Brams–Taylor model of fairdivision for divisible and indivisible items
In this article, the fairdivision problem for two participants in the presence of both divisible and indivisibleitems is considered. Three interrelated modifications of the notion of fairdivision–profitably, uniformly and equitably fairdivisions–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 necessary and sufficient conditions of the existence of proportional and equitable division were found. The statements of the article are illustrated by various examples.