This thesis gives a short introduction to the Dynamic Positioning(DP) domain and focuses on developing a fuel optimal thrust allocation algorithm for marine DP vessels with a diesel electric power plant. Obtained data is used to develop a static model for the fuel consumption of a diesel generator, as a function of its produced power. This model is used to formulate a convex Quadratic Programming(QP)-problem that finds fuel optimal solutions to the thrust allocation problem. This is possible due to the fact that DP vessels are usually over-actuated in terms of their thrusters. The fuel optimal thrust allocation algorithm shows promising results with respect to minimizing consumed fuel of the generators, when compared to thrust allocation algorithms that minimizes produced thrust or consumed power by the thrusters. The simulations in this thesis typically gives a fuel reduction on a rather common Platform Supply Vessel(PSV) of up to 2% of its maximum possible fuel consumption, when compared to thrust and power minimizing thrust allocation algorithms. The fuel optimization can be implemented as a standard (QP)-problem by recalculation of its cost function weights based on linear and quadratic model approximations at the current operation point. A method for reducing load variations in the diesel generators produced power, and its implications on fuel consumption, sooting and NOx emission is proposed and discussed. Additionally, simulations of the thrust allocation, assisting the Power Management System(PMS) by reserving power on the bus for external consumers about to connect are presented, and it is shown that it might prevent start-up of extra generators.