The standard approach to fair rent division assumes that agents have quasi-linear utilities, and seeks allocations that are envy free; it underlies an algorithm that is widely used in practice. However, this approach does not take budget constraints into account, and, therefore, may assign agents to rooms they cannot afford. By contrast, we design a polynomial-time algorithm that takes budget c...

Budgets are important management tools recognized for their help in planning, communication, monitoring the expense performance, and even motivating collaborators. However, recently there has been criticism of traditional Budgeting Process due to its cumbersomeness, long duration, eventual diversion focus from day-to-day activities. Thus, improving by incorporating Expense component uncertainti...

The purpose of this article is to introduce mathematical models for two budget problems. The first problem, which deals to the construction of a particular budget, is solved based on an algorithm for the maximum flow problem in bipartite network. The method constructs an efficient budget by repeating a maximum flow computation. The second problem is the budget exercise and studies how the budge...