Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays

• Published in: Journal of combinatorial optimization Vol. 36; no. 3; pp. 871 - 895
• Main Author: Mallach, Sven
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2018; Springer Nature B.V
• Subjects: Combinatorics; Convex and Discrete Geometry; Formulations; Integer programming; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematical programming; Mathematics; Mathematics and Statistics; Modelling; Multiprocessing; Operations Research/Decision Theory; Optimization; Production scheduling; Scheduling; Theory of Computation; Upper bounds; Multiprocessor scheduling; Integer programming; Communication delays
• ISSN: 1382-6905; 1573-2886
• DOI: 10.1007/s10878-017-0199-9

We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered ordering -based, and the other assignment -based. We first reveal redundancies in the encoding of feasible solutions found in present formulations and discuss how they can be avoided. For the assignment-based approach, we propose new inequalities that lead to provably stronger continuous relaxations and better performance in practice. Moreover, we derive a third, novel modeling strategy and show how to more compactly linearize assignment formulations with quadratic constraints. In a comprehensive experimental comparison of representative models that reflect the state-of-the-art in terms of strength and size, we evaluate not only running times but also the obtained lower and upper bounds on the makespan for the harder instances of a large scale benchmark set.