Nowadays, many manufacturing companies are trying to improve the performance of their processes using available innovative technologies such as collaborative robots (cobots). Cobots are robots with whom no safety distance is necessary. Through cooperation with human workers, they can help increase the production speed of existing workstations. The well-known job shop scheduling problem is, therefore, extended with the addition of a cobot to the workstation assignment. The considered objective is to maximize the normalized sum of production costs and makespan. To solve this problem, we propose a hybrid genetic algorithm with a biased random-key encoding and a variable neighborhood search. The hybrid method combines the exploration aspects of a genetic algorithm with the exploitation abilities of a variable neighborhood search. The developed algorithm is applied to real-world data and artificially generated data. To demonstrate the performance of this algorithm, a constraint programming model is implemented and the results are compared. Additionally, benchmark instances from a related problem from the cobot assignment and assembly line balancing, have been solved. The results from the real-world data show how much the objective function can be improved by the deployment of additional robots. The normalized objective function could be improved by up to 54% when using five additional cobots. As a methodological contribution, the biased random-key encoding is compared with a typical integer-based encoding. A comparison with a dataset from the literature shows that the developed algorithm can compete with state-of-the-art methods on benchmark instances.