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.

scholarly journals Batch Scheduling with Proportional-Linear Deterioration and Outsourcing

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Cuixia Miao ◽  
Fanxiao Meng ◽  
Juan Zou ◽  
Binglin Jia
Keyword(s):  
Dynamic Programming Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Third Party ◽  
Batch Scheduling ◽  
Programming Algorithm ◽  
Release Dates ◽  
Linear Deterioration ◽  
Total Penalty ◽  
Maximum Completion Time

We consider the bounded parallel-batch scheduling with proportional-linear deterioration and outsourcing, in which the actual processing time is pj=αj(A+Dt) or pj=αjt. A job is either accepted and processed in batches on a single machine by manufactures themselves or outsourced to the third party with a certain penalty having to be paid. The objective is to minimize the maximum completion time of the accepted jobs and the total penalty of the outsourced jobs. For the pj=αj(A+Dt) model, when all the jobs are released at time zero, we show that the problem is NP-hard and present a pseudo-polynomial time algorithm, respectively. For the pj=αjt model, when the jobs have distinct m (<n) release dates, we provide a dynamic programming algorithm, where n is the number of jobs.

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].

scholarly journals Scheduling Simple Linear Deteriorating Jobs with Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Zou ◽  
Yuzhong Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Machine Model ◽  
Time Approximation ◽  
Total Penalty ◽  
Polynomial Time Approximation

We consider the problems of scheduling deteriorating jobs with release dates on a single machine (parallel machines) and jobs can be rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. For a single machine model, the objective is to minimize the maximum lateness of the accepted jobs plus the total penalty of the rejected jobs. We show that the problem is NP-hard in the strong sense and presents a fully polynomial time approximation scheme to solve it when all jobs have agreeable release dates and due dates. For parallel-machine model, the objective is to minimize the maximum delivery completion time of the accepted jobs plus the total penalty of the rejected jobs. When the jobs have identical release dates, we first propose a fully polynomial time approximation scheme to solve it. Then, we present a heuristic algorithm for the case where all jobs have to be accepted and evaluate its efficiency by computational experiments.

SCHEDULING DETERIORATING JOBS ON A SINGLE MACHINE WITH RELEASE TIMES AND REJECTION

2012 ◽  
Vol 04 (02) ◽  
pp. 1250032 ◽  
Author(s):  
MING LIU ◽  
FEIFENG ZHENG ◽  
CHENGBIN CHU ◽  
YINFENG XU
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Deteriorating Jobs ◽  
Release Time ◽  
Starting Time ◽  
Release Times ◽  
Deteriorating Job ◽  
Total Penalty ◽  
Programming Algorithms ◽  
Increasing Function

This paper considers scheduling deteriorating jobs on a single machine with release times and rejection. Deteriorating job means that its actual processing time is a increasing function on its execution starting time. In this situation, jobs can be rejected by paying penalties. Each job is associated with a release time. The objective is to minimize the makespan plus the total penalty incurred by rejecting jobs. We present two dynamic programming algorithms and then design an FPTAS for the considered 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.

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.

SCHEDULING PROPORTIONALLY DETERIORATING JOBS IN TWO-MACHINE OPEN SHOP WITH A NON-BOTTLENECK MACHINE

2011 ◽  
Vol 28 (05) ◽  
pp. 623-631 ◽  
Author(s):  
SHISHENG LI
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Open Shop ◽  
Ordinary Sense ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Decision Version ◽  
Bottleneck Machine ◽  
Polynomial Time Approximation

We address the problem of scheduling proportionally deteriorating jobs in two-machine open shop in which one of the machines is non-bottleneck. The objective is to minimize the makespan. We show that the decision version of the problem is [Formula: see text]-complete in the ordinary sense, and present for it a fully polynomial-time approximation scheme.

Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan

2011 ◽  
Vol 210 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Shisheng Li ◽  
C.T. Ng ◽  
T.C.E. Cheng ◽  
Jinjiang Yuan
Keyword(s):  
Deteriorating Jobs ◽  
Batch Scheduling ◽  
Release Dates
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