Minimizing Carbon Emission in Hybrid Flow Shop Scheduling: A Comparative Analysis of Flow-based and Set Partitioning Formulations

Abstract

This article addresses the Hybrid Flow Shop Green Scheduling Problem with Sequence and Machine Dependent Setup Times (HFSGSP-SMDST) in the context of Industry 4.0. The objective is to minimize carbon emission while optimizing scheduling. Two mathematical formulations, a flow-based positional formulation (FB) and a set partitioning positional formulation (HCG), are proposed to provide tighter lower bounds. The FB formulation is solved using a commercial solver, while the HCG algorithm incorporates an Iterated Local Search (ILS) to generate initial solutions and an upper bound for the problem. Computational experiments demonstrate that HCG achieves better lower bounds, although it requires more time compared to FB. The proposed algorithms offer valuable solutions for carbon emission optimization and scheduling in Industry 4.0, with a trade-off between lower bounds and convergence speed.