OPTIMAL PREEMPTIVE SEMI-ONLINE ALGORITHM FOR SCHEDULING TIGHTLY-GROUPED JOBS ON TWO UNIFORM MACHINES

2006 ◽  
Vol 23 (01) ◽  
pp. 77-88 ◽  
Author(s):  
YIWEI JIANG ◽  
YONG HE
Keyword(s):  
Online Algorithm ◽  
Size Ratio ◽  
Speed Ratio ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Time Zero ◽  
Uniform Machines ◽  
Machine Speed

In this paper, we consider a semi-online preemptive scheduling problem on two uniform machines, where we assume that all jobs have sizes between p and rp for some p > 0 and r ≥ 1. The goal is to maximize the continuous period of time (starting from time zero) when both machines are busy. We present an optimal semi-online algorithm for any combination of the job size ratio r and machine speed ratio s.

scholarly journals A Competitive Online Algorithm for Minimizing Total Weighted Completion Time on Uniform Machines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xuyang Chu ◽  
Jiping Tao
Keyword(s):  
Completion Time ◽  
Online Algorithm ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Online Setting ◽  
Weighted Completion Time ◽  
Waiting Strategy ◽  
Machine Speed ◽  
Over Time

We consider the classic online scheduling problem on m uniform machines in the online setting where jobs arrive over time. Preemption is not allowed. The objective is to minimize total weighted completion time. An online algorithm based on the directly waiting strategy is proposed. Its competitive performance is proved to be max2smax1−1/2∑si,2smax/1+smax2.5−1/2m by the idea of instance reduction, where sm is the fastest machine speed after being normalized by the slowest machine speed.

Online Hierarchical Scheduling on Two Uniform Machines with Bounded Job Sizes

2015 ◽  
Vol 32 (05) ◽  
pp. 1550032 ◽  
Author(s):  
Xinrong Lu ◽  
Zhaohui Liu
Keyword(s):  
Speed Ratio ◽  
Scheduling Problem ◽  
Optimal Algorithms ◽  
Hierarchical Scheduling ◽  
Uniform Machines

This paper studies the online hierarchical scheduling problem on two uniform machines with bounded job sizes, where the first machine M1 receives both low and high hierarchy jobs, while the second machine M2 only receives high hierarchy jobs. The machines have a speed ratio of s(s ≥ 1), and M2 runs faster. Jobs are revealed one by one, and before the current job is scheduled, we have no information about next jobs except that the size of any job is in the interval [1, t]. The objective is to minimize the makespan. We present optimal algorithms for all (s, t) pairs.

ONLINE MINIMUM MAKESPAN SCHEDULING WITH A BUFFER

2014 ◽  
Vol 25 (05) ◽  
pp. 525-536 ◽  
Author(s):  
NING DING ◽  
YAN LAN ◽  
XIN CHEN ◽  
GYÖRGY DÓSA ◽  
HE GUO ◽  
...  
Keyword(s):  
Competitive Ratio ◽  
Online Algorithm ◽  
Buffer Size ◽  
Scheduling Problem ◽  
Uniform Machines ◽  
Minimum Makespan ◽  
Identical Machines ◽  
Better Than

In this paper we study an online minimum makespan scheduling problem with a reordering buffer. We obtain the following results: (i) for m > 51 identical machines, we give a 1.5-competitive online algorithm with a buffer of size ⌈1.5m⌉; (ii) for three identical machines, we give an optimal online algorithm with a buffer size six, better than the previous nine; (iii) for m uniform machines, using a buffer of size m, we improve the competitive ratio from 2 + ε to 2 − 1/m+ ε, where ε > 0 is sufficiently small and m is a constant.

scholarly journals Online Makespan Scheduling with Job Migration on Uniform Machines

Algorithmica ◽  
2021 ◽  
Author(s):  
Matthias Englert ◽  
David Mezlaf ◽  
Matthias Westermann
Keyword(s):  
Competitive Ratio ◽  
Online Algorithm ◽  
Parallel Machines ◽  
Scheduling Algorithm ◽  
Input Sequence ◽  
Job Migration ◽  
Average Completion Time ◽  
Uniform Machine ◽  
Uniform Machines ◽  
Completion Times

