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

Abstract

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