scholarly journals Scheduling on identical parallel machines with controllable processing times to minimize the makespan

2016 ◽  
Author(s):  
Daniel Oron ◽  
Dvir Shabtay ◽  
George Steiner
Keyword(s):  
Parallel Machines ◽  
Controllable Processing Times ◽  
Identical Parallel Machines ◽  
Processing Times

SEMI-ONLINE MACHINE COVERING

2007 ◽  
Vol 24 (03) ◽  
pp. 373-382 ◽  
Author(s):  
SHENG-YI CAI
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
First Case ◽  
Machine Covering

This paper investigates two different semi-online versions of the machine covering, which is the problem of assigning a set of jobs to a system of m(m ≥ 3) identical parallel machines so as to maximize the earliest machine completion time. In the first case, we assume that the largest processing times is known in advance. In the second case, we assume that the total processing times of all jobs is known in advance. For each version we propose a semi-online algorithm and investigate its competitive ratio. The competitive ratio of each algorithm is [Formula: see text], which is shown to be the best possible competitive ratio for each semi-online problem.

scholarly journals Preemptive Scheduling with Controllable Processing Times on Parallel Machines

2015 ◽  
Vol 3 (1) ◽  
pp. 68-76
Author(s):  
Guiqing Liu ◽  
Kai Li ◽  
Bayi Cheng
Keyword(s):  
Polynomial Time ◽  
Resource Use ◽  
Parallel Machines ◽  
Optimal Algorithm ◽  
Parallel Machine Scheduling ◽  
Controllable Processing Times ◽  
Scheduling Problems ◽  
Processing Times ◽  
Online Problems ◽  
Machine Scheduling Problems

AbstractThis paper considers several parallel machine scheduling problems with controllable processing times, in which the goal is to minimize the makespan. Preemption is allowed. The processing times of the jobs can be compressed by some extra resources. Three resource use models are considered. If the jobs are released at the same time, the problems under all the three models can be solved in a polynomial time. The authors give the polynomial algorithm. When the jobs are not released at the same time, if all the resources are given at time zero, or the remaining resources in the front stages can be used to the next stages, the offline problems can be solved in a polynomial time, but the online problems have no optimal algorithm. If the jobs have different release dates, and the remaining resources in the front stages can not be used in the next stages, both the offline and online problems can be solved in a polynomial time.

Online Parallel-Machine Scheduling in KRT Environment to Minimize Total Weighted Completion Time

2018 ◽  
Vol 35 (04) ◽  
pp. 1850024
Author(s):  
Wenjie Li ◽  
Hailing Liu ◽  
Shisheng Li
Keyword(s):  
Online Algorithm ◽  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Identical Parallel Machines ◽  
Feasible Schedule ◽  
Processing Times ◽  
Online Setting ◽  
Completion Times ◽  
Equal Processing Times

This paper studies online scheduling on [Formula: see text] identical parallel machines under the KRT environment, where jobs arrive over time and “KRT” means that in the online setting no jobs can be released when all of the machines are busy. The goal is to determine a feasible schedule to minimize the total of weighted completion times. When [Formula: see text], we prove that WSPT is an optimal online algorithm. When [Formula: see text], we first present a lower bound [Formula: see text], and then show that WSPT is a 2-competitive online algorithm for the case [Formula: see text]. For the case in which [Formula: see text] and all jobs have equal processing times, we provide a best possible online algorithm with a competitive ratio of [Formula: see text].

Scheduling with Discretely Compressible Processing Times to Minimize Makespan

2014 ◽  
Vol 575 ◽  
pp. 926-930
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Processing Time ◽  
Parallel Machines ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
Release Times ◽  
Scheduling Model

In this paper, we address the scheduling model with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost on identical parallel machines. Jobs may have simultaneous release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

Just-in-time scheduling with controllable processing times on parallel machines

2009 ◽  
Vol 19 (3) ◽  
pp. 347-368 ◽  
Author(s):  
Yaron Leyvand ◽  
Dvir Shabtay ◽  
George Steiner ◽  
Liron Yedidsion
Keyword(s):  
Parallel Machines ◽  
Just In Time ◽  
Controllable Processing Times ◽  
Processing Times ◽  
Time Scheduling

scholarly journals Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021 ◽  
Vol 11 (8) ◽  
pp. 3677
Author(s):  
Yassine Ouazene ◽  
Nhan-Quy Nguyen ◽  
Farouk Yalaoui
Keyword(s):  
Computational Analysis ◽  
Parallel Machines ◽  
Production Systems ◽  
Identical Parallel Machines ◽  
Workload Balancing ◽  
Processing Times ◽  
Use Of Resources ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Identical Jobs

This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

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