  Due to uncertainty in demand, sometimes management may delay their planning
of shifts later in the horizon when they have more information. We consider a
novel dynamic and flexible system for scheduling personnel for work shifts
planned at the last minute called 'on-call' shifts. The flexibility in the
system allows employees to freely select or reject shifts offered to them.
Senior employees may also replace or bump junior employees from the current
schedule if no other shift of their choice is available provided certain
conditions are met. The operator seeks to quickly assign all available shifts
to employees while ensuring minimum total bumps. We develop several
easy-to-implement policy approximations as well as deep reinforcement
learning-based policies to efficiently operate the system. A comparison of all
the developed policies is made using real data from our industrial partner. We
identify the best policies under different settings and significantly improve
upon the current practices.
