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Flow-shop with time delays, linear modeling and exact solution approaches

Abstract : In this thesis, we study the two-machine flow-shop problem with time delays in order to minimize the makespan. First, we propose a set of Mixed Integer Programming (MIP) formulations for the problem. In particular, we introduce a new compact mathematical formulation for the case where operations are identical per machine. The proposed mathematical formulations are then used to develop lower bounds and a branch-and-cut method. A set of valid inequalities is proposed in order to improve the linear relaxation of the MIPs. These inequalities are based on proposing new dominance rules and computing optimal solutions of polynomial-time-solvable sub-instances. These sub-instances are extracted by computing all maximal cliques on a particular Interval graph. In addition to the valid inequalities, the branch-and-cut method includes the consideration of a heuristic method and a node pruning procedure. Finally, we propose a branch-and-bound method. For which, we introduce a local search-based heuristic and dominance rules. Experiments were conducted on a variety of classes of instances including both literature and new proposed ones. These experiments show the efficiency of our approaches that outperform the leading methods published in the research literature.
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Submitted on : Wednesday, May 30, 2018 - 12:21:11 PM
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  • HAL Id : tel-01803409, version 1



Mohamed Amine Mkadem. Flow-shop with time delays, linear modeling and exact solution approaches. Operations Research [cs.RO]. Université de Technologie de Compiègne, 2017. English. ⟨NNT : 2017COMP2390⟩. ⟨tel-01803409⟩



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