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.

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.

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.

Single Machine Scheduling with an Availability Constraint and Rejection

2014 ◽  
Vol 31 (05) ◽  
pp. 1450037 ◽  
Author(s):  
Chuanli Zhao ◽  
Hengyong Tang
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Time Interval ◽  
Availability Constraint ◽  
Np Hard Problem ◽  
Rejection Penalty

This paper considers single machine scheduling with an availability constraint and rejection. It is assumed that the machine is not available for processing during a given time interval. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the weighted total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. For this NP-hard problem, we present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

Scheduling Deteriorating Jobs with Availability Constraints to Minimize the Makespan

2016 ◽  
Vol 33 (06) ◽  
pp. 1650048
Author(s):  
Chuanli Zhao ◽  
Hengyong Tang
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Worst Case ◽  
Time Approximation ◽  
Starting Time ◽  
Polynomial Time Approximation Algorithm ◽  
Availability Constraints ◽  
Increasing Function ◽  
Polynomial Time Approximation

In this paper, we consider the scheduling problem in which the processing time of a job is a linear increasing function of its starting time and machine with availability constraints. The objective is to minimize the makespan. We first present a fully polynomial-time approximation scheme (FPTAS) for the case with a single machine. We then show that there exists no polynomial time approximation algorithm with a constant worst-case bound for the case with two identical machines unless [Formula: see text].

A PTAS FOR MINIMIZING TOTAL COMPLETION TIME OF BOUNDED BATCH SCHEDULING

2002 ◽  
Vol 13 (06) ◽  
pp. 817-827 ◽  
Author(s):  
XIAOTIE DENG ◽  
HAODI FENG ◽  
GUOJUN LI ◽  
GUIZHEN LIU
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Approximation Scheme ◽  
Processing System ◽  
Handling Time ◽  
Batch Scheduling ◽  
Total Completion Time ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
System P

We consider a batch processing system {pi : i = 1, 2,…,n} where pi is the processing time of job i, and up to B jobs can be processed together such that the handling time of a batch is the longest processing time among jobs in the batch. The number of job types m is not fixed and all the jobs are released at the same time. Jobs are executed non-preemptively. Our objective is to assign jobs to batches and sequence the batches so as to minimize the total completion time. The best previously known result is a 2–approximation algorithm. In this paper, we establish the first polynomial time approximation scheme (PTAS) for the problem.

scholarly journals Batch Scheduling of Deteriorating Products

2007 ◽  
Vol 1 (2) ◽  
pp. 25-34
Author(s):  
Maksim S. Barketau ◽  
T.C. Edwin Cheng ◽  
Mikhail Y. Kovalyov ◽  
C.T. Daniel Ng
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Setup Time ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Performance Guarantee ◽  
Negative Number ◽  
Time Approximation ◽  
Starting Time ◽  
Increasing Function

In this paper we consider the problem of scheduling N jobs on a single machine, where the jobs are processed in batches and the processing time of each job is a simple linear increasing function depending on job’s waiting time, which is the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. Each batch starts from the setup time S. Jobs which are assigned to the batch are being prepared for the processing during time S0 S. After this preparation they are ready to be processed one by one. The non-negative number bi is associated with job i. The processing time of the i-th job is equal to bi(si − (sib + S0)), where sib and si are the starting time of the b-th batch to which the i-th job belongs and the starting time of this job, respectively. The objective is to minimize the completion time of the last job. We show that the problem is NP-hard. After that we present an O(N) time algorithm solving the problem optimally for the case bi = b. We further present an O(N2) time approximation algorithm with a performance guarantee 2.

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.

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