an environmentally-friendly method of removal is to use algae to clean this runoff water. The algae consume the minerals as part of their growth process. In addition to cleaning the water, the created algal bio-mass has a variety of applications including production of bio-diesel, animal feed, products for pharmaceutical and cosmetic purposes, or it can even be used as a source of heating or electricity.

The aim of this paper is to develop a model of algae production and use this model to investigate how best to optimize algae farms to satisfy the dual goals of maximizing growth and removing mineral contaminants.

With this aim in mind the paper is split into five main sections. In the first a review of the biological literature is undertaken with the aim of determining what factors effect the growth of algae. The second section contains a review of exciting mathematical models from the literature, and for each model a steady-state analysis is performed. Moreover, for each model the strengths and weaknesses are discussed in detail. In the third section, a new two-stage model for algae production is proposed, careful estimation of parameters is undertaken and numerical solutions are presented. In the next section, a new one-dimensional spatial-temporal model is presented, numerically

solved and optimization strategies are discussed. Finally, these elements are brought together and recommendations of how to continue are drawn.

In this paper we focus on the allocation process to determine the settings for each thruster that results in the minimal total power and thus fuel consumption. The mathematical formulation of this situation leads to a nonlinear optimization problem with equality and inequality constraints, which can be solved by applying Lagrange multipliers.

We give three approaches: first of all, the full problem was solved using the MATLAB fmincon routine with the solution from the linearised problem as a starting point. This implementation, with robust handling of the situations where the thrusters are overloaded, lead to promising results: an average reduction in fuel consumption of approximately two percent. However, further analysis proved useful. A second approach changes the set of variables and so reduces the number of equations. The third and last approach solves the Lagrange equations with an iterative method on the linearized Lagrange problem.

In this paper, we present a linear programming model for maximizing the amount

of decentralized power generation while respecting the load limitations of the

network.

We describe a prototype showing that for an example network the maximization

problem can be solved efficiently. We also modeled the case were the power consumption and decentralized power generation are considered as stochastic variables, which is inherently more complex.