Semi-infinite transportation problems

AbstractA semi-infinite transportation dual-program pair is specified which involves general pairings of linear spaces stemming from an infinite number of destination requirements, but where in the primal program least-cost flows of goods are sought from only a finite number of origins to these destinations. Building on the work of M. J. Todd [Solving the generalized market area problem, Management Sci. 24 (1978), 1549–1554] a finite-dimensional dual unconstrained concave program is developed for the primal semi-infinite program but without certain measure-theoretic restrictions on the cost functions themselves.Optimality conditions for the dual-program pair are specified involving generalized column number conditions which parellel but extend those of the classical finite-dimensional transportation problem