We present a numerical method that finds the path of operation that gives minimum total entropy production rate in a tubular steam reformer. The method was applied to the three main reformer reactions in a tubular plug flow reactor with pressure drop and heat exchange. The total entropy production rate was minimized subject to a given production of hydrogen, a fixed inlet pressure, a fixed total molar flow rate at the inlet, and a fixed molar flow rate of inert gas. The inlet and outlet temperatures, the outlet pressure, and the inlet mixture composition were allowed to vary. The temperature profile of the furnace gases was the control variable. Compared to a typical path of operation, we obtained a reduction of more than 60% in the total entropy production rate for the optimal path. The results suggested that a shorter reactor may perform equally well. Interestingly, the optimal path showed regions of either a constant thermal force or a constant chemical force. The new path of operation was not realistic, however, so more work is needed to realise some of the potential gain. (C) 2004 Elsevier B.V. All rights reserved.