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Allocation of resources with efficiency and weak justice in the utilitarian social welfare

Abstract:

Currently, the problem of allocating non-divisible resources directly impacts the world of computing; for example, in the medical supplies distribution system. This work proposes a method to find efficient and weakly fair resource allocations. The strategy is to find efficient resource allocations, in the sense of Pareto optimality, considering social welfare criteria. To do this, transitional allocations, in terms of matrices, are defined, and it is shown that they are equivalent to all those that maximize utilitarian social welfare. Then, using Nash welfare function, it is shown that there are transitory allocations that maximize the utilitarian welfare, globally, and they are locally envy freeness up to 0ne good (weak justice). The matrix approach and the assumption of nonnegative and additive utilities are fundamental for this research.