A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management
I will introduce the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the actual date of demand realization.
I will present parameterized mixed-integer rounding inequalities that describe the convex hull of the second stage mixed-integer problem. I will also present a modified integer L-shaped method with prioritized branching strategy and a new multicut approach. The model will be applied to nurse staffing and scheduling using 3.5 years of patient census data from Northwestern Memorial Hospital. A time-series forecasting model will be used to generate 1000 patient census scenarios for the model. The extensive form of the resulting model has 115,913 general integer variables and 336,000 continuous variables.
Solving 20 problem instances, I will show that my new solution approach significantly improves the computational efficiency both in terms of the required number of nodes and the computation time to solve the problem to optimality. I will also show that the stochastic programming based solution can save the cost of hiring nurses. Finally I will introduce the software package developed for general two-stage stochastic programs and discuss potential applications at Argonne National Laboratory.