This dissertation introduces and analyzes the Bus Evacuation Problem (BEP), a unique Vehicle Routing Problem motivated both by its humanitarian significance and by the routing and scheduling challenges of planning transit-based, regional evacuations. First, a variant where evacuees arrive at constant, location-specific rates is introduced. In this problem, a fleet of capacitated buses must transport all evacuees to a depot/shelter such that the last scheduled pick-up and the end of the evacuee arrival process occurs at a location-specific time. The problem seeks to minimize their accumulated waiting time, restricts the number of pick-ups on each location, and exploits efficiencies from service choice and from allowing buses to unload evacuees at the depot multiple times. It is shown that, depending on the problem instance, increasing the maximum number of pick-ups allowed may reduce both the fleet size requirement and the evacuee waiting time, and that, past a certain threshold, there exist a range of values that guarantees an efficient usage of the available fleet and equitable reductions in waiting time across pick-up locations. Second, an extension of the Ritter (1967) Relaxation Algorithm, which explores the inherent structure of problems with complicating variables and constraints, such as the aforementioned BEP variant, is presented. The modified algorithm allows problems with linear, integer, or mixed-integer subproblems and with linear or quadratic objective functions to be solved to optimality. Empirical studies demonstrate the algorithm viability to solve large optimization problems. Finally, a two-stage stochastic formulation for the BEP is presented. Such variant assumes that all evacuees are at the pick-up locations at the onset of the evacuation, that the set of possible demands is provided, and, more importantly, that the actual demands become known once buses visit the pick-up locations for the first time. The effect of exploratory visits (sampling) and symmetry is explored, and the resulting insights used to develop an improved formulation for the problem. An iterative (dynamic) solution algorithm is proposed. / Ph. D.