting property. This study investigates the performance of the proposed models using Gurobi solver. These programs' numerical calculations are based on actual problems in the Indonesian city of Bandung's plastics industry. On four identical parallel injection molding machines, 318 jobs must be finished in 22 periods. The real scheduling method is contrasted with these two MILP models. The maximum workload imbalance, the maximum relative percentage of imbalance, and the makespan of these three scheduling systems are used to evaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue of scheduling identical parallel machines on injection molding machines to reduce makespan, resulting in a 36% average decrease. The MILP model's job-splitting property can reduce makespan by an additional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP without job-splitting property, and actual scheduling based on the makespan minimization, workload imbalance, and relative percentage of imbalance.

show abstract

Split scheduling with uniform setup times

Cited by 13 publications

References 12 publications

Empowering the configuration-IP: new PTAS results for scheduling with setup times

Empowering the configuration-IP: new PTAS results for scheduling with setup times

Empowering the Configuration-IP $-$ New PTAS Results for Scheduling with Setups Times

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear Programming

Contact Info

Product

Resources

About