Cyclic Job Shop Problem with varying processing times

Hamaz, Idir; Houssin, Laurent; Cafieri, Sonia

doi:10.1016/j.ifacol.2017.08.908

Cited by 3 publications

(2 citation statements)

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“…Then, these scenarios are included in the master problem by generating the corresponding recourse decision variables on the fly. This process repeats until a solution that is feasible for all scenarios is found [3,4,6,7]. Figure 5 depicts the scheme of the column and constraint generation algorithm.…”

Section: Column and Constraint Generation Algorithmmentioning

confidence: 99%

Constraint Programming for the Robust Two-Machine Flow-Shop Scheduling Problem with Budgeted Uncertainty

Juvin

Houssin

López

2023

Lecture Notes in Computer Science

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This paper addresses the robust two-machine permutation flow-shop scheduling problem considering non-deterministic operation processing times associated with an uncertainty budget. The objective is to minimize the makespan of the schedule. Exact solution methods incorporated within the framework of a twostage robust optimization are proposed to solve the problem. We first prove that under particular conditions the robust two-machine permutation flow-shop scheduling problem can be solved in polynomial time by the well-known Johnson's algorithm usually dedicated to the deterministic version. Then we tackle the general problem, for which we propose a column and constraint generation algorithm. We compare two versions of the algorithm. In the first version, a mixed-integer linear programming formulation is used for the master problem. In the second version, we use a constraint programming model for the master problem. To the best of our knowledge, the use of constraint programming for a master problem in a two-stage robust optimization problem is innovative. The experimental results show the very good performance of the method based on the constraint programming formulation. We also notice that Johnson's algorithm is surprisingly efficient for the robust version of the general problem.

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Section: Column and Constraint Generation Algorithmmentioning

confidence: 99%

Constraint Programming for the Robust Two-Machine Flow-Shop Scheduling Problem with Budgeted Uncertainty

Juvin

Houssin

López

2023

Lecture Notes in Computer Science

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“…Draper et al (1999) proposed an alternative formulation to solve CJSP problems as constraint satisfaction problems. Hamaz et al (2018b) studied the CJSP with uncertain processing time. Houssin (2011) proposed an exact method to solve a CJSP using (max, plus) algebra.…”

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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