We consider mathematical models for tubular reactors in the form of dynamic distributed parameter systems. The goal is to maximize the overall profit over a fixed time horizon, where the number of cleaning operations, the length of the reactor operation between successive cleanings, and the reactor feed rates for each time interval are to be computed. We assume that product prices and consumer demands are time-dependent. It must be guaranteed that the decrease of the free cross-sectional area of the tube caused by coke deposition never exceeds a certain limit. Moreover, there are time and position dependent constraints for the state and control variables such as a maximum bound for the temperature. The mathematical model and the applied discretization scheme are outlined in detail. Numerical results are presented for a case study, where optimal input feeds and maintenance times of an acetylene reactor are computed. Of special interest is the behaviour of the program under real-time conditions, when changes in the process data or price and user demand functions require a restart of the calculation.