nurse rostering
TRANSCRIPT
Stephen Feyer, Arjun Gopalratnam, Thomas McCarthy, Stephanie Reese
NURSE ROSTERING
Allocating nurses optimally
Feyer, gopalratnam, mccarthy, and reese
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.
01. Difficult real-world problem
Hospitals have many needs
Feyer, gopalratnam, mccarthy, and reese
Hard constraints Soft constraints
Each nurse can only work once per day
Minimum staffing needs
Consecutive shifts rules
Each nurse must have requisite skills
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Nurses have many requests
Feyer, gopalratnam, mccarthy, and reese
Optimal staffing needs
Min / max consecutive days on / off
Nurse shift preferences
Work full weekend
Min / max number of work days
Max number of working weekends
Hard constraints Soft constraints
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Nurse parameters
sets and parameters are straight forward
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
constraints require some finesse
Feyer, gopalratnam, mccarthy, and reese
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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.
Solution with 30 nurses after one hour
Feyer, gopalratnam, mccarthy, and reese
Interesting insights from the solution
Feyer, gopalratnam, mccarthy, and reese
9294 variables
510
Total penalty when objective is to minimize the maximum penalty
on any one nurse, then to minimize the overall penalty.
780
Objective value of main problem. Total penalty is 300
for entire roster plus 210 spread across 3 nurses.
8617 Constraints
>1 hr solve time
Expand the problem going forward
Feyer, gopalratnam, mccarthy, and reese
Penalty ρ1
week one week two week three
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.