A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.