LP-Based Row Generation Using Optimization-Based Sorting Method for Solving Budget Allocation with a Combinatorial Number of Constraints

Abstract

A novel approach was developed that combined LP-based row generation with optimization-based sorting to tackle computational challenges posed by budget allocation problems with combinatorial constraints. The proposed approach dynamically generated constraints using row generation and prioritized them using optimization-based sorting to ensure a high-quality solution. Computational experiments and case studies revealed that as the problem size increased, the proposed approach outperformed simplex solutions in terms of solution search time. Specifically, for a problem with 50 projects (N = 50) and 2,251,799,813,685,250 constraints, the proposed approach found a solution in just 1.4 s, while LP failed due to the problem size. The proposed approach demonstrated enhanced computational efficiency and solution quality compared to traditional LP methods.