scholarly journals Scheduling Jobs with Stochastic Processing Time on Parallel Identical Machines

2019 ◽  
Author(s):  
Richard Stec ◽  
Antonin Novak ◽  
Premysl Sucha ◽  
Zdenek Hanzalek
Keyword(s):  
Processing Time ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Computational Aspect ◽  
Scheduling Problems ◽  
Stochastic Processing Time ◽  
Stochastic Processing ◽  
Identical Machines ◽  
Parallel Machine Scheduling Problem ◽  
Price Approach

Many real-world scheduling problems are characterized by uncertain parameters. In this paper, we study a classical parallel machine scheduling problem where the processing time of jobs is given by a normal distribution. The objective is to maximize the probability that jobs are completed before a given common due date. This study focuses on the computational aspect of this problem, and it proposes a Branch-and-Price approach for solving it. The advantage of our method is that it scales very well with the increasing number of machines and is easy to implement. Furthermore, we propose an efficient lower bound heuristics. The experimental results show that our method outperforms the existing approaches.

ONLINE ALGORITHMS FOR SCHEDULING WITH MACHINE ACTIVATION COST

2007 ◽  
Vol 24 (02) ◽  
pp. 263-277 ◽  
Author(s):  
YONG HE ◽  
SHUGUANG HAN ◽  
YIWEI JIANG
Keyword(s):  
Lower Bound ◽  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Identical Machines ◽  
Parallel Machine Scheduling Problem

In this paper, we consider a variant of the classical parallel machine scheduling problem. For this problem, we are given m potential identical machines to non-preemptively process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and activation cost of machines. We first present two optimal online algorithms with competitive ratios of 3/2 and 5/3 for m = 2, 3 cases, respectively. Then we present an online algorithm with a competitive ratio of at most 2 for general m ≥ 4, while the lower bound is 1.88.

scholarly journals A New Approach Based on Matching Theory and Simulated Annealing for Parallel Machine Scheduling Problems

2021 ◽  
Author(s):  
Maissa Moussa ◽  
Adel Azar ◽  
Ali Rajabzadeh Ghatari
Keyword(s):  
Simulated Annealing ◽  
Hybrid Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Matching Theory ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Suggested Algorithm ◽  
Parallel Machine Scheduling Problem

Abstract As an extension of the classical Parallel Machine Scheduling Problem (PMSP), Unrelated Parallel Machine Scheduling Problem (UPMSP) is a much substantial issue in the modern manufacturing environment. It has been demonstrated to be a NP-hard problem. This research suggests a hybrid algorithm that combines Matching Theory (MT) and Simulated Annealing (SA) for solving an UPMSP with sequence-dependent setup time aimed at minimizing the total completion time. The hybrid algorithm is based on allocation of works to the best machine that can do it, and the determination of the order in which jobs have to be handled on the machines. The hybridization of MT and SA that integrates the features of these two individual parts is the main innovation aspect of the strategy. MT encourages the convergence, while SA promotes the diversity. Therefore, the designed algorithm can balance the intensification and diversification very well. Some tests were conducted using 16 tests for two problems to assess the efficiency of the suggested algorithm. Furthermore, the execution of the suggested algorithm with that of other meta-heuristic methods was contrasted. The outcome revealed that the performance dimensions of the suggested algorithm overrated those of other techniques.

scholarly journals Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

2021 ◽  
Author(s):  
Bartłomiej Przybylski
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Positive Function ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problems ◽  
Processing Times ◽  
Maximum Completion Time ◽  
Machine Scheduling Problems

AbstractWe consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

scholarly journals Online Parallel Machine Scheduling to Maximize the Number of Early Jobs

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Feifeng Zheng ◽  
Ming Liu ◽  
Chengbin Chu ◽  
Yinfeng Xu
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Arrival Time ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Time Algorithm ◽  
Maximization Problem ◽  
Due Date ◽  
Identical Machines ◽  
Over Time

We study a maximization problem: online scheduling onmidentical machines to maximize the number of early jobs. The problem is online in the sense that all jobs arrive over time. Each job's characteristics, such as processing time and due date, become known at its arrival time. We consider thepreemption-restart model, in which preemption is allowed, while once a job is restarted, it loses all the progress that has been made on this job so far. If in some schedule a job is completed before or at its due date, then it is calledearly(oron time). The objective is to maximize the number of early jobs. Formidentical machines, we prove an upper bound1-(1/2m)of competitive ratio and show thatECT(earliest completion time) algorithm is1/2-competitive.

A Best Possible Online Algorithm for the Parallel-Machine Scheduling to Minimize the Maximum Weighted Completion Time

2015 ◽  
Vol 32 (04) ◽  
pp. 1550030 ◽  
Author(s):  
Wenjie Li
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Completion Time ◽  
Processing Time ◽  
Online Algorithm ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Identical Machines ◽  
Weighted Completion Time ◽  
Over Time

In this paper, we consider the online scheduling on m identical machines in which jobs arrive over time. The goal is to determine a nonpreemptive schedule that minimizes the weighted makespan, i.e., the maximum weighted completion time of jobs. When m = 1, we first present a lower bound 2, and then provide an online algorithm with a competitive ratio of 3. For the case in which m ≥ 1, and all jobs have a common processing time p > 0, we obtain a best possible online algorithm with a competitive ratio of [Formula: see text].

scholarly journals IDENTICAL PARALLEL MACHINES SCHEDULING USING GENETIC ALGORITHM

2018 ◽  
Vol 18 (2) ◽  
pp. 321-330
Author(s):  
Aseel J Haleel
Keyword(s):  
Genetic Algorithm ◽  
Processing Time ◽  
Parallel Machines ◽  
Machine Scheduling ◽  
Setup Time ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Identical Parallel Machine ◽  
Parallel Machine Scheduling Problem

Minimizing the scheduling production time consider one of the most important factors forcompanies which their objectives is achieve the maximum profits. This paper studies theidentical parallel machine scheduling problem which involves the assignment numbers ofjob (N) to set of identical parallel machine (M) in order to minimize the makespan(maximum completion time of all job). There are numerous troubles in solving the largesize of “parallel machine scheduling” problem with an excessive jobs and machines, sothe genetic algorithm was proposed in this paper which is consider an efficient algorithmthat fits larger size of identical “parallel machine scheduling” for minimizing themakespan. Most studies in the scheduling field suppose setup time is insignificant orincluded in the processing time, in this paper both the sequence independent setup timesand processing time were considered. The solutions of algorithms are coding in(MATLAB). A numerical example of (11) jobs are schedule on (3) machines todemonstrative the effectiveness of algorithm solution. The result show the algorithm caneffectively solve large size of scheduling problem and given the best schedule withminimum makespan.

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