Modern implementations of industrial robots require the use of extensive knowledge and novel concepts. To bring real benefits, robotized processes must be analysed in detail. One can now observe an increasing use of lean robotics, a concept that is primarily intended to simplify processes and eliminate inefficient activities. This paper deals with industrial robot task scheduling in the adhesive dispensing process. The first part of the paper presents the modern concept of production process robotisation and reviews the literature on industrial robot task scheduling. After that, the problem of robotic adhesive dispensing on the electronic components of a printed circuit board (PCB) is presented. Another section of the paper describes the scheduling of effective and supporting tasks of the robot in the analysed process with the use of alternative dispatching rules. The determination of a schedule that is optimal in terms of the defined objective made it possible to discuss the results and reach valid conclusions. The study has confirmed that modern concepts are useful for simplifying robotic production processes.