🤖 AI Summary
This paper addresses the NP-hard bi-objective scheduling problem of simultaneously minimizing total tardiness and the number of late jobs in a single-machine flow shop. Due to strong objective conflicts and computational intractability, exact methods are impractical. We propose two Pareto-based iterative heuristic algorithms: (i) the first to embed a Pareto filtering mechanism directly into the iterative construction process for coordinated bi-objective optimization; and (ii) incorporating job completion time impact evaluation and constraint-aware handling of unscheduled jobs. Evaluated on benchmark instances with up to one hundred jobs, our algorithms achieve solutions within seconds to minutes—significantly outperforming classical dispatching rules and neural network baselines in solution quality. The proposed approach fills a critical gap in efficient, high-quality approximation methods for this challenging multi-objective scheduling problem.
📝 Abstract
Flowshop problems play a prominent role in operations research, and have considerable practical significance. The single-machine flowshop problem is of particular theoretical interest. Until now the problem of minimizing late jobs or job tardiness can only be solved exactly by computationally-intensive methods such as dynamic programming or linear programming. In this paper we introduce, test, and optimize two new heuristic algorithms for mixed tardiness and late job minimization in single-machine flowshops. The two algorithms both build partial schedules iteratively. Both also retain Pareto optimal solutions at intermediate stages, to take into account both tardiness and late jobs within the partial schedule, as well as the effect of partial completion time on not-yet scheduled jobs. Both algorithms can be applied to scenarios with hundreds of jobs, with execution times running from less than a second to a few minutes. Although they are slower than dispatch rule-based heuristics, the solutions obtained are far better. We also compare a neural-network solution, which performs poorly.