Scheduling identical parallel machines to minimize total tardiness

Biskup, Dirk; Herrmann, J. Berenike; Gupta, Jatinder N. D.

doi:10.1016/j.ijpe.2008.04.011

Cited by 88 publications

(47 citation statements)

References 24 publications

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“…With regards to the computational complexity of the investigated issue, it is worth noting that Biskup et al (2008) put in evidence that the total tardiness minimization problem on identical parallel machines is NP-hard. A PMTCS problem can be easily relaxed to a classical parallel machine scheduling issue when the life of a tool tends to infinity.…”

Section: Problem Descriptionmentioning

confidence: 99%

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Costa¹,

Cappadonna²,

Fichera³

2016

10.5267/j.ijiec

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This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. A new model that considers the effects of the tool wear on the quality characteristics of the worked product is proposed. Since no mathematical programming-based approach has been developed by literature so far, two distinct mixed integer linear programming models, able to schedule jobs as well as tool change activities along the provided production horizon, have been devised. The former is an adaptation of a well-known model presented by the relevant literature for the single machine scheduling problem with tool changes. The latter has been specifically developed for the issue at hand. After a theoretical analysis aimed at revealing the differences between the proposed mathematical models in terms of computational complexity, an extensive experimental campaign has been fulfilled to assess performances of the proposed methods under the CPU time viewpoint. Obtained results have been statistically analyzed through a properly arranged ANOVA analysis.

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Section: Problem Descriptionmentioning

confidence: 99%

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Costa¹,

Cappadonna²,

Fichera³

2016

10.5267/j.ijiec

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show abstract

“…This problem is also NP-hard in the ordinary sense since 1|| j T j has been shown to be NPhard in the ordinary sense by Du & Leung (1990). However, various efficient branch-and-bound algorithms (e.g., Azizoglu & Kirca, 1998;Yalaoui & Chu, 2002;Shim & Kim, 2007b;Tanaka & Araki, 2008;Schaller, 2009;Shim, 2009) and heuristics (e.g., Biskup et al, 2008) have been developed for P m|| j T j . These findings can be used to develop sequence-oriented solution procedures for the problem with fixed delivery dates.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness

Mensendiek

Gupta

Herrmann

2015

European Journal of Operational Research

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“…On the one hand, many real manufacturing settings are naturally formulated as parallel machine scheduling problems. Examples discussed in the literature span a variety of industries from semiconductor manufacturing (Shim and Kim, 2007;Detienne et al, 2011) to beverage, printing, and pharmaceutical industries (Biskup et al, 2008). On the other hand, parallel machine scheduling is the immediate generalization of single-machine scheduling from a theoretical point of view, and parallel machine scheduling subproblems are the building blocks of decomposition procedures for multi-stage systems (Pinedo, 2008, p.111).…”

Section: Introductionmentioning

confidence: 99%

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

Bülbül

źEn

2016

J Sched

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The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds.

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Scheduling identical parallel machines to minimize total tardiness

Cited by 88 publications

References 24 publications

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

Scheduling identical parallel machines with fixed delivery dates to minimize total tardiness

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

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