The term work assignment in the question is too general. It could mean the task of assigning different duties or responsibilities to different people employed in an organization as a part of organization design, or it could refer to detailed production or project planning tasks. It could mean something in between the above two examples. For example, it could mean assigning repair jobs to different persons or teams in a maintenance department. Mathematical modelling is also used by large airlines for scheduling their planes and crew.
Yes, mathematical models and quantitative techniques are used in many of the work assignment areas identified above. For example, mathematical models and graphical models such as CPM (Critical Path Method), and PERT (Project Evaluation and Review Techniques) are used extensively for planning and controlling of projects. Many different types of PPC (Project Planning and Control) algorithms are used for planning of production activities involving multiple work orders being processed on multiple work centers and involving different work sequence for each batch. Queueing techniques are used commonly for situations where work flow follows a random pattern and as such can be performed on any one of multiple work stations. A technique called line balancing is used for taking decisions on the operations to be performed at each work station of assembly lines for mass-produced items.
The types of work assignment tasks is very large and accordingly the list of quantitative techniques that can be used for work assignment tasks is also very long.