A theoretical minimal solution for heuristics: The case of the spatial harvest timber problem

Heuristic methods are widely used to address the spatial optimization of timber harvests at the forest level. These methods have been shown to solve the timber harvest problem in a timely and computationally efficient manner. However, solutions provided by any heuristic are often suboptimal, and inquiries often arise regarding the quality of those solutions. One way to assess the quality of the solutions is to compare them against a minimum solution estimated using probability functions associated with the theoretical distribution of the solution space. A thorough theoretical framework is proposed to estimate the parameters of the probability distribution of the solution space based on the noncentral chi-square (chi(2)) distribution as an underlying distribution for the instances. A case study using the Lincoln Tract dataset suggests that the best objective function out of six thousand solutions was 0.26, whereas the theoretical minimal solution was 2 x 10(-6).