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In many multiple criteria optimization problems preserving fairness among individual outcomes becomes an important issue. This is particularly true for systems that are designed for multiple users or services like computer or telecommunication networks. In this paper we investigate a new approach to the resource allocation preserving the, so called, Max-Min Fairness (MMF) in the solution. We analyze its applicability to a hard discrete multiple commodity network flow problem, where the flow (bandwidth) for each pair of nodes is allocated to exactly one path chosen from a predefined set.

There is no common definition of fairness. Intuitively, one wants the uniform criteria to be treated equally and impartially. For example, in the multiple users system resources can be allocated in a way that each user gets the same outcome. Obviously, this approach becomes inefficient when, for some reason, one of the users can get only very small value because then everyone gets the same small value. One of the ways to overcome this difficulty is the application the so called Max-Min Fairness concept. This allows to achieve not only fair solutions but also decently efficient in terms of the system utilization.