The two-machine flowshop total completion time problem: Branch-and-bound algorithms based on network-flow formulation

• Published in: European Journal of Operational Research Vol. 252; no. 3; pp. 750 - 760
• Main Authors: Detienne, Boris, Sadykov, Ruslan, Tanaka, Shunji
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2016; Elsevier BV; Elsevier Sequoia S.A; Elsevier
• Subjects: [INFO.INFO-RO] Computer Science [cs]/Operations Research [math.OC]; [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO]; Algorithms; Branch & bound algorithms; Branch-and-bound; Completion time; Computer Science; Filtering; Filtration; Flowshop; Formulations; Job shops; Lagrange multiplier; Lagrangian relaxation; Network flow problem; Operational research; Operations Research; Optimization; Optimization algorithms; Production management; Scheduling; Setup times; Studies; Branch-and-bound; Scheduling; Flowshop; Lagrangian relaxation
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2016.02.003

•We study the two-machine flowshop problem with sequence-independent setup times to minimize total completion time.•Strong Lagrangian bounds are proposed based on large scale network flow formulations.•To cope with their size, filtering procedures are developed.•Numerical experiments assess the efficiency of branch-and-bound algorithms. We consider the flowshop problem on two machines with sequence-independent setup times to minimize total completion time. Large scale network flow formulations of the problem are suggested together with strong Lagrangian bounds based on these formulations. To cope with their size, filtering procedures are developed. To solve the problem to optimality, we embed the Lagrangian bounds into two branch-and-bound algorithms. The best algorithm is able to solve all 100-job instances of our testbed with setup times and all 140-job instances without setup times, thus significantly outperforming the best algorithms in the literature.