An exact algorithm for scheduling identical coupled tasks

Ahr, Dino; Békési, József; Galambos, Gábor; Oswald, Marcus; Reinelt, Gerhard

doi:10.1007/s001860300328

Cited by 32 publications

(55 citation statements)

References 5 publications

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“…maximization) problem is given as the ratio between the value of the approximation solution returned by the algorithm A on an instance I and the optimum i.e. ρ ≤ max I A(I) OPT (I) 1 Star graph with only incoming arcs for the central node arc. 2 Star graph with at least one outcoming arc for the central node.…”

Section: Performance Ratiomentioning

confidence: 99%

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

et al. 2016

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Abstract. We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain, . . .).In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters.

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Section: Performance Ratiomentioning

confidence: 99%

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

et al. 2016

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“…The best known algorithm for n identical tasks, to our knowledge, has complexity O(nr 2L ), where r ≤ a−1 √ a (Ahr et al [1]). Note, however, that this is not an algorithm for which the time complexity is polynomial in the size of the instance.…”

Section: Coupled Tasksmentioning

confidence: 99%

“…We want to adapt the algorithm of Ahr et al [1] so that it solves this cyclic case. We briefly outline the method in order to explain the necessary modifications.…”

Section: Theoremmentioning

confidence: 99%

“…The vertex set V consists of all possible patterns and there is an arc from pattern p i to p j with weight l if the placement of the corresponding tasks yields a right-shift of l units (as explained for p 1 and p 2 in Figure 2). In Ahr et al [1] only an approximate value for the number of vertices |V | is given. The exact number is obtained by the following formula:…”

Section: Theoremmentioning

confidence: 99%

“…Then the optimal schedule length is given by L(n) + (a + L + b). In Ahr et al [1], determining the shortest path is done in a rather uneconomical manner, where for each vertex all successors together with the different arc weights are memorized.…”

Section: Theoremmentioning

confidence: 99%

See 2 more Smart Citations

Scheduling of coupled tasks and one-machine no-wait robotic cells

Brauner

Finke

Lehoux-Lebacque

et al. 2009

Computers & Operations Research

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Coupled task scheduling problems were first studied more than 25 years ago. Several complexity results have been established in the meantime, but the status of the identical task case still remains unsettled. We describe a new class of equivalent one-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresponds to the production of a single part type in a robotic cell. We describe new algorithmic procedures to solve this robotic cell problem, allowing lower and upper bounds on the production time, and discussing in particular cyclic production plans.

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A branch-and-bound algorithm for the coupled task problem

et al. 2014

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The coupled task problem is to schedule jobs on a single machine where each job consists of two subtasks and where the second subtask has to be started after a given time interval with respect to the first one. The problem has several applications and is NP-hard. In this paper we present a branch-and-bound algorithm for this problem and compare its performance with four integer programming models.

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An exact algorithm for scheduling identical coupled tasks

Cited by 32 publications

References 5 publications

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

Some complexity and approximation results for coupled-tasks scheduling problem according to topology

Scheduling of coupled tasks and one-machine no-wait robotic cells

A branch-and-bound algorithm for the coupled task problem

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