A New Optimization Model for Spatially Constrained Harvest Scheduling under Area Restrictions through Maximum Flow Problem

We propose a new optimization model to solve spatially constrained harvest scheduling problems with maximum opening size constraints, which utilizes flow network constraints in a maximum flow problem. The idea of the maximum flow problem is to identify aggregated units in each cluster. The proposed model consists of a spatial component for aggregation and connectivity, a temporal component, and an integrated component that binds all the components together by linkage constraints between spatial and temporal features. Spatial connection for forest units in each cluster is conducted by a newly introduced approach of sequential triangle connection, under the adjacency relationship of common boundaries and common corner edges, which gives explicit connectivity in each cluster. Using 18 examples with two small hypothetical forests and two real-life forests, our computational comparison against the bucket formulation without a priori numeration and the path formulation with a priori numeration shows that our proposed model outperforms the bucket formulation in all cases, and outperforms the path formulation in 10 out of the 18 cases. When 2 and 3 green-up periods are considered over a planning horizon of 10 periods, our proposed model shows constant superiority against the bucket and the path formulations.