A branch and bound algorithm for the two-machine flowshop problem with unit-time operations and time delays
RAIRO - Operations Research - Recherche Opérationnelle, Volume 48 (2014) no. 2, pp. 235-254.

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set of unit-time operations subject to time delays with respect to the makespan. This problem is known to be \hbox{𝒩P} 𝒩𝒫 -hard in the strong sense. We propose an algorithm based on a branch and bound enumeration scheme. This algorithm includes the implementation of new lower and upper bound procedures, and dominance rules. A computer simulation to measure the performance of the algorithm is provided for a wide range of test problems.

DOI: 10.1051/ro/2014004
Classification: 9008
Keywords: branch and bound, dominance rule, flowshop, lower and upper bounds, time delays
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     title = {A branch and bound algorithm for the two-machine flowshop problem with unit-time operations and time delays},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {235--254},
     publisher = {EDP-Sciences},
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Moukrim, Aziz; Rebaine, Djamal; Serairi, Mehdi. A branch and bound algorithm for the two-machine flowshop problem with unit-time operations and time delays. RAIRO - Operations Research - Recherche Opérationnelle, Volume 48 (2014) no. 2, pp. 235-254. doi : 10.1051/ro/2014004. http://archive.numdam.org/articles/10.1051/ro/2014004/

[1] E. Balas and P. Toth, Branch and bound methods, chapter 10, in The traveling salesman problems: a guided tour of Combinatorial Opt., edited by E.L. Lawler. John Wiley (1985). | MR | Zbl

[2] T.H. Cormen, C.E. Leiserson and R.L. Rivest, Introduction to Algorithms. McGraw-Hill (1990). | MR | Zbl

[3] S. French, Sequencing and scheduling: an introduction to the mathematics of the job-shop. Series: Math. and its Appl. Ellis Horwood Ltd. (1982). | MR | Zbl

[4] T. Gonzalez and S. Sahni, Flow shop and job shop schedules: complexity and approximations. Oper. Res. 26 (1978) 36-52. | MR | Zbl

[5] S. Johnson, Optimal two- and three-stage production with set-up times included. Nav. Res. Log. Quart. 1 (1954) 61-68.

[6] A. Munier-Kordon and D. Rebaine, Polynomial time algorithms for the UET permutation flowshop problem with time delays. Comput. Oper. Res. 35 (2008) 525-537. | MR | Zbl

[7] V.J. Rayward-Smith and D. Rebaine, Analysis of heuristics for the UET two-machine flow shop. Comput. Oper. Res. 35 (2008) 3298-3310. | Zbl

[8] D. Rebaine, Permutation shop vs. non permutation flow shop with delays. J. Comput. Industrial Engrg. 48 (2005) 357-362.

[9] W. Yu, H. Hoogeveen and J.K. Lenstra, Minimizing makespan in a two-machine flow with delays and unit-time operations is NP-hard. J. Schedul. 7 (2004) 333-348. | MR | Zbl

[10] W. Yu, The two-machine flow shop problem and the one-machine total tardiness problem. Ph.D. thesis, Eindhoven University of Technology, The Netherlands (1996). | MR | Zbl

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