The grid packing problem: Selecting a harvesting pattern in an area with forbidden regions

The problem of determining the maximum value or maximum volume cutting pattern in a forested area which is divided into a regular grid is approached as a 0–1 integer programming model. Constraints are included to preclude harvests in blocks which are adjacent to one another in an effort to reduce large forest openings which can have negative environmental impacts. One form of adjacency constraints can be used to exclude the cutting of blocks which share a common edge. Other forms can prevent harvesting blocks which share an edge or point. The challenge is to write these constraints in a form that favors 0–1 solutions. The integer-friendly forms that are chosen are applied to large tracts of land in which significant areas are excluded from cutting because of habitat preservation requirements or other prohibitions. More than 100 experimental runs with hypothetical data were conducted.