Beam search heuristics for quadratic earliness and tardiness scheduling

• Published in: The Journal of the Operational Research Society Vol. 61; no. 4; pp. 620 - 631
• Main Author: Valente, J M S
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.04.2010; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Algorithms; Applied sciences; beam search; Business and Management; Children; Costs; Dispatching; Exact sciences and technology; Fines & penalties; Heuristic; Heuristics; Job shops; Lateness; Management; Objective functions; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; Optimal solutions; Production scheduling; quadratic earliness; quadratic tardiness; Schedules; Scheduling; Scheduling, sequencing; single machine; Studies; Supply chain management; Theoretical Paper; Theoretical Papers; Total cost assessment; scheduling; quadratic earliness; heuristics; quadratic tardiness; single machine; beam search; Dispatching problem; Branch and bound method; Variability; Scheduling; Quadratic programming; Due date; Delay; Search algorithm; Function evaluation; Computation time; Deadtime; Filter; Heuristic method; Earliness; Single machine
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2008.191

In this paper, we present beam search heuristics for the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. These heuristics include classic beam search procedures, as well as filtered and recovering algorithms. We consider three dispatching heuristics as evaluation functions, in order to analyse the effect of different rules on the performance of the beam search procedures. The computational results show that using better dispatching heuristics improves the effectiveness of the beam search algorithms. The performance of the several heuristics is similar for instances with low variability. For high variability instances, however, the detailed, filtered and recovering beam search (RBS) procedures clearly outperform the best existing heuristic. The detailed beam search algorithm performs quite well, and is recommended for small- to medium-sized instances. For larger instances, however, this procedure requires excessive computation times, and the RBS algorithm then becomes the heuristic of choice.