scholarly journals Single-machine Pareto-scheduling with multiple weighting vectors for minimizing the total weighted late works

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shuen Guo ◽  
Zhichao Geng ◽  
Jinjiang Yuan
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Pareto Frontier ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Late Work ◽  
Weighting Vector ◽  
Late Works

<p style='text-indent:20px;'>In this paper, we study the single-machine Pareto-scheduling of jobs with multiple weighting vectors for minimizing the total weighted late works. Each weighting vector has its corresponding weighted late work. The goal of the problem is to find the Pareto-frontier for the weighted late works of the multiple weighting vectors. When the number of weighting vectors is arbitrary, it is implied in the literature that the problem is unary NP-hard. Then we concentrate on our research under the assumption that the number of weighting vectors is a constant. For this problem, we present a dynamic programming algorithm running in pseudo-polynomial time and a fully polynomial-time approximation scheme (FPTAS).</p>

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).

TWO-MACHINE FLOW SHOP SCHEDULING WITH INDIVIDUAL OPERATION'S REJECTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450002 ◽  
Author(s):  
QIANG GAO ◽  
XIWEN LU
Keyword(s):  
Approximation Scheme ◽  
Flow Shop ◽  
Dynamic Programming Algorithm ◽  
Flow Shop Scheduling ◽  
Programming Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Shop Scheduling ◽  
Processing Times ◽  
Total Penalty

A two-machine flow shop scheduling problem with rejection is considered in this paper. The objective is to minimize the sum of makespan of accepted operations and total penalty of rejected operations. Each job has two operations that could be rejected, respectively. Operations on the first machine have penalties α1 times of their processing times and operations on the second machine have penalties α2 times of their processing times. A [Formula: see text]-approximation algorithm is presented for the case where min{α1, α2} < 1 and max{α1, α2} ≥ 1. A dynamic programming algorithm is provided for general α1 and α2. A fully polynomial-time approximation scheme (FPTAS) is designed for all NP-hard cases.

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.

scholarly journals Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

2017 ◽  
Vol 51 (4) ◽  
pp. 1177-1188 ◽  
Author(s):  
Imed Kacem ◽  
Myriam Sahnoune ◽  
Günter Schmidt
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Time Minimization ◽  
Weighted Completion Time ◽  
Polynomial Time Approximation

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

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