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Working paper

Справедливые дележи с делимыми и неделимыми пунктами

In the work the fair division problem for two participants in presence of both divisible and indivisible items is considered. The set of all the divisions is formally described; it is demonstrated that fair (in terms of Brams and Taylor) divisions, unlikely the case where all the items are divisible, not always exist. The necessary and sufficient conditions of existence of proportional and equitable division were found. Three interrelated modifications of the notion of fair division – profitably, uniformly and equitably fair divisions – were introduced. Computationally efficient algorithm for finding all of them was designed. The algorithm includes repetitive solutions of integer knapsack-type problems as its essential steps. The statements of the article are illustrated by various examples.