A note on minimizing the normalized sum of squared workload deviations on m parallel processors

Walter, Rico; Lawrinenko, Alexander

doi:10.1016/j.cie.2014.07.004

Cited by 6 publications

(4 citation statements)

References 2 publications

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“…A strong correlation between the two criteria C ∆ and NSSWD was suspected by different authors in the literature [13,14,19]. However, their different analyses were based on empirical study.…”

Section: General Case With Different Jobsmentioning

confidence: 99%

“…The first is the relative percentage of imbalances (RPI) introduced by Rajakumar et al [11,12]. However, Walter and Lawrinenko [13] showed that this criterion is equivalent to maximum completion time minimization and does not provide perfectly balanced schedule.…”

Section: Introductionmentioning

confidence: 99%

“…Ho et al [14] also stated that, in the case of identical parallel machines, a NSSWDoptimal schedule is necessarily a C max -optimal schedule as well. However, [13] provided a counter-example for the case with more than two machines to prove that this result was wrong. They also carried out a computational study to give an overview on C max as well as NSSWD optimal schedules and empirically analyzed the correlation between both criteria.…”

Section: Introductionmentioning

confidence: 99%

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Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021

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This paper considers the problem of assigning nonpreemptive jobs on identical parallel machines to optimize workload balancing criteria. Since workload balancing is an important practical issue for services and production systems to ensure an efficient use of resources, different measures of performance have been considered in the scheduling literature to characterize this problem: maximum completion time, difference between maximum and minimum completion times and the Normalized Sum of Square for Workload Deviations. In this study, we propose a theoretical and computational analysis of these criteria. First, we prove that these criteria are equivalent in the case of identical jobs and in some particular cases. Then, we study the general version of the problem using jobs requiring different processing times and establish the theoretical relationship between the aforementioned criteria. Based on these theoretical developments, we propose new mathematical formulations to provide optimal solutions to some unsolved instances in order to enhance the latest benchmark presented in the literature.

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Section: General Case With Different Jobsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

2021

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“…They prove that an NSSWDoptimal schedule is necessarily a makespan-optimal one. Walter and Lawrinenko [19] explain such a proof is incorrect under the case of m ≥ 3. For solving the problem under the case of m ≥ 3, Schwerdfeger and Walter [20] propose an algorithm based on a local search procedure.…”

Section: Parallel Machine Workload Balancing Problemmentioning

confidence: 99%

Identical Parallel Machine Scheduling Considering Workload Smoothness Index

2023

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Workload balance is significant in the manufacturing industry. However, on the one hand, some existing specific criteria cannot achieve the minimization workload imbalance of parallel machines. On the other hand, there are few algorithms in existing studies that can effectively solve the parallel machine scheduling problem with the objective of minimizing workload imbalance. Inspired by this, we investigate an identical parallel machine scheduling problem with the objective of the minimum workload smoothness index. We first establish a mathematical model for the considered problem and then linearize its objective function. We prove the NP-hardness of the problem by reducing the PARTITION problem to it, and we provide both the upper bound and lower bound of the studied problem. An efficient genetic algorithm and an improved list scheduling algorithm are also proposed to efficiently address the considered problem. The numerical results demonstrate the effectiveness of the proposed methods.

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A fast and effective subset sum based improvement procedure for workload balancing on identical parallel machines

Schwerdfeger

Walter

2016

Computers & Operations Research

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A note on minimizing the normalized sum of squared workload deviations on m parallel processors

Cited by 6 publications

References 2 publications

Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

Identical Parallel Machine Scheduling Considering Workload Smoothness Index

A fast and effective subset sum based improvement procedure for workload balancing on identical parallel machines

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