Uniform Machine Scheduling Problem with Deteriorating Jobs and Rejection

2013 ◽  
Vol 433-435 ◽  
pp. 2429-2432
Author(s):  
Sheng Hua Zhao ◽  
Cheng Xin Luo
Keyword(s):  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Nondecreasing Function ◽  
Machine Scheduling ◽  
Scheduling Problem ◽  
Penalty Cost ◽  
Uniform Machine ◽  
Starting Time ◽  
Uniform Machine Scheduling ◽  
Rejection Penalty

In this paper, we consider uniform machine scheduling problem with deteriorating jobs and rejection. Each job's processing time is a linear nondecreasing function of its starting time. A job can be rejected by paying a penalty cost. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We propose a fully polynomial-time approximation scheme (FPTAS), which shows that the problem is NP-hard in the ordinary sense.

An FPTAS for Uniform Parallel-Machine Scheduling Problem with Deteriorating Jobs and Rejection

2013 ◽  
Vol 433-435 ◽  
pp. 2335-2338
Author(s):  
Cheng Xin Luo
Keyword(s):  
Deteriorating Jobs ◽  
Nondecreasing Function ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Total Load ◽  
Penalty Cost ◽  
Parallel Machine Scheduling Problem ◽  
Uniform Parallel Machine Scheduling

This paper studies uniform parallel-machine scheduling problem with deteriorating jobs and rejection. The processing time of each job is a linear nondecreasing function of its starting time. A job can be rejected by paying a penalty cost. The objective is to minimize the sum of the total load of the accepted jobs on all machines and the total rejection penalties of the rejected jobs. We propose a fully polynomial-time approximation scheme (FPTAS) for this problem.

An FPTAS for Uniform Machine Scheduling to Minimize the Total Completion Time and the Total Rejection Penalty

2013 ◽  
Vol 433-435 ◽  
pp. 2339-2342
Author(s):  
Dan Wu ◽  
Cheng Xin Luo
Keyword(s):  
Completion Time ◽  
Approximation Scheme ◽  
Total Completion Time ◽  
Np Hard ◽  
Penalty Cost ◽  
Starting Time ◽  
Uniform Machine Scheduling ◽  
Np Hard Problem ◽  
Increasing Function ◽  
Rejection Penalty

In this paper, we study the NP-hard problem of schedulingjobs onuniform machines to minimize the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. Each job's processing time is a simple linear increasing function of its starting time. A job can be rejected by paying a penalty cost. We propose a fully polynomial-time approximation scheme (FPTAS) to show the problem is NP-hard in the ordinary sense.

scholarly journals General parametric scheme for the online uniform machine scheduling problem with two different speeds

2018 ◽  
Vol 134 ◽  
pp. 18-23 ◽  
Author(s):  
Alexandre Dolgui ◽  
Vladimir Kotov ◽  
Aliaksandr Nekrashevich ◽  
Alain Quilliot
Keyword(s):  
Machine Scheduling ◽  
Scheduling Problem ◽  
Uniform Machine ◽  
Uniform Machine Scheduling

Uniform Parallel-Machine Scheduling with Deteriorating Jobs and Rejection

2014 ◽  
Vol 644-650 ◽  
pp. 2030-2033 ◽  
Author(s):  
Qi Zhang ◽  
Cheng Xin Luo
Keyword(s):  
Processing Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Polynomial Time Approximation Scheme ◽  
Starting Time ◽  
Uniform Parallel Machine Scheduling ◽  
Increasing Function

This paper considers uniform parallel-machine scheduling with linear deterioration and rejection. The processing time of a job is a linear increasing function of its starting time and jobs can be rejected by paying penalties. The objective is to find a schedule which minimizes the time by which all jobs are delivered. We propose a fully polynomial-time approximation scheme to solve this problem.

scholarly journals Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Juan Zou ◽  
Cuixia Miao
Keyword(s):  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Release Dates ◽  
Ordinary Sense ◽  
Starting Time ◽  
Total Penalty ◽  
Batching Machine ◽  
Increasing Function

We consider the unbounded parallel batch scheduling with deterioration, release dates, and rejection. Each job is either accepted and processed on a single batching machine, or rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense. Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem. Furthermore, we provide an optimalO(nlog⁡n)time algorithm for the case where jobs have identical release dates.

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