A two-agent single-machine scheduling problem to minimize the total cost with release dates

2015 ◽  
Vol 21 (3) ◽  
pp. 805-816 ◽  
Author(s):  
Du-Juan Wang ◽  
Yunqiang Yin ◽  
Wen-Hsiang Wu ◽  
Wen-Hung Wu ◽  
Chin-Chia Wu ◽  
...  
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Total Cost

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.

An investigation on a two-agent single-machine scheduling problem with unequal release dates

2012 ◽  
Vol 39 (12) ◽  
pp. 3062-3073 ◽  
Author(s):  
Yunqiang Yin ◽  
Wen-Hsiang Wu ◽  
Shuenn-Ren Cheng ◽  
Chin-Chia Wu
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem

scholarly journals Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 133 ◽  
Author(s):  
Xiaofei Liu ◽  
Weidong Li
Keyword(s):  
Single Machine ◽  
Exact Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Scheduling Problem ◽  
Combinatorial Algorithm ◽  
Processing Times ◽  
Primal Dual ◽  
Rejection Penalty

In this paper, we consider the single machine scheduling problem with release dates and nonmonotone submodular rejection penalty. We are given a single machine and multiple jobs with probably different release dates and processing times. For each job, it is either accepted and processed on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a nonmonotone submodular function. We design a combinatorial algorithm based on the primal-dual framework to deal with the problem, and study its property under two cases. For the general case where the release dates can be different, the proposed algorithm have an approximation ratio of 2. When all the jobs release at the same time, the proposed algorithm becomes a polynomial-time exact algorithm.

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