We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, as in the case of the absolute mean deviation, it...

Given a set of elements, each having a profit and cost associated with it, and a budget, the 0-1 knapsack problem finds a subset of the elements with maximum possible combined profit subject to the combined cost not exceeding the budget. In this paper we study a stochastic version of the problem...