Risk-Aware Parallel Simulation–LBBD Framework for Integrated Multi-Skill Nursing-Home Staffing and Rostering

Abstract

Healthcare worker scheduling is an optimization problem that is difficult because of the interaction between skills and workers. Uncertain service demand, regulatory constraints, requirements, and workload balance. This study proposes a Risk-Aware Parallel Simulation–Logic Based Benders Decomposition (LBBD) framework for integrated Stochastic demand nursing-home staffing and rostering with multi-skill workers. The proposed approach uses a risk-aware mathematical framework, along with Conditional Value-at-Risk (CVaR) and parallel scenarios. The techniques used are simulation, adaptive cut generation, and a hybrid Bandit-CMSA metaheuristic embedded in the LBBD optimization process. The framework separates strategic rostering from "scenario"- related service evaluations, allowing efficient exploration of uncertain operating conditions while maintaining valid evaluations. Optimality bounds. We ran computational experiments on a nursing-home benchmark instance with identical scenarios, computational resources and a time limit of 300 seconds. The 13 people were six CNAs, four nurses, and two pharmacists. The dataset includes three LPNs, three RNs, three competence levels, sixteen 1-hour intervals, twelve lawful shifts, four stochastic demand scenarios, and one thousand out-of-sample validation scenarios. The proposed framework achieved an optimal objective value of 11,169.019, and the lower bound of 11,169.019 was achieved and is valid. The lower bound was 10,754.446, leading to a final optimality gap of 3.712%. This schedule improved the objective value by 19.36% over the first feasible solution. The results also show the effectiveness of the integrated learning-based search mechanisms, with the bandit strategy identifying the most useful ones: an improved neighborhood operator and more exploration of the primal solution space. The proposed framework is a scalable and powerful optimization method that can create high-quality nurse schedules while ensuring the rostering process runs smoothly. It manages operating costs, risk, and employee balance under fluctuating demand.