In the classical maximal flow problem, the objective is to maximize the supply to a single sink in a capacitated network. In this paper we consider general capacitated networks with multiple sinks: the objective is to optimize a general "concave" preference relation on the set of feasible supply vectors. We show that an optimal solution can be obtained by a marginal allocation procedure. An efficient implementation results in an adaptation of the augmenting path algorithm. We also discuss an application of the procedure for an investment company that deals in oil and gas ventures.
Federgruen, Awi, and Henri Groenevelt. "Optimal flows in networks with multiple sources and sinks, with applications to oil and gas lease investment programs." Operations Research 34, no. 2 (1986): 218-225.
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