scholarly journals Semi-Online Scheduling on Two Machines withGoSLevels and Partial Information of Processing Time

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Taibo Luo ◽  
Yinfeng Xu
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Partial Information ◽  
Online Scheduling ◽  
Scheduling Problems ◽  
Total Processing Time ◽  
Grade Of Service ◽  
Two Machines

This paper investigates semi-online scheduling problems on two parallel machines under a grade of service (GoS) provision subject to minimize the makespan. We consider three different semi-online versions with knowing the total processing time of the jobs with higherGoSlevel, knowing the total processing time of the jobs with lowerGoSlevel, or knowing both in advance. Respectively, for the three semi-online versions, we develop algorithms with competitive ratios of3/2,20/13, and4/3which are shown to be optimal.

Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing

2019 ◽  
Vol 36 (01) ◽  
pp. 1950002
Author(s):  
Xianglai Qi ◽  
Jinjiang Yuan
Keyword(s):  
Load Balancing ◽  
Online Algorithms ◽  
Processing Time ◽  
Scheduling Problems ◽  
Total Processing Time ◽  
Hierarchical Scheduling ◽  
Lp Norm ◽  
Maximum Value ◽  
Identical Machines ◽  
Two Machines

This paper investigates semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the [Formula: see text]-norm of the machines’ loads. We consider two semi-online versions with knowing the total processing time [Formula: see text] of all jobs, or knowing the total processing time [Formula: see text] of the jobs of hierarchy [Formula: see text] for [Formula: see text] in advance. For the two semi-online versions, the best possible online algorithms are designed with competitive ratios of [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the maximum value of the function [Formula: see text] in [Formula: see text]. When [Formula: see text], our results cover the known results for minimizing the makespan.

Online and semi-online scheduling to minimize makespan on single machine with an availability constraint

2015 ◽  
Vol 07 (03) ◽  
pp. 1550021
Author(s):  
Qiang Gao ◽  
Ganggang Li ◽  
Xiwen Lu
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Online Scheduling ◽  
Scheduling Problems ◽  
Total Processing Time ◽  
Release Date ◽  
Availability Constraint ◽  
Online Problems ◽  
Over Time

Online and semi-online scheduling problems on a single machine with an availability constraint are considered in this paper. The machine has one unavailable interval in which jobs cannot be processed. Preemption is not allowed. Jobs arrive over time. The objective is to minimize makespan. First we discuss the online version of the problem. After giving its lower bound, we prove that Earliest Release Date (ERD) algorithm is an optimal algorithm. Then we study some semi-online problems in which the largest processing time, the total processing time, the largest release date, or the optimal makespan is known in advance. For these semi-online problems, we give their lower bounds, design semi-online algorithms and prove their competitive ratios, respectively.

Scheduling Stochastic Jobs with a Two-Point Distribution on Two Parallel Machines

1989 ◽  
Vol 3 (1) ◽  
pp. 89-116 ◽  
Author(s):  
E.G. Coffman ◽  
M. Hofri ◽  
G. Weiss
Keyword(s):  
Optimal Policy ◽  
Hazard Rate ◽  
Processing Time ◽  
Parallel Machines ◽  
Flow Time ◽  
Constant Independent ◽  
Total Flow ◽  
Point Distribution ◽  
Two Machines ◽  
Expected Increase

We analyze the optimal preemptive sequencing of n jobs on two machines to minimize expected total flow time. The running times of the jobs are independent samples from the distribution Pr(X = 1) = p, Pr(X = κ + 1) = 1 − p. We verify that the shortest-expected-remaining-processing-time (SERPT) policy, which is optimal for independent and identically distributed (i.i.d.) running times with a monotone hazard-rate distribution, is not optimal for this distribution. However, we prove that if p ≥ 1/κ, then the number of decisions where SERPT and an optimal policy disagree is bounded by a constant independent of n. For p < 1/k, we prove that the expected number of such decisions has a similar bound. In addition, bounds on the expected increase in flow times under SERPT are derived; these bounds are also independent of n.

scholarly journals Two Stage Flow Shop Scheduling Model Including Transportation Time with Equipotential Machines at Every Stage

2019 ◽  
Vol 8 (12) ◽  
pp. 5090-5094
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Flow Shop ◽  
Solution Algorithm ◽  
Flow Shop Scheduling ◽  
Two Stage ◽  
Transportation Time ◽  
Shop Scheduling ◽  
Scheduling Model ◽  
Two Machines

This study presents a solution algorithm for the problem of minimizing the makespan on equipotential parallel machines at every stage in two stage flow shop scheduling model. The processing time of all the jobs on all the two machines is given and the time for which parallel equipotential machines are available is also given. Transportation time for moving the jobs from first machine to second machine is also taken into consideration. A mathematical illustration is also given in support of the algorithm proposed

Semi-Online Machine Covering under a Grade of Service Provision

2011 ◽  
Vol 101-102 ◽  
pp. 484-487
Author(s):  
Yong Wu ◽  
Min Ji ◽  
Qi Fan Yang
Keyword(s):  
Service Provision ◽  
Competitive Ratio ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Online Version ◽  
Scheduling Problems ◽  
Grade Of Service ◽  
Identical Machines ◽  
Machine Covering ◽  
Parallel Identical Machines

Two semi-online scheduling problems on two parallel identical machines under a grade of service (GoS) provision were studied. The goal is to maximize the minimum machine load. For the semi-online version where the largest processing time of all jobs is known in advance, we show that no competitive algorithm exists. For the semi-online version where the optimal offline value is known in advance, we propose an optimal algorithm with competitive ratio 2.

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