Robust scheduling of parallel machines considering total flow time

Hematian, Milad; Moslehi, Ghasem

doi:10.1016/j.cie.2015.12.024

Cited by 18 publications

(5 citation statements)

References 19 publications

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“…Así, el problema de programación β-robust consiste en encontrar la secuencia que maximice la probabilidad que el TFT no exceda un límite predeterminado 𝑆 (nivel de servicio al cliente). Este problema es conocido como 𝑃|β − RSP|𝑇𝐹𝑇 ≤ 𝑆 [4].…”

Section: Problema De Programación 𝛽 -Robustunclassified

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An Application of the Piecewise Linear Approximation Method to Solve the β-Robust Scheduling Problem in a Parallel Machine Environment

Pérez¹

2023

Proceedings of the 21th LACCEI International Multi-Conference for Engineering, Education and Technology (LACCEI 2023): “Leaders

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In the industries, the presence of uncertainties in the duration of production tasks can lead to unsatisfactory production scheduling, in situations where variability is significant, and a deterministic approach is used. In this case, a stochastic or robust approach is more appropriate. In particular, this article deals with the β-robust scheduling problem in a parallel machine environment and considering the presence of uncertainty in the duration of the tasks. This problem consists of finding the execution order of a set of tasks on a set of machines, with the objective of maximizing the probability that the total flow time is less than a limit. The difficulty in solving this problem lies in its combinatorial, stochastic and nonlinear nature of its formulation. To overcome this difficulty, an efficient mathematical model is built that makes use of the piecewise linear approximation method. The proposed model proves to be able to obtain the solution of the problem with precision and in a short computational time.Keywords--β-robust scheduling problem; mathematical model; piecewise linear approximation method; central limit theorem.

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Section: Problema De Programación 𝛽 -Robustunclassified

“…En la Referencia [4], los autores propusieron un algoritmo Branch and Bound para resolver el problema en un ambiente de máquinas en paralelo. Además, se desarrollaron un límite inferior, tres límites superiores y dos reglas de dominancia para el algoritmo Branch and Bound.…”

Section: Introductionunclassified

An Application of the Piecewise Linear Approximation Method to Solve the β-Robust Scheduling Problem in a Parallel Machine Environment

Pérez¹

2023

Proceedings of the 21th LACCEI International Multi-Conference for Engineering, Education and Technology (LACCEI 2023): “Leaders

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“…More efficient and heuristic algorithms were also addressed by Wu et al (2009). Latter, Alimoradi et al (2016) generalized the problem to parallel identical machines setting and obtained an exact algorithm that has better performance on the data set. Recently, Zhang et al (2018) addressed another variant, where the independent normal distribution assumption is not required.…”

Section: Related Workmentioning

confidence: 99%

Scheduling Stochastic Jobs - Complexity and Approximation Algorithms

Tao

Chen

Zhang

2021

ICAPS

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Uncertainty is an omnipresent issue in real-world optimization problems. This paper studies a fundamental problem concerning uncertainty, known as the beta-robust scheduling problem. Given a set of identical machines and a set of jobs whose processing times follow a normal distribution, the goal is to assign jobs to machines such that the probability that all the jobs are completed by a given common due date is maximized. We give the first systematic study on the complexity and algorithms for this problem. A strong negative result is shown by ruling out the existence of any polynomial-time algorithm with a constant approximation ratio for the general problem unless P=NP. On the positive side, we provide the first FPT-AS (fixed parameter tractable approximation scheme) parameterized by the number of different kinds of jobs, which is a common parameter in scheduling problems. It returns a solution arbitrarily close to the optimal solution, provided that the job processing times follow a few different types of distributions. We further complement the theoretical results by implementing our algorithm. The experiments demonstrate that by choosing an appropriate approximation ratio, the algorithm can efficiently compute a near-optimal solution.

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“…(), in which the makespan minimization is subject to job splitting, sequence‐dependent setup times, and scheduling in unrelated machines; Alimoradi et al. (), aiming at maximizing the probability of the total flow time to exceed a given due date, with identical machines, and uncertain processing times; Cheng and Huang (), requiring the minimization of the total completion time, which is related to jobs' earliness and tardiness, on unrelated machines; and Hamzadayi and Yildiz (), aiming at minimizing the makespan, where setup times are sequence‐dependent and carried out by a server.…”

Section: Introductionmentioning

confidence: 99%

“…Alimoradi et al. () proposed a branch‐and‐bound algorithm in which each node of the tree represents a partial sequence of jobs. The tree is searched in a depth‐first way.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective pseudo‐variable neighborhood descent for a bicriteria parallel machine scheduling problem with setup time

Queiroz

Mundim

2019

Int Trans Operational Res

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A multiobjective variable neighborhood descent (VND) based heuristic is developed to solve a bicriteria parallel machine scheduling problem. The problem considers two objectives, one related to the makespan and the other to the flow time, where the setup time depends on the sequence, and the machines are identical. The heuristic has a set of neighborhood structures based on swap, remove, and insertion moves. We propose changing the local search inside the VND to a sequential search through the neighborhoods to obtain nondominated points for the Pareto‐front quickly. In the numerical tests, we consider a single‐objective version of the heuristic, comparing the results on 510 benchmark instances to show that it is quite effective. Moreover, new instances are generated in accordance with the literature for the bicriteria problem, showing the ability of the proposed heuristic to return an efficient set of nondominate solutions compared with the well‐known nondominated sorting genetic algorithm II.

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Robust scheduling of parallel machines considering total flow time

Cited by 18 publications

References 19 publications

An Application of the Piecewise Linear Approximation Method to Solve the β-Robust Scheduling Problem in a Parallel Machine Environment

An Application of the Piecewise Linear Approximation Method to Solve the β-Robust Scheduling Problem in a Parallel Machine Environment

Scheduling Stochastic Jobs - Complexity and Approximation Algorithms

Multiobjective pseudo‐variable neighborhood descent for a bicriteria parallel machine scheduling problem with setup time

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