scholarly journals Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Shuguang Li
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
List Scheduling ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Delivery Times ◽  
Specific Subset ◽  
Job Delivery

The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived.

Parallel Machine Scheduling Problem with a Resumable Availability Constraint

2014 ◽  
Vol 1061-1062 ◽  
pp. 708-711
Author(s):  
Qi Zhang ◽  
Cheng Xin Luo
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Ordinary Sense ◽  
Polynomial Time Approximation Scheme ◽  
Approximation Solution ◽  
Availability Constraint ◽  
Parallel Machine Scheduling Problem

This paper considers a scheduling problem of two parallel machines with a resumable availability constraint. The objective is to minimize the makespan. The problem is NP-hard in the ordinary sense. Therefore, we need to find an approximate solution that fulfills the required error bound. To get a better approximation solution in a polynomial running time, we propose a fully polynomial-time approximation scheme (FPTAS) by trimming states space.

PARALLEL MACHINE SCHEDULING WITH JOB DELIVERY COORDINATION

2017 ◽  
Vol 58 (3-4) ◽  
pp. 306-313
Author(s):  
J. M. DONG ◽  
X. S. WANG ◽  
L. L. WANG ◽  
J. L. HU
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Performance Ratio ◽  
Worst Case ◽  
Identical Machine ◽  
Worst Case Performance Ratio ◽  
Job Delivery ◽  
Identical Machine Scheduling

We analyse a parallel (identical) machine scheduling problem with job delivery to a single customer. For this problem, each job needs to be processed on $m$ parallel machines non-pre-emptively and then transported to a customer by one vehicle with a limited physical capacity. The optimization goal is to minimize the makespan, the time at which all the jobs are processed and delivered and the vehicle returns to the machine. We present an approximation algorithm with a tight worst-case performance ratio of $7/3-1/m$ for the general case, $m\geq 3$.

A PTAS for single-machine scheduling with release dates and job delivery to minimize makespan

2019 ◽  
Vol 53 (4) ◽  
pp. 1261-1266 ◽  
Author(s):  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Round Trip ◽  
Time Approximation ◽  
Job Delivery ◽  
Capacitated Vehicle

We consider the single-machine scheduling problem with release dates and job delivery to minimize makespan. Preemption is not allowed in the processing of the jobs. All jobs are first processed on a single machine and then delivered by a capacitated vehicle to a single customer. The vehicle can deliver at most c ≥ 1 jobs in each shipment. The round-trip transportation time between the machine and customer is a constant T > 0. The problem was proved to be strongly NP-hard and a 3/2-approximation algorithm was presented in the literature. In this paper we provide a polynomial-time approximation scheme (PTAS) for the problem.

scholarly journals Due window assignment and scheduling on parallel machines: a FPTAS for a bottleneck criterion

2014 ◽  
Vol 62 (4) ◽  
pp. 805-808
Author(s):  
A. Janiak ◽  
W. Janiak ◽  
M.Y. Kovalyov
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Window Size ◽  
Identical Parallel Machines ◽  
Polynomial Time Approximation Scheme ◽  
Maximum Cost ◽  
Time Approximation ◽  
Due Window ◽  
Job Tardiness ◽  
Due Window Assignment

Abstract A fully polynomial time approximation scheme (FPTAS) with run time is developed for a problem which combines common due window assignment and scheduling n jobs on m identical parallel machines. The problem criterion is bottleneck (min-max) such that the maximum cost, which includes job earliness, job tardiness and due window size costs, is minimized.

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.

TWO APPROXIMATION SCHEMES FOR SCHEDULING ON PARALLEL MACHINES UNDER A GRADE OF SERVICE PROVISION

2012 ◽  
Vol 29 (05) ◽  
pp. 1250029 ◽  
Author(s):  
WEIDONG LI ◽  
JIANPING LI ◽  
TONGQUAN ZHANG
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Approximation Scheme ◽  
Approximation Schemes ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Running Time ◽  
Grade Of Service ◽  
Special Case ◽  
Polynomial Time Approximation

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

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