The break scheduling problem: complexity results and practical algorithms

Widl, Magdalena; Musliu, Nysret

doi:10.1007/s12293-014-0131-0

Cited by 19 publications

(6 citation statements)

References 14 publications

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“…The reason for this approach as opposed to the approach used in Musliu et al (2009) is that duties have a strong interference in satisfying the staffing requirements, and therefore it is difficult to find effective crossover operations when a meme represents a duty. This memetic algorithm is also used in Widl and Musliu (2014). In this paper it is also proven that break scheduling is generally NP-complete, even under the condition that all feasible break patterns of each duty are given explicitly in the input.…”

Section: Break Schedulingmentioning

confidence: 99%

Solving the shift and break design problem using integer linear programming

Akkermans¹,

Post

Uetz

2019

Ann Oper Res

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In this paper we propose a two-phase approach to solve the shift and break design problem using integer linear programming. In the first phase we create the shifts, while heuristically taking the breaks into account. In the second phase we assign breaks to each occurrence of any shift, one by one, repeating this until no improvement is found. On a set of benchmark instances, composed by both randomly-generated and real-life ones, this approach obtains better results than the current best known method for shift and break design problem.

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Section: Break Schedulingmentioning

confidence: 99%

Solving the shift and break design problem using integer linear programming

Akkermans¹,

Post

Uetz

2019

Ann Oper Res

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“…They are especially suited for NP-hard problems, which exact methods often cannot solve in reasonable time. Memetic algorithms have been applied to many NP-hard problems, including timetabling (Burke et al [1995]), traveling salesperson problem (Gong et al [2019]), break scheduling (Widl and Musliu [2010] and Widl and Musliu [2014]), graph coloring (Lü and Hao [2010]), graph partitioning (Benlic and Hao [2011]), job shop scheduling (Liu et al [2013]), bin packing (Spencer et al [2019]), and multidimensional knapsack (Puchinger et al [2005]).…”

Section: State-of-the-art Of Memetic Algorithmsmentioning

confidence: 99%

Solving the paintshop scheduling problem with memetic algorithms

Weintritt

Musliu

Winter

2021

Proceedings of the Genetic and Evolutionary Computation Conference

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“…To the best of our knowledge, Widl and Musliu (2014) are the only authors who previously addressed the complexity of the break assignment problem. Their NP-complete proof is based on reduction from 'Exact Cover by 3-Sets' (X3C) and is limited to arbitrary break patterns with 3 or more breaks.…”

Section: Complexity Analysismentioning

confidence: 99%

The flexible break assignment problem for large tour scheduling problems with an application to airport ground handlers

Kiermaier

Frey

Bard

2020

J Sched

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The paper examines the complexity of assigning multiple breaks to shifts in the context of large-scale tour scheduling. A mixed-integer programming (MIP) model is presented that includes shift and days-off scheduling along with break assignments for a multi-skilled workforce. To achieve tractability, a two-stage decomposition procedure is proposed that separates the tour scheduling problem (TShP) from the break assignment problem (BAP). The former MIP is first solved to determine the shifts and days off for the workforce that minimize labor and shortages costs over the planning horizon. The results are used as input to a second MIP that optimally places the breaks to minimize the costs of working hours and uncovered periods. Three implicit BAP formulations are investigated. To better understand the literature and the models previously developed, a 3-field break classification scheme is introduced. The first field characterizes the number of breaks permitted per shift, the second specifies whether the length of the breaks is fixed or variable, and the third limits their position in a shift. A complexity analysis of the resulting 12 BAPs along with a few special cases is also included. Most problems are shown to be strongly NP-hard. Computations are presented for a wide variety of scenarios for both the TShP and the BAP using data provided by a European airport ground handler company. In all, over 500 instances were investigated using high and low demand fluctuation curves and the various break and shift flexibility options. The results indicate that increasing flexibility in break regulations can make a significant difference in coverage, but the degree depends on the underlying structure of the demand curve as well as on the types of shifts permitted. Formulations with the most flexible shift and break regulations reduced undercoverage by up to 16.68% compared to the most common scenarios in which shifts are limited to a single lunch break.

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The break scheduling problem: complexity results and practical algorithms

Cited by 19 publications

References 14 publications

Solving the shift and break design problem using integer linear programming

Solving the shift and break design problem using integer linear programming

Solving the paintshop scheduling problem with memetic algorithms

The flexible break assignment problem for large tour scheduling problems with an application to airport ground handlers

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