Treffer: Enhanced logic-based Benders decomposition methods for the distributed heterogeneous non-permutation flow shop scheduling problem.

This paper addresses the Distributed Heterogeneous Non-Permutation Flowshop Scheduling Problem (DHNPFSP), where jobs are assigned to factories organised as non-permutation flowshops. Unlike the Distributed Heterogeneous Permutation Flowshop Scheduling Problem (DHPFSP), DHNPFSP allows varying job sequences across machines, expanding the solution space and potentially improving makespan. However, optimising multiple sequences simultaneously introduces significant computational challenges. To solve small-sized DHNPFSP instances, we formulate a Manne-based Mixed Integer Linear Programming (MILP) model and a Constraint Programming (CP) model. Given the $ \mathcal {NP} $ NP -hard nature of the problem, we also integrate advanced techniques such as strong subproblem relaxations, tightened lower bound, iterated greedy, CP, and problem structure property, resulting in five enhanced Logic-Based Benders Decomposition (LBBD) approaches. These methods decompose the problem into an assignment master problem and multiple scheduling subproblems, which are solved using MILP and CP. Computational experiments show that CP-based methods outperform other approaches for small-sized instances, while the enhanced LBBD methods excel for medium- and large-sized instances. Comparative analysis indicates that in distributed flow shop production environments, the non-permutation scheme significantly improves makespan compared to the permutation scheme. Sensitivity analysis further reveals that increasing the number of factories and machines substantially escalates complexity, while the number of jobs has a minimal impact. [ABSTRACT FROM AUTHOR]

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