Abstract
The paper considers a problem of scheduling n jobs in a two-machine open shop to minimise the makespan, provided that preemption is not allowed and the interstage transportation times are involved. In general, this problem is known to be NP-hard. We present a linear time algorithm that finds an optimal schedule if no transportation time exceeds the smallest of the processing times. We also describe an algorithm that creates a heuristic solution to the problem with job-independent transportation times. Our algorithm provides a worst-case performance ratio of 8/5 if the transportation time of a job depends on the assigned processing route. The ratio reduces to 3/2 if all transportation times are equal.
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Rebaine, D., Strusevich, V. Two-machine open shop scheduling with special transportation times. J Oper Res Soc 50, 756–764 (1999). https://doi.org/10.1057/palgrave.jors.2600769
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DOI: https://doi.org/10.1057/palgrave.jors.2600769