MILP-guided evolutionary optimization for glass jars and vacuum flask production

We study production planning in a glass-container factory that operates a single furnace feeding three molding machines to produce vacuum-flask inserts and glass jars. The problem features industry-specific requirements, such as ramp-up behavior, safety stock, and furnace extraction limits, which we model explicitly in a mixed-integer linear program (MILP). We then develop two hybrid evolutionary approaches, a simple Genetic Algorithm (GA) and a Multi-Population GA (MPGA), that optimize the binary decisions of the MILP, while the remaining variables are computed exactly via the embedded solver. A benchmark of 400 artificial instances, calibrated from factory data, and a real quarterly plan are used for validation. The results show that CPLEX Branch-and-Cut (B&C) solves only the smallest instances to optimality. In contrast, GA and MPGA find feasible solutions across the entire testbed within the time limit. The proposed model captures key shop-floor effects, and the multi-population hybridization yields robust, high-quality plans when exact methods become computationally prohibitive.