Chance-Constrained Generalized Networks

An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relations are established for appropriate pairs of such chance-constrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relations may be exploited in order to obtain actual solutions to chance-constrained generalized network problems.