Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam, Senthilkumar; Narayanan, S.

doi:10.4236/iim.2010.28056

Cited by 14 publications

(3 citation statements)

References 75 publications

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“…The authors derived tight bounds based on machine speeds. For more literature on parallel machines and uniform parallel machine scheduling, readers are referred to the works in [41,42].…”

Section: Literature Reviewmentioning

confidence: 99%

Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling

Bamatraf,

Gharbi

2024

Systems

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This paper investigates a uniform parallel machine scheduling problem for makespan minimization. Due to the problem’s NP-hardness, much effort from researchers has been directed toward proposing heuristic and metaheuristic algorithms that can find an optimal or a near-optimal solution in a reasonable amount of time. This work proposes two versions of a variable neighborhood search (VNS) algorithm with five neighborhood structures, differing in their initial solution generation strategy. The first uses the longest processing time (LPT) rule, while the second introduces a novel element by utilizing a randomized longest processing time (RLPT) rule. The neighborhood structures for both versions were modified from the literature to account for the variable processing times in uniform parallel machines. We evaluated the performance of both VNS versions using a numerical example, comparing them against a genetic algorithm and a tabu search from existing literature. Results showed that the proposed VNS algorithms were competitive and obtained the optimal solution with much less effort. Additionally, we assessed the performance of the VNS algorithms on randomly generated instances. For small-sized instances, we compared their performance against the optimal solution obtained from a mathematical formulation, and against lower bounds derived from the literature for larger instances. Computational results showed that the VNS version with the randomized LPT rule (RLPT) as the initial solution (RVNS) outperformed that with the LPT rule as the initial solution (LVNS). Moreover, RVNS found the optimal solution in 90.19% of the small instances and yielded an average relative gap of about 0.15% for all cases.

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“…The authors derived tight bounds based on machine speeds. For more literature on parallel machines and uniform parallel machine scheduling, readers are referred to the works in [41,42].…”

Section: Literature Reviewmentioning

confidence: 99%

Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling

Bamatraf,

Gharbi

2024

Systems

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“…Panneerselvam Senthilkumar and Sockalingam Narayanan [2] have done a comprehensive review of literature of single machine scheduling problem with uniform parallel machines, in which 17 classifications were discussed. Prabuddha De and Thomas E.Morton [3] have developed a new heuristic to schedule jobs on uniform parallel processors to minimize makespan.…”

Section: Literature Reviewmentioning

confidence: 99%

GA Based Heuristic to Minimize Makespan in Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam¹,

Narayanan²

2011

IIM

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This paper considers the single machine scheduling problem with uniform parallel machines in which the objective is to minimize the makespan. Four different GA based heuristics are designed by taking different combinations of crossover methods, viz. single point crossover method and two point crossover method, and job allocation methods while generating initial population, viz. equal number of jobs allocation to machines and proportionate number of jobs allocation to machines based on machine speeds. A detailed experiment has been conducted by assuming three factors, viz. Problem size, crossover method and job allocation method on 135 problem sizes each with two replications generated randomly. Finally, it is suggested to use the GA based heuristic with single point crossover method, in which the proportionate number of jobs allocated to machines based on machine speeds

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“…The PMSP can be classified according to the speed to process the tasks in each of the parallel machines. Senthilkumar and Narayanan (2010) classify the problem in three distinct categories: the Identical Parallel Machine Scheduling Problem, the Uniform Parallel Machine Scheduling Problem and the Unrelated Parallel Machine Scheduling Problem.…”

Section: Introductionmentioning

confidence: 99%

<b>A genetic algorithm and variable neighborhood search for the unrelated parallel machine scheduling problem with sequence dependent setup time

et al. 2018

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This paper presents the evaluation of two metaheuristics to solve the Unrelated Parallel Machine Scheduling Problem with Sequence Machine Dependent Setup Time. Considering such a problem, there is no relation between the time to process each task and the machine; and this is why the machines are referred to as unrelated. Furthermore, the setup time between the executions of two tasks depends on both, the task sequence and its associated machine. A metaheuristic genetic algorithm and a variable neighborhood search were used in order to solve the problem due to the difference among their characteristics. The maximal time for the schedule to be completed, also called makespan, was the performance measure used to evaluate the solutions. The results obtained by both metaheuristics were directly compared according to their performance to try to reduce this makespan. The results showed that the variable neighborhood algorithm search outperformed the genetic algorithm regarding the solutions quality and execution time.Algoritmo genético e busca em vizinhança variável para o problema de sequenciamento de máquinas paralelas não-relacionadas com setup dependente da sequência RESUMO. Este artigo avalia a aplicação de duas meta-heurísticas na resolução do problema de escalonamento de máquinas paralelas não relacionadas com o tempo de preparação dependente da sequência e máquina associada. Para esse problema, não existe relação entre a máquina e o tempo de processamento de cada tarefa, por isso as máquinas são denominadas de não relacionadas. Além disso, o tempo de preparação entre a execução de duas tarefas depende de ambos os processos -sequência das tarefas e máquina a elas associadas. As meta-heurísticas algoritmo genético e busca em vizinhança variável foram escolhidas para resolver o problema pela diferença existente entre suas características. A medida de desempenho utilizada para avaliar as soluções é o tempo máximo para conclusão do escalonamento, também denominado makespan. Os resultados obtidos por ambas as meta-heurísticas são diretamente comparados de acordo com seu desempenho na tentativa de redução do makespan. Os resultados demonstram que a busca em vizinhança variável obteve melhor desempenho comparado ao algoritmo genético no que confere à qualidade das soluções e tempo de processamento.Palavras-chave: problema de escalonamento; escalonamento de máquinas; metaheurísticas.

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Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Cited by 14 publications

References 75 publications

Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling

Variable Neighborhood Search for Minimizing the Makespan in a Uniform Parallel Machine Scheduling

GA Based Heuristic to Minimize Makespan in Single Machine Scheduling Problem with Uniform Parallel Machines

<b>A genetic algorithm and variable neighborhood search for the unrelated parallel machine scheduling problem with sequence dependent setup time

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