A dynamic nonlinear flow algorithm to model patient flow

Area of Science:

• Healthcare Systems Engineering
• Operations Research
• Network Flow Analysis

Background:

• Hospitals are complex systems with dynamic and nonlinear patient flow.
• Existing flow algorithms primarily focus on transportation and telecommunication, with limitations in healthcare applications.
• Hospital bottlenecks arise from ward behavior (capacity, staff, service time) and care pathway distribution.

Purpose of the Study:

• To develop a modified flow algorithm for modeling dynamic patient flow in hospitals.
• To identify and quantify bottlenecks within hospital networks.
• To provide a holistic view of hospital performance and analyze dynamic ward behavior.

Main Methods:

• A modified network flow algorithm is proposed.
• The algorithm iterates over patient arrival rates, considering vertices' capacities, servers, service time variability, and edge distribution probability.
• A dynamic residual graph is generated to measure bottleneck persistency and severity.

Main Results:

• The algorithm effectively measures patient flow dynamics within a hospital network.
• It identifies bottlenecks, their root causes, and the nonlinear behavior of hospital wards.
• The dynamic residual graph provides insights into bottleneck severity and persistence over time.

Conclusions:

• The modified flow algorithm offers a novel approach to analyzing hospital patient flow.
• It enables a comprehensive understanding of hospital operational performance and bottleneck dynamics.
• This method aids in optimizing hospital resource allocation and improving patient care pathways.