The automotive industry is facing a rapid technological evolution and the request of a very high level of customization of the products. This requires production systems able to manage a high variety of products with low volumes. To this aim, this paper focuses on multi-product assembly lines consisting of a set of stations with a robot operating the transportation and handling of the parts. Due to the high variety of the parts to be processed, perfect balancing is not possible, hence, proper control policies are requested to operate the line. The paper proposes a predictive–reactive scheduling approach to minimize the batch completion time by sequencing the tasks operated by shared resources in a context with uncertain processing times. The viability of the approach is demonstrated through the application to an industrial problem in the automotive industry. © 2021