A mixed-integer formulation of the minimum patch size problem

Forest harvest scheduling models have addressed wildlife habitat concerns in a variety of ways. One way is through minimum patch size constraints specifying that a certain amount of the forest must consist of patches meeting both minimum size and minimum age requirements. Patch size requirements may be necessary because a forest with only small patches of mature habitat may not be able to support populations of some wildlife species. Maximum harvest opening size constraints, which are often imposed for legal or policy reasons, tend to divide forest habitat into small patches. Minimum patch size constraints may be able to help mitigate the negative impact of maximum harvest opening size restrictions. Patch size requirements have been considered elsewhere, but a mixed-integer linear programming (MILP) formulation has never been presented. This article presents such a formulation, which allows minimum patch size problems to be solved using the branch and bound algorithm available through commercial solver packages. An example problem is formulated, solved, and discussed.