Abstract
This paper considers the problem of minimizing the schedule length of a two-machine shop in which not only can a job be assigned any of the two possible routes, but also the processing times depend on the chosen route. This problem is known to be NP-hard. We describe a simple approximation algorithm that guarantees a worst-case performance ratio of 2. We also present some modifications to this algorithm that improve its performance and guarantee a worst-case performance ratio of 3/2.
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Strusevich, V.A., van de Waart, A.J.A. & Dekker, R. A 3/2 Algorithm for Two-Machine Open Shop with Route-Dependent Processing Times. Journal of Heuristics 5, 5–28 (1999). https://doi.org/10.1023/A:1009643112214
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DOI: https://doi.org/10.1023/A:1009643112214