Who is Working When?

I introduced the Traveling Salesman Problem near the launch of this blog. The Nurse Scheduling Problem is another optimization problem that is studied in operations research. Although it is called the Nurse Scheduling Problem, it applies to any workforce scheduling scenario. Warehouses, retail shops, and restaurants are typical places where this problem would apply. Like the Traveling Salesman Problem, it is also an NP-hard problem (mathematically very complex).

The problem aims to fulfill the hospital's objectives (i.e., shift coverage) while meeting the nurses' preferences as much as possible. Both the objectives of the hospital and the nurse's requirements are constraints of the problem. Constraints can be hard (must be met) or soft (preferences). Hard constraints can be shift coverage and labour regulations (consecutive shifts, hour limits, minimum rest hours). Soft constraints may be hospital policies or nurse preferences (nurses to have similar hours and shifts, nurse-specific preferences, team preferences).

There are different ways this problem can be addressed.

Integer Programming and Constraint Programming - If the number of nurses and constraints is small, exact methods may be used. Integer Programming/Mixed-Integer Programming or Constraint Programming formulates scheduling as mathematical equations with constraints and solves for the optimal solution.

Heuristics - The previous methods will reach a point where current computers will be unable to solve it. With this method, rule-based scheduling assigns shifts based on priority of rules, and then adjustments may be made to improve upon fairness and other soft constraints.

AI and Machine Learning - Reinforcement Learning and Neural Networks may be used to improve demand forecasts and scheduling.

Hybrid - In practice, this problem is usually addressed using software that includes one or more of the computational techniques above and human input (intervention).

In addition to applying to workforce scheduling, schedule optimization has parallels with project scheduling. Instead of matching workers, shifts, and coverage of a workplace, a project's resources/workers, tasks, and deadlines can be mathematically expressed and optimized similarly. By having a good model for addressing this problem, we can then use the model to test constraints for efficiency gains. For example, we may adapt available resources based on changing policies without compromising coverage or vice versa.