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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ERIM Article Series (EAS)
Journal of Heuristics
Erasmus Research Institute of Management

Strusevich, V, Dekker, R, & Waart, A.J.A. (1999). A 3/2 Algorithm for Two-Machine Open Shop with Route-Dependent Processing Times. Journal of Heuristics, 5–28. doi:10.1023/A:1009643112214