A generalized optimal transport problem with application to firm location

This paper studies a generalized optimal transport problem with two sources and one target in R2 when the mass is not necessarily preserved during transportation. Instead of following the standard assumption in the existing transport literature that the outgoing mass is a sum of incoming mass at each node, we introduce a transformation function which measures the outgoing mass as a general function of incoming mass. Such a generalized optimal transport problem is proved to be well defined for a very broad class of transformation functions with an analytical solution provided for a Euclidean space. We apply this generalized transport model to study a firm location problem in a two-step optimization framework.;Keywords. Optimal Transport Problem; Transformation Function; Firm Location.