Road network, landing location, and routing optimization for forest smallholders landscapes

We present two mixed integer linear programming (MILP) formulations for a well-known integrated network, timber landing location, and routing problem that arises in forest management. The models seek to jointly optimize the construction and maintenance schedule of forest road networks with landing site selection and transportation routing for timber production. This problem is, in general, difficult to solve as it contains the so-called fixed charge network flow problem, which is known to be NP-hard. One of the proposed MILP formulations considers 3-index continuous variables to represent timber flows on road segments in each period. The presence of Big-M constraints leads to weak linear relaxation bounds. Disaggregating flow variables, according to timber origin, results in a novel 4-index formulation with very tight linear relaxation bounds. Nevertheless, the number of variables increases prohibitively. This research makes use of spatial constraints common to Smallholding Forested Landscapes to develop a solution approach that reduces the number of flow variables in the new 4-index model. Results from a real-world case study located in Northwest Portugal show that, with the 4-index formulation, the proposed solution approach makes it possible to obtain optimal solutions in a short computational time.