Approximation algorithm for the parallel-machine scheduling problem with release dates and submodular rejection penalties

2022 ◽  
Author(s):  
Hongye Zheng ◽  
Suogang Gao ◽  
Wen Liu ◽  
Weili Wu ◽  
Ding-Zhu Du ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Release Dates ◽  
Scheduling Problem ◽  
Parallel Machine Scheduling Problem

scholarly journals A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

BicriteriaHeuristic for Unrelated Parallel Machine Scheduling Problem

2014 ◽  
Vol 1016 ◽  
pp. 824-828
Author(s):  
Yang Kuei Lin ◽  
Hao Chen Lin
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Release Dates ◽  
Scheduling Problem ◽  
Unrelated Parallel Machines ◽  
Weighted Tardiness ◽  
Unrelated Parallel Machine Scheduling ◽  
Parallel Machine Scheduling Problem

In this research, a bi-criteria heuristic is proposed to find non-dominated solutions for scheduling unrelated parallel machines with release dates that minimizes makespan andtotal weighted tardiness.

scholarly journals Using Approximation within Constraint Programming to Solve the Parallel Machine Scheduling Problem with Additional Unit Resources

2020 ◽  
Vol 34 (02) ◽  
pp. 1512-1519 ◽  
Author(s):  
Arthur Godet ◽  
Xavier Lorca ◽  
Emmanuel Hebrard ◽  
Gilles Simonin
Keyword(s):  
Experimental Data ◽  
Approximation Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Unrelated Machines ◽  
Reference Models ◽  
Parallel Machine Scheduling Problem ◽  
Constraint Model

In this paper, we consider the Parallel Machine Scheduling Problem with Additional Unit Resources, which consists in scheduling a set of n jobs on m parallel unrelated machines and subject to exactly one of r unit resources. This problem arises from the download of acquisitions from satellites to ground stations. We first introduce two baseline constraint models for this problem. Then, we build on an approximation algorithm for this problem, and we discuss about the efficiency of designing an improved constraint model based on these approximation results. In particular, we introduce new constraints that restrict search to executions of the approximation algorithm. Finally, we report experimental data demonstrating that this model significantly outperforms the two reference models.

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