Design Patterns and Fractional Primal-Dual Optimization in Healthcare Management Systems

Abstract

Composable and maintainable software architectures are essential for Healthcare Management Systems (HMS), and performance metrics such as patient wait times need to be optimized. In this paper, a hybrid of creational design pattern and an innovative optimization algorithm is suggested to achieve both tasks. First, we design an architecture for the HMS using Abstract Factory and Builder pattern where the scheduling and billing parts are modular, extensible and decoupled. The common set of related object families (e.g. appointments, billing data) are kept in separate sections of the design—based on the type of hospital—in order to reduce the scalability and the maintainability of the code. We then propose a new Projected Fractional Primal-Dual Dinkelbach (PF-PD-Dk) algorithm to solve fractional nonlinear programming (FNLP) problems, which are often used in HMS operations. The PF-PD-Dk algorithm is developed based on a primal-dual iterative solver for constrained fractional objectives and the convergence is proved under standard convexity