A robust optimization approach protected harvest scheduling decisions against uncertainty

Abstract

Harvest scheduling decisions are made in an uncertain environment, and current modeling techniques that consider uncertainty impose severe difficulties when solving real problems. In this paper we describe a robust optimization methodology that explicitly considers randomness in most of the model coefficients while keeping the model computationally tractable. We apply the method to schedule harvest decisions when both timber yield and demand of two products are uncertain. Since uncertain coefficients must be independent, uniform, and symmetrically distributed, we only address uncertainty attributable to estimate errors of forecast models. The methodology was applied to a 245 090 ha forest in British Columbia, Canada. We compared the change in harvest decisions and objective function when robust solutions are implemented relative to deterministic solutions. Although probability bounds can be used to a priori define the probability of constraint violations, they produce conservative solutions. We therefore tested the rates of constraint violations by simulation. While traditional deterministic decisions were always infeasible when uncertain data were simulated, robust decisions were much less sensitive to uncertainty and were, to a large extent, protected against the occurrence of infeasibilities. In exchange, reasonable reductions in the objective function were observed.