Minimizing workload balancing criteria on identical parallel machines

Cossari, Anthony; Ho, Johnny C.; Paletta, Giuseppe; Ruíz-Torres, Alex J.

doi:10.1080/21681015.2013.795504

Cited by 8 publications

(4 citation statements)

References 12 publications

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“…Efficient algorithms for these problems and some of their special cases have been developed by Cossari et al (2012); Schwerdfeger and Walter (2016); Christ et al (2019). Other equity functions that have been proposed include the relative percentage of imbalance (which is equivalent to minimizing C max ) (Rajakumar et al, 2004) and normalized mean difference (Cossari et al, 2013).…”

Section: Manufacturingmentioning

confidence: 99%

Generating balanced workload allocations in hospitals

Smet

2023

Operations Research for Health Care

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Section: Manufacturingmentioning

confidence: 99%

Generating balanced workload allocations in hospitals

Smet

2023

Operations Research for Health Care

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“…These two operators are simple and flexible, and have been used in many problems with similar settings such as the workload balancing problem on parallel machine [34,35], the task allocation problem [36], and the parallel machine scheduling problem [37,26]. We use these two operators to search the neighborhood of the incumbent solution sequentially.…”

Section: Job Assignment Problemmentioning

confidence: 99%

Robust Optimization on Unrelated Parallel Machine Scheduling with Setup Times

Gao¹,

Wang²,

Shi³

2020

Preprint

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The parallel machine scheduling problem has been a popular topic for many years due to its theoretical and practical importance. This paper addresses the robust makespan optimization problem on unrelated parallel machine scheduling with sequence-dependent setup times, where the processing times are uncertain, and the only knowledge is the intervals they take values from. We propose a robust optimization model with min-max regret criterion to formulate this problem. To solve this problem, we prove that the worst-case scenario with the maximum regret for a given solution belongs to a finite set of extreme scenarios. Based on this theoretical analysis, the procedure to obtain the maximum regret is proposed and an enhanced regret evaluation method (ERE) is designed to accelerate this process. A multi-start decomposition-based heuristic algorithm (MDH) is proposed to solve this problem. High-quality initial solutions and an upper bound are examined to help better solve the problem. Computational experiments are conducted to justify the performance of these methods. * Since s 0 is a worst-case scenario for schedule π, s f is also a worst-case scenario for π.

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“…Cossari et al [10] noted that there is no established performance measure in the literature to characterize the workload balancing problem. However, different criteria have been proposed in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…More specifically, it aims to investigate the theoretical relationships between P||C max , P||NSSWD and P||C ∆ problems. As mentioned by Cossari et al [10], while workload balancing is an important practical criterion given the need of production systems to efficiently use all of their resources, there is no established measure of performance in the scheduling literature that characterizes total workload balance. Different criteria have been addressed in the literature and some of them are trivial.…”

Section: Introductionmentioning

confidence: 99%

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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Minimizing workload balancing criteria on identical parallel machines

Cited by 8 publications

References 12 publications

Generating balanced workload allocations in hospitals

Generating balanced workload allocations in hospitals

Robust Optimization on Unrelated Parallel Machine Scheduling with Setup Times

Workload Balancing on Identical Parallel Machines: Theoretical and Computational Analysis

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