Efficient algorithms for discrete resource allocation problems under degressively proportional constraints

Abstract

The problem of a fair distribution is considered in relation to many areas and phenomena. The most deeply rooted in the theory of justice are proportional divisions. However, they may be perceived as unfair for common ventures, where strong participants should not dominate the weaker ones. The European Parliament composition and the cost sharing problem of a common infrastructure development are examples. In this paper, we propose an expert system that is based on a mathematical model describing discussed issues as the discrete resource allocation problem under degressively proportional constraints. This approach involves advantages of degressive proportionality to prevent mentioned domination and a proportional division generally perceived as fair to determine an unambiguous allocation. The decision making process is carried out by solving the formulated optimization problem using our highly scalable parallel branch and bound algorithm and the computationally efficient metaheuristic. The experiments prove that our approach can be successfully applied for the considered cases studies.