Forest Management: A Multicommodity Flow Formulation and Sensitivity Analysis

We formulate the Forest Management Problem as a Multicommodity Network Flow Problem with a convex cost function. We then show how to transfer the problem to an equivalent Single-Commodity Network Flow formulation in order to address several sensitivity analysis questions using results by Granot and Veinott (Granot, F., A. F. Veinott, Jr. 1985. Substitutes, complements and ripples in network flows. Math. Oper. Res. 10 471--497.). The answers can subsequently be used to help forest managers respond to changes in the environment such as fires or changes in market prices, without any additional computation. Furthermore, the characterization of the response we provide requires no prior knowledge of optimal management policies.