Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Computers and Operations Research
Design and Analysis of Experiments
Design and Analysis of Experiments
Multicriteria Scheduling: Theory, Models and Algorithms
Multicriteria Scheduling: Theory, Models and Algorithms
Computers and Operations Research
A Review and Evaluation of Multiobjective Algorithms for the Flowshop Scheduling Problem
INFORMS Journal on Computing
A decomposition algorithm for the single machine total tardiness problem
Operations Research Letters
Setting a common due date in a constrained flowshop: A variable neighbourhood search approach
Computers and Operations Research
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This paper studies the flowshop scheduling problem with a complex bicriteria objective function. A weighted sum of makespan and maximum tardiness subject to a maximum tardiness threshold value is to be optimized. This problem, with interesting potential applications in practice, has been sparsely studied in the literature. We propose global and local dominance relationships for the three-machine problem and a fast and effective genetic algorithm (GA) for the more general m-machine case. The proposed GA incorporates a novel three-phase fitness assignment mechanism specially targeted at dealing with populations in which both feasible as well as infeasible solutions might coexist. Comprehensive computational and statistical experiments show that the proposed GA outperforms the two most effective existing heuristics by a considerable margin in all scenarios. Furthermore, the proposed GA is also faster and able to find more feasible solutions. It should be noted that when the weight assigned to maximum tardiness is zero, then the problem is reduced to minimizing makespan subject to a maximum tardiness threshold value. Heuristics for both problems have been provided in the literature recently but they have not been compared. Another contribution of this paper is to compare these recent heuristics with each other.