AbstractIn the classic minimum makespan scheduling problem, we are given an input sequence of n jobs with sizes. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we allow the online algorithm to change the assignment of up to k jobs at the end for some limited number k. For m identical machines, Albers and Hellwig (Algorithmica 79(2):598–623, 2017) give tight bounds on the competitive ratio in this model. The precise ratio depends on, and increases with, m. It lies between 4/3 and $$\approx 1.4659$$ ≈ 1.4659 . They show that $$k = O(m)$$ k = O ( m ) is sufficient to achieve this bound and no $$k = o(n)$$ k = o ( n ) can result in a better bound. We study m uniform machines, i.e., machines with different speeds, and show that this setting is strictly harder. For sufficiently large m, there is a $$\delta = \varTheta (1)$$ δ = Θ ( 1 ) such that, for m machines with only two different machine speeds, no online algorithm can achieve a competitive ratio of less than $$1.4659 + \delta $$ 1.4659 + δ with $$k = o(n)$$ k = o ( n ) . We present a new algorithm for the uniform machine setting. Depending on the speeds of the machines, our scheduling algorithm achieves a competitive ratio that lies between 4/3 and $$\approx 1.7992$$ ≈ 1.7992 with $$k = O(m)$$ k = O ( m ) . We also show that $$k = \varOmega (m)$$ k = Ω ( m ) is necessary to achieve a competitive ratio below 2. Our algorithm is based on maintaining a specific imbalance with respect to the completion times of the machines, complemented by a bicriteria approximation algorithm that minimizes the makespan and maximizes the average completion time for certain sets of machines.

Preemptive scheduling with transportation delays between machines

2020 ◽  
Vol 15 (3) ◽  
pp. 829-847
Author(s):  
Ryma Zineb Badaoui ◽  
Mourad Boudhar ◽  
Mohammed Dahane
Keyword(s):  
Linear Programming ◽  
Neighborhood Search ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Programming Formulation ◽  
Content Type ◽  
Decision Variables ◽  
Linear Programming Formulation ◽  
Local Search Strategy ◽  
Two Stages

Purpose This paper studies the preemptive scheduling problem of independent jobs on identical machines. The purpose of this paper is to minimize the makespan under the imposed constraints, namely, the ones that relate the transportation delays which are required to transport a preempted job from one machine to another. This study considers the case when the transportation delays are variable. Design/methodology/approach The contribution is twofold. First, this study proposes a new linear programming formulation in real and binary decision variables. Then, this study proposes and implements a solution strategy, which consists of two stages. The goal of the first stage is to obtain the best machines order using a local search strategy. For the second stage, the objective is to determine the best possible sequence of jobs. To solve the preemptive scheduling problem with transportation delays, this study proposes a heuristic and two metaheuristics (simulated annealing and variable neighborhood search), each with two modes of evaluation. Findings Computational experiments are presented and discussed on randomly generated instances. Practical implications The study has implications in various industrial environments when the preemption of jobs is allowed. Originality/value This study proposes a new linear programming formulation for the problem with variable transportation delays as well as a corresponding heuristic and metaheuristics.

An Optimal Preemptive Algorithm for the Single-Server Parallel-Machine Scheduling with Loading and Unloading Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450039 ◽  
Author(s):  
Yiwei Jiang ◽  
Huijuan Wang ◽  
Ping Zhou
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Solution Algorithm ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Loading And Unloading

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

scholarly journals Preemptive scheduling on uniform machines to minimize mean flow time

2009 ◽  
Vol 36 (10) ◽  
pp. 2816-2821 ◽  
Author(s):  
Svetlana A. Kravchenko ◽  
Frank Werner
Keyword(s):  
Flow Time ◽  
Preemptive Scheduling ◽  
Mean Flow ◽  
Mean Flow Time ◽  
Uniform Machines
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