The Goal Programming Formulation

The Patchworks program uses a goal programming formulation to simultaneously represent multiple objectives within the planning process. A goal programming problem operates by trying to minimize the difference between outcomes and target values for a series of sub-objectives.

The difference between the outcome and the target is measured for each planning period for each target. Outcomes that achieve or exceed target levels are ignored. Each 'delta' between outcome and target can be scaled and weighted as is appropriate for the particular problem. The overall objective is to minimize the sum (over each sub-objective and each planning period) of the scaled, weighted delta values. The lower the summed delta values, the closer that the outcomes meet the targets, and the better the solution.

It is easy to implement and assess multiple targets (sub-objectives) using this formulation. There is no requirement that the sub-objectives have the same units of measure. This means that problems can be set up to jointly schedule to achieve both harvest volume (m3/year), habitat retention (ha), and patch size distributions (% area/size class/period).