Solving environmental problems with integer programming: recent experience and challenges

For most real-world problems, especially those arising in environmental decisionmaking, natural models are nonlinear. In optimization, the complexity of solving nonlinear problems can be reduced by introducing some appropriate problem-dependent simplification that transforms the nonlinear problem to a more easily solved integer linear programming problem. Such techniques are increasingly being utilized in the modelling and solution of environmental problems, not least because the resulting formulations can often be solved in practice: progress in linear and integer programming solvers and software tools over the last ten years or so has meant more reliable and rapid solution of even large-scale problems. This talk will describe two cases of environmental problems tackled with integer progamming, highlighting its modelling power. The first case concerns river systems, and decisions about environmental flows, addressing questions such as how much to release, and when. The second case concerns forestry. Harvest scheduling in forestry has for some time been planned with the aid of integer programming tools; now environmental considerations, such as habitat preservation, are being incorporated in such models. Solution approaches used, and future challenges, will also be discussed