A Two-Machine Learning Date Flow-Shop Scheduling Problem with Heuristics and Population-Based GA to Minimize the Makespan

This paper delves into the scheduling of two-machine flow-shop problem with step-learning, a scenario in which job processing times decrease if they commence after their learning dates. The objective is to optimize resource allocation and task sequencing ensure efficient time utilization timely completion all jobs, also known as makespan. identified established NP-hard due its reduction single machine for common date. To address this complexity, introduces an initial integer programming model, followed by development branch-and-bound algorithm augmented two lemmas lower bound attain exact optimal solution. Additionally, proposes four straightforward heuristics inspired Johnson rule, along enhanced counterparts. Furthermore, population-based genetic formulated offer approximate solutions. performance proposed methods rigorously evaluated through numerical experimental studies.