A robust basic cyclic scheduling problem

Hamaz, Idir; Houssin, Laurent; Cafieri, Sonia

doi:10.1007/s13675-018-0100-3

Cited by 12 publications

(8 citation statements)

References 25 publications

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“…A robust version of the BCSP, named U Γ -BCSP, is studied in [10]. The authors consider that the processing time values are uncertain and defined by the budgeted uncertainty set introduced in [3].…”

Section: Robust Versionmentioning

confidence: 99%

The robust cyclic job shop problem

Hamaz¹,

Houssin

Cafieri

2024

European Journal of Operational Research

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Section: Robust Versionmentioning

confidence: 99%

The robust cyclic job shop problem

Hamaz¹,

Houssin

Cafieri

2024

European Journal of Operational Research

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“…The BCSP problem under the uncertainty set U Γ is studied in [13]. Three exact algorithms are proposed to solve the problem.…”

Section: Cjsp Problem With Uncertain Processing Times (U γ -Cjsp)mentioning

confidence: 99%

“…In other words, we aim to find a cycle α and occurrence shifts (K ij ) (i,j)∈D such that, for each possible value of the processing times p ∈ U Γ , there always exists a feasible vector of starting time (t i ) i∈T . Note that, once the occurrence shifts are fixed, the problem can be solved as a robust BCSP by using the algorithms described in [13]. The following theorem characterizes the value of the optimal cycle time for U Γ -CJSP: Theorem 2 ( [13]).…”

Section: Cjsp Problem With Uncertain Processing Times (U γ -Cjsp)mentioning

confidence: 99%

“…Note that, once the occurrence shifts are fixed, the problem can be solved as a robust BCSP by using the algorithms described in [13]. The following theorem characterizes the value of the optimal cycle time for U Γ -CJSP: Theorem 2 ( [13]). The optimal cycle time α of the U Γ -CJSP is characterized by…”

Section: Cjsp Problem With Uncertain Processing Times (U γ -Cjsp)mentioning

confidence: 99%

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A Branch-and-Bound Procedure for the Robust Cyclic Job Shop Problem

Hamaz

Houssin

Cafieri

2018

Lecture Notes in Computer Science

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This paper deals with the cyclic job shop problem where the task durations are uncertain and belong to a polyhedral uncertainty set. We formulate the cyclic job shop problem as a two-stage robust optimization model. The cycle time and the execution order of tasks executed on the same machines correspond to the here-and-now decisions and have to be decided before the realization of the uncertainty. The starting times of tasks corresponding to the wait-and-see decisions are delayed and can be adjusted after the uncertain parameters are known. In the last decades, different solution approaches have been developed for two-stage robust optimization problems. Among them, the use of affine policies, column generation algorithms, row and row-and-column generation algorithms. In this paper, we propose a Branch-and-Bound algorithm to tackle the robust cyclic job shop problem with cycle time minimization. The algorithm uses, at each node of the search tree, a robust version of the Howard's algorithm to derive a lower bound on the optimal cycle time. We also develop a heuristic method that permits to compute an initial upper bound for the cycle time. Finally, encouraging preliminary results on numerical experiments performed on randomly generated instances are presented.

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“…This problem has been studied a lot since it has applications in many fields such as parallel processing (Hanen and Munier (1995)), staff scheduling (Karp and Orlin (1981)), or robotic scheduling (Ioachim and Soumis (1995), Kats and Levner (1996)). Hamaz et al (2018a) studied the a BCSP where the processing times are affected by an uncertainty effect.…”

Section: Introductionmentioning

confidence: 99%

A mixed integer linear programming modelling for the flexible cyclic jobshop problem

2019

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This paper addresses the Cyclic Jobshop Problem in a flexible context. The flexibility feature means that machines are able to perform several kinds of tasks. Hence, a solution of the scheduling problem does not only concern the starting times of the elementary tasks, but also the assignment of these tasks to a unique machine. The objective considered in this paper is the minimisation of the cycle time of a periodic schedule. We formulate the problem as a Mixed Integer Linear Problem and propose a Benders decomposition method along with a heuristic procedure to speed up the solving of large instances. It consists in reducing the number of machines available for each task. Results of numerical experiments on randomly generated instances show that the MILP modelling has trouble solving difficult instances, while our decomposition method is more efficient for solving such instances. Our heuristic procedure provides good estimates for difficult instances.

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A robust basic cyclic scheduling problem

Cited by 12 publications

References 25 publications

The robust cyclic job shop problem

The robust cyclic job shop problem

A Branch-and-Bound Procedure for the Robust Cyclic Job Shop Problem

A mixed integer linear programming modelling for the flexible cyclic jobshop problem

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