The present invention provides a system, method and apparatus for allocating resources with a linear programming model comprising an objective function and a set of constraints describing feasible allocations of the resources. The method ranks constraints based on a numerical measure derived from criteria selected from at least a first and second group and selects one or more of the top-ranked constraints. A new problem is determined from the model's objective function, the previously selected constraints, and the newly selected constraints, and a tentative resource allocation is determined based on the new problem. Whenever the tentative resource allocation violates a model constraint not in the current problem, one or more of the top-ranked such violated constraints are selected, and the new problem determination and tentative resource allocation steps are repeated. The resources are allocated according to the tentative resource allocation when it does not violate any model constraints.