Integrated tri-objective scheduling and internal logistics optimization in U-shaped flexible flow shops: a mathematical model and metaheuristic framework

This paper addresses an integrated tri-objective scheduling and internal logistics optimization problem in a U-shaped flexible flow shop under operational uncertainties, including raw material delays, setup times, and machine/mold failures. From a systems science perspective, the coupled production-logistics system is modeled as a mixed-integer nonlinear program (MINLP) that jointly minimizes: earliness-tardiness penalties, weight-dependent loading and transportation times, and congestion-driven logistics delays. A linearized reformulation is solved exactly via GAMS for small-to-medium instances. For large-scale problems, a problem-specific Simulated Annealing (SA) meta-heuristic is developed. Using real world data from an automotive rubber-metal parts supplier, the exact method optimizes instances up to 24 tasks and 6 logistics units within ~30 minutes (1% optimality gap). For larger instances, SA achieves average gaps below 9% with substantial runtime reductions. Uncertainty is managed via 50 independent scenarios using Sample Average Approximation. Statistical tests (paired t-test, ANOVA) confirm robustness and scalability. Benchmarking against an Improved Hybrid Genetic Algorithm (IHGA) demonstrates the competitive performance of the proposed SA. Sensitivity analyses quantify trade-offs among throughput, congestion, resource availability, and due-date slack. Key contributions include an integrated production-logistics model under multiple uncertainties, a tri-objective MINLP capturing timeliness, transport effort, and congestion, and a tailored SA for industrial-scale systems.