Max-min fair distribution of modular network flows on fixed paths

In English In this paper a new aspect of the classical max-min fairness fixed-path problem is investigated. The considered (multi-criteria) optimization problem is almost identical to the continuous-flow problem, with the additional complicating assumption that flows must be integral. We show that such an extension makes the problem substantially more difficult (in fact NP-hard). Through comparison with the closely related continuous-flow problem, a number of properties for the solution of the extended problem are derived. An algorithm, based on sequential resolution of linear programs, that shows to be useful (produce optimal solutions) for many instances of the considered problem, is given. It follows that this algorithm can be made exact, through substituting the involved linear programs by mixed-integer programs.