Solution approach to infinite linear programming problem with capacity constraints

The purpose of this article is to investigate a kind of infinite linear programming problem (ILPP) arising from infinite multiclass network equilibrium problems. In several cases, we construct special feasible solutions to the ILPP. By virtue of the nature of network, we prove that the solutions are optimal. Marcotte and Zhu (Oper Res Lett 37:211?C214, 2009) proved the existence of the valid tolls for the infinite multiclass network equilibrium problems. Based on this, we analyze the property of the tolls vector, i.e., the relationship between breakpoints and the tolls. We also consider the solutions in the network where origin-destination pairs may differ in their probability density functions.