We study a planning problem to coordinate production and transportation scheduling, where a set of jobs needs to be transported from a holding area to a single batch machine for further processing. A number of results for this combined transportation-and-scheduling environment have recently been published. They look into the complexity status of the minimization of the sum of total processing time and processing cost, and of the sum of makespan and processing cost, for a fixed number of transporters. In this paper, we add to these results in that (1) we show that the earlier complexity results are still valid when the processing cost is removed from the objective, thus reducing to more "classic" scheduling objectives; (2) we assess the complexity status of the relevant problem variants with free number of transporters; and (3) we prove that the weighted-completion-time objective leads to an intractable problem even with a single transporter, contrary to the unweighted case.
Zhu, H., Leus, R., & Zhou, H. (2016). New results on the coordination of transportation and batching scheduling. Applied Mathematical Modelling, 40(5–6), 4016–4022. https://doi.org/10.1016/j.apm.2015.10.042