Formulating the integrated forest harvest-scheduling model to reduce the cost of the road-networks

The integrated harvest-scheduling model addresses the tactical forest management planning problem of maximizing harvest revenues minus road construction and transportation costs. This paper considers the problem of developing innovations to this model such that it can: (1) be used to generate solutions to problem instances containing a large set of candidate roads, with many circuits; (2) yield improved solutions when compared to prior formulations; and (3) achieve improvements in the solutions by reducing the total construction and transportation costs. To the end, a new formulation of the integrated model was developed using the following strategy: (a) each candidate road was represented in the model by two directed arcs (instead of one undirected edge, as used in prior formulations); and (b) a set of strengthening constraints including clique constraint was developed to exploit the property of the directness of the candidate roads. The new model was tested and compared with prior formulations on eight problem instances, ranging in size from 900 to 4900 stands and containing candidate roads ranging in number from 3424 to 19,184. Results show that the new formulation: (1) entails the use of larger set of constraints than prior formulations; (2) produced tighter root-LP gaps, than prior models, as the problem instances grew in size and complexity; and (3) produced solutions with the tightest relative gap, the highest objective function value, and major reductions in the cost of constructing a road network, as the problem instances grew in size and complexity. Our conclusion is that the strategy of formulating the integrated model, used in this paper, may be useful to future researchers and practitioners working on this problem.