Analysis of Close-to-optimal Zones in LP Decision-support Models

This project combines the latest insights of different strands of knowledge in order to support environmental policy decision making. Concretely, we use highly efficient computational methods based on mathematical insights of optimization problems to describe all feasible solutions of a linear programming problem that are not optimal but lie “within epsilon” of the optimal solution. These feasible solutions all have some properties in common (not only that they are within a certain cost range, but also that certain functions defined on the solution space (e.g., environmental impact indicators) also lie within certain ranges). In order to identify relevant invariants we project the feasible solutions into two-dimensional planes to make them accessible for direct scrutiny by human eyes. As an example we have applied this method to the GAINS optimization module that is used, inter alia, by European policy makers to design air pollution policies. The method we have developed can be used to efficiently estimate the additional cost for tightening or relaxing environmental constraints. The results generated so far allow us to specifically describe the trade-offs between global and local cost considerations, between different environmental objectives, or between preferences of different regions or countries. The method can also be used to identify directions of the solution spaces that are particularly “flat” with respect to the optimum