A dynamical model of water recycling in a mine-processing enterprise

We consider a mine-processing enterprise, which runs a number of production plants. Each plant uses a considerable amount of water which is polluted during the production process. The aim is to determine the optimal amounts of water to be taken from a river or to be pumped back from a waste water reservoir. The problem is decomposed in two tasks. Task 1 is formulated as a time-discrete optimal control model and determines the amounts of water pumped in each period. The solution method used is dynamic programming. While Task 1 has an ecological objective (minimize environmental damage), in Task 2 the aim is to determine by which pump configurations the desired quantities of water are most efficiently brought to reservoir (with least cost). Because of the special structure of this linear programming problem it can be solved simply by sorting with respect to unit costs.