Adaptive fruit fly optimization-assisted logic-based benders decomposition for distributed parallel precast flowshop scheduling

This paper addresses a distributed precast flowshop scheduling problem that minimizes a weighted combination of delivery time and production–transportation cost in heterogeneous factories with parallel production lines and shared resources. We formulate mixed-integer linear programming (MILP) and constraint programming (CP) models for small-scale instances. For larger instances, we develop two exact decomposition algorithms that exploit the problem’s hierarchical structure. The first algorithm, adaptive fruit fly optimization-assisted logic-based Benders decomposition with scheduling subproblem relaxations (AL_LBBD_SSR), enhances logic-based Benders decomposition with three key strategies: adaptive fruit fly optimization to generate high-quality initial solutions, strong lower bounds to tighten the search space, and subproblem relaxations to accelerate convergence. The second algorithm, branch-and-check with scheduling subproblem relaxations (BCH_SSR), employs a branch-and-check framework strengthened with problem-specific inequalities and effective relaxations. Computational experiments on 180 benchmark instances demonstrate that both algorithms significantly outperform direct MILP and CP approaches, achieving near-optimal solutions with average optimality gaps below 1%. AL_LBBD_SSR excels for large-scale instances with more than 80 orders, while BCH_SSR is more effective for moderate-sized problems with up to 50 orders. These results highlight the potential of combining nature-inspired metaheuristics with exact optimization for complex industrial scheduling problems.