Two Pareto Optimum-based Heuristic Algorithms for Minimizing Tardiness and Late Jobs in the Single Machine Flowshop Problem

TL;DR

This paper introduces and tests two new Pareto-based heuristic algorithms for minimizing tardiness and late jobs in single-machine flowshop scheduling, offering better solutions than existing methods and a neural network approach.

Contribution

The paper presents two novel Pareto optimality-based heuristics for mixed tardiness and late job minimization, optimized for large problem instances in single-machine flowshops.

Findings

Both algorithms handle hundreds of jobs efficiently.

Solutions are significantly better than dispatch rule heuristics.

Neural network approach performs poorly in comparison.

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.