A short-term operating room surgery scheduling problem integrating multiple nurses roster constraints

Operating room (OR) surgery scheduling determines the individual surgery's operation start time and assigns the required resources to each surgery over a schedule period, considering several constraints related to a complete surgery flow and the multiple resources involved. This task plays a decisive role in providing timely treatments for the patients while balancing hospital resource utilization. The originality of the present study is to integrate the surgery scheduling problem with real-life nurse roster constraints such as their role, specialty, qualification and availability. This article proposes a mathematical model and an ant colony optimization (ACO) approach to efficiently solve such surgery scheduling problems.

A modified ACO algorithm with a two-level ant graph model is developed to solve such combinatorial optimization problems because of its computational complexity. The outer ant graph represents surgeries, while the inner graph is a dynamic resource graph. Three types of pheromones, i.e. sequence-related, surgery-related, and resource-related pheromone, fitting for a two-level model are defined. The iteration-best and feasible update strategy and local pheromone update rules are adopted to emphasize the information related to the good solution in makespan, and the balanced utilization of resources as well. The performance of the proposed ACO algorithm is then evaluated using the test cases from (1) the published literature data with complete nurse roster constraints, and 2) the real data collected from a hospital in China.

The scheduling results using the proposed ACO approach are compared with the test case from both the literature and the real life hospital scheduling. Comparison results with the literature shows that the proposed ACO approach has (1) an 1.5-h reduction in end time; (2) a reduction in variation of resources' working time, i.e. 25% for ORs, 50% for nurses in shift 1 and 86% for nurses in shift 2; (3) an 0.25h reduction in individual maximum overtime (OT); and (4) an 42% reduction in the total OT of nurses. Comparison results with the real 10-workday hospital scheduling further show the advantage of the ACO in several measurements. Instead of assigning all surgeries by a surgeon to only one OR and the same nurses by traditional manual approach in hospital, ACO realizes a more balanced surgery arrangement by assigning the surgeries to different ORs and nurses. It eventually leads to shortening the end time within the confidential interval of [7.4%, 24.6%] with 95% confidence level.

The ACO approach proposed in this paper efficiently solves the surgery scheduling problem with daily nurse roster while providing a shortened end time and relatively balanced resource allocations. It also supports the advantage of integrating the surgery scheduling with the nurse scheduling and the efficiency of systematic optimization considering a complete three-stage surgery flow and resources involved.