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Nurse Rostering
- 1. NURSE ROSTERING Stephen Feyer, Arjun Gopalratnam, Thomas McCarthy, Stephanie Reese
- 2. Allocating nurses optimally Feyer, gopalratnam, mccarthy, and reese 01. Difficult real-world problem Many current paper-based approaches are not provably optimal or do not consider all constraints. 02. nurse rostering competition Partial solution using actual competition data but in a limited time window. 03. Realistic framework Solution includes all data types and constraints specified in competition rules.
- 3. Hospitals have many needs Hard constraints Soft constraints Each nurse can only work once per day Minimum staffing needs Feyer, gopalratnam, mccarthy, and reese Consecutive shifts rules Each nurse must have requisite skills 1 2 3 4
- 4. Nurses have many requests Hard constraints Soft constraints Optimal staffing needs Min / max consecutive days on / off Nurse shift preferences Feyer, gopalratnam, mccarthy, and reese Work full weekend Min / max number of work days Max number of working weekends 1 2 3 4 5 6
- 5. sets and parameters are straight forward Nurse parameters Feyer, gopalratnam, mccarthy, and reese • Shift preferences • Skill sets • Contract type Contract parameters Hospital parameteres N D,T S,Z R C • Min / Max consecutive days on • Min / Max consecutive days off • Min nurses per skill per shift • Goal of minimizing penalties
- 6. constraints require some finesse 1 2 3 Nurse cannot work more than 5 consecutive days. Nurse cannot be off less than 2 consecutive days. If a nurse works Saturday, the nurse should also work Sunday. Feyer, gopalratnam, mccarthy, and reese
- 7. Solution with 30 nurses after one hour Feyer, gopalratnam, mccarthy, and reese
- 8. Interesting insights from the solution Feyer, gopalratnam, mccarthy, and reese 9294 variables 510 780 Total penalty when objective is to minimize the maximum penalty on any one nurse, then to minimize the overall penalty. Objective value of main problem. Total penalty is 300 for entire roster plus 210 spread across 3 nurses. 8617 Constraints >1 hr solve time
- 9. Expand the problem going forward week one week two week three Penalty ρ1 Feyer, gopalratnam, mccarthy, and reese Penalty ρ2 Penalty ρ3 Penalty for ≤ 2 or ≥ 6 consecutive days worked can be met across periods. Complete problem includes datasets for 120 nurses. Computation time grows non-linearly. Long term objective is to minimize Σρi which may result in suboptimal allocations in some periods.