Robust mathematical programming for natural resource modelling under parametric uncertainty

Abstract

Inaccurate specification of model coefficients can lead to false or distorted findings in modeling investigations of natural resource management. Hence, this paper outlines a decision framework for optimization problems in which only the bounded set of outcomes for uncertain parameters is known. These models can be solved with standard mathematical programming software and are no larger than their deterministic equivalent. The robust approach is contrasted against deterministic analysis and is demonstrated for two applications regarding the management of natural resources. Deterministic plans are infeasible in at least 40% of cases when parameters vary from their point estimates. Inclusion of robust constraints immunizes against this infeasibility, thereby removing errors arising from false certainty. Additionally, incorporation of bounded parameters in the objective function yields interval-valued sets containing potential outcomes. However, this increase in the general relevance of model output introduces some degree of suboptimality as deterministic plans are buffered to proactively account for potential variability. The cost of robustness increases with the simulated spread of uncertain coefficients but may be reduced through accounting for the uncertainty aversion of decision makers.