The Weighted Fair Sequences Problem

Pessoa, Bruno Jefferson de S.; Aloise, Daniel; Cabral, Lucídio dos Anjos Formiga

doi:10.1016/j.cor.2017.11.008

Cited by 3 publications

(44 citation statements)

References 14 publications

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“…An extended MIP model using additional variables is also developed and additional algorithmic enhancements are discussed. In Section 3 we present a computational study using the instances from Pessoa et al (2018). The results show that our algorithm outperforms the algorithm from Pessoa et al (2018) by up two orders of magnitude.…”

Section: Contribution and Outlinementioning

confidence: 99%

“…In Section 3 we present a computational study using the instances from Pessoa et al (2018). The results show that our algorithm outperforms the algorithm from Pessoa et al (2018) by up two orders of magnitude. We are able to solve 404 of 440 instances from literature to proven optimality, most of them within fives minutes.…”

Section: Contribution and Outlinementioning

confidence: 99%

“…Section 4 concludes the paper. In the remainder of this section, we give a short overview of the model and algorithms for the WFS proposed in Pessoa et al (2018).…”

Section: Contribution and Outlinementioning

confidence: 99%

“…The WFS is NP-hard (Pessoa et al, 2018) and falls within the class of scheduling problems, which are concerned with the proportional sharing of resources over time. In these so-called fair sequencing problems (Kubiak, 2004), the same tasks are executed successively, and the goal is to obtain a schedule fulfilling certain fairness criteria, e.g., the (temporal) distance of successive executions of the same tasks should be similar for all type of considered tasks.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the concept of fair sequences also has interesting applications in the area of political representation (Tijdeman, 1980) and resource allocation in computer operating systems (Waldspurger and Weihl W., 1995). Additional applications of the WFS discussed in (Pessoa et al, 2018) include TV advertising (Bar-Noy and Ladner, 2003;García-Villoria and Salhi, 2015) and periodic machine maintenance (Anily et al, 1998;Bar-Noy et al, 2002).…”

Section: Introductionmentioning

confidence: 99%

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An iterative exact algorithm for the weighted fair sequences problem

Sinnl¹

2021

Preprint

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In this work, we present a new iterative exact solution algorithm for the weighted fair sequences problem, which is a recently introduced NP-hard sequencing problem with applications in diverse areas such as TV advertisement scheduling, periodic machine maintenance and real-time scheduling. In the problem we are given an upper bound on the allowed solution sequence length and a list of symbols. For each symbols, there is a positive weight and a number, which gives the minimum times the symbol has to occur in a feasible solution sequence. The goal is to find a feasible sequence, which minimizes the maximum weight-distance product, which is calculated for each consecutive appearance of each symbol in the sequence, including the last and first appearance in the sequence, i.e., the sequence is considered to be circular for the calculation of the objective function.Our proposed solution algorithm is based on a new mixed-integer programming model for the problem for a fixed sequence length. The model is enhanced with valid inequalities and variable fixings. We also develop an extended model, which allows the definition of an additional set of valid inequalities and present additional results which can allow us to skip the solution of the mixed-integer program for some sequence lengths.We conduct a computational study on the instances from literature to assess the efficiency of our newly proposed solution approach. Our approach manages to solve 404 of 440 instances to optimality within the given timelimit, most of them within five minutes. The previous best existing solution approach for the problem only managed to solve 229 of these instances, and its exactness depends on an unproven conjecture. Moreover, our approach is up to two magnitudes faster compared to this best existing solution approach.

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Section: Contribution and Outlinementioning

confidence: 99%

Section: Contribution and Outlinementioning

confidence: 99%

“…Section 4 concludes the paper. In the remainder of this section, we give a short overview of the model and algorithms for the WFS proposed in Pessoa et al (2018).…”

Section: Contribution and Outlinementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An iterative exact algorithm for the weighted fair sequences problem

Sinnl¹

2021

Preprint

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An iterative exact algorithm for the weighted fair sequences problem

Sinnl

2022

Computers & Operations Research

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An efficient implementation of a VNS heuristic for the weighted fair sequences problem

Rocha¹,

Pessoa

Aloise

et al. 2022

Int Trans Operational Res

Self Cite

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In the weighted fair sequences problem (WFSP), one aims to schedule a set of tasks or activities sthat the maximum product between the largest temporal distance between two consecutive executions of a task and its priority is minimized. The WFSP covers a large number of applications in different areas, ranging from automobile production on a mixed‐model assembly line to the sequencing of interactive applications to be aired in a digital TV environment. This paper proposes an iterative heuristic method for the WFSP centered on an efficient implementation of a variable neighborhood search heuristic. Computational experiments on benchmark instances show that the proposed metaheuristic outperforms the state‐of‐the‐art method proposed to the problem, obtaining comparable solution values in much less computational time.

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The Weighted Fair Sequences Problem

Cited by 3 publications

References 14 publications

An iterative exact algorithm for the weighted fair sequences problem

An iterative exact algorithm for the weighted fair sequences problem

An iterative exact algorithm for the weighted fair sequences problem

An efficient implementation of a VNS heuristic for the weighted fair sequences problem

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