Geodesic
Effective algorithms for one scheduling problem on two machines with makespan minimization
Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 4, pp. 63-79

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We consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order between the jobs, with an objective to minimize the makespan. An approximation algorithm with performance guarantee is proposed for this problem. Polynomial solvability of the problem is proved in the case when each job on the first machine is in precedence relation with two jobs on the second machine. Ill. 9, bibliogr. 8.
Keywords: cross-docking problem, schedule, partial order, approximation algorithm. 
@article{DA_2015_22_4_a4,
     author = {A. A. Romanova},
     title = {Effective algorithms for one scheduling problem on two machines with makespan minimization},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {63--79},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2015_22_4_a4/}
}
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A. A. Romanova. Effective algorithms for one scheduling problem on two machines with makespan minimization. Diskretnyj analiz i issledovanie operacij, Tome 22 (2015) no. 4, pp. 63-79. http://geodesic.mathdoc.fr/item/DA_2015_22_4_a4/