Inverse optimization refers to the fact that each time a Lagrangean derived from a given mathematical programming problem is solved, it produces an optimal solution to some problem with a different right hand side. This paper reports on the application of inverse optimization to the capacitated plant location problem including the study of implied mappings of dual variables into the space of demand vectors. A new parametric method based on inverse optimization and subgradient optimization is also presented.Research supported, in part, by the National Science Foundation under Grant No. MCS77-24654.