As exploration in space increases through the use of larger telescopes, more sophisticated structures, and physical exploration, the use of autonomous robots will become instrumental to build and maintain the infrastructures required for this exploration. These systems must be autonomous to deal with the infeasibility of teleoperation due signal delay and task complexity. The reality of using robots in the real world without direct human input will require the autonomous systems to have the capability of responding to errors that occur in an assembly scenario on their own. As such, a system must be in place to allow for the sequencing and allocation of tasks to the robotic workforce autonomously, giving the ability to re-plan in real world stochastic environments. This work presents four contributions towards a system allowing for the autonomous sequencing and allocation of tasks for in-space assembly problems. The first contribution is the development of the Stochastic Assembly Problem Definition (SAPD) to articulate all of the features in an assembly problem that are applicable to the task sequencing and allocation. The second contribution is the formulation of a mixed integer program to solve for assembly schedules that are optimal or a quantifiable measurement from optimal. This contribution is expanded through the development of a genetic algorithm formulation to utilize the stochastic information present in the assembly problem. This formulation extends the state-of-the-art techniques in genetic algorithms to allow for the inclusion of new constraints required for the in-space assembly domain. The third contribution addresses how to estimate a robot's ability to complete a task if the robot must be assigned to a task it was previously not expected to work on. This is accomplished through the development of four metrics and analyzed through the use of screw theory kinematics. The final contribution focuses on a set of metrics to guide the selection of a good scheduling method for different assembly situations. The experiments in this work demonstrate how the developed theory can be utilized and shows the scheduling systems producing the best or close to the best schedules for assemblies. It also shows how the metrics used to quantify and estimate robot ability are applied. The theory developed in this work provides another step towards autonomous systems that are capable of assembling structures in-space without the need for human input. / Doctor of Philosophy / As space exploration continues to progress, autonomous robots are needed to allow for the necessary structures to be built in-space, on Mars, and on the Lunar surface. Since it is not possible to plan for every possible thing that could go wrong or break, the robots must be able to figure out how to build and repair structures without human input. The work presented here develops a framework that allows this in-space assembly problem to be framed in a way the robots can process. It then provides a method for generating assembly schedules that describe very good, if not the best way to complete the assembly quickly while still taking into account randomness that may be present. Additionally, this work develops a way to quantify and estimate how good robots will be at a task they have not attempted before. Finally, a set of considerations are proposed to aid in determining what scheduling method will work best for different assembly scenarios. The experiments in this work demonstrate how the developed theory can be used and shows the scheduling systems producing the best or close to the best schedules for assemblies. It also shows how the methods used to define robot ability are applied. The work developed here provides another step towards autonomous systems that are capable of assembling structures in-space without the need for human input.