Location theory is concerned with understanding where social-economic activities should be located or why certain patterns or clusters of activity develop. In the core of many location analyses, there is often an optimization problem which involves searching for location patterns that optimize one or more objectives based on certain assumptions of system operation and rational behavior. Furthermore, distance is a key factor in the spatial organization of social-economic activities and plays an important role in locational analyses. This dissertation addresses the so-called closest assignment (CA) conditions in location modeling which assume that in the allocation phase of a location-allocation model, each user will choose or be assigned to the facility or activity site which involves the smallest distance or the least transport/interaction cost.

The goals of this dissertation are two-fold. The first goal is to analyze closest assignment conditions in relation to user optimality in location modeling. In particular, the dissertation investigates (1) applications in location modeling in which CA conditions are required, (2) when it is necessary to enforce CA conditions using explicit constraints, and (3) generalized forms of explicit CA constraints that can be used for new model constructs in location analysis.

The second objective of this dissertation is to develop new location-allocation models that specifically take into account user perspectives or user optimality. The new models developed serve both as motivation for developing the CA constructs as well as for providing computational experience and insight into how assumption of user optimality changes location patterns. To this end, we have developed user optimal models in the context of container logistics, extended existing interdiction models which are useful in identifying critical infrastructure, proposed new reliability models that locate facilities in anticipation of random facility failure, and user optimal models in hub-and-spoke systems which can account for user preferences for least cost routes. We also used generalized closest assignment constructs to model multi-assignments and multi-facility interactions and proposed two general models that unify a large number of existing location allocation models including classic median, center problems and facility dispersion problems. Finally, we conclude with a summary and possible future work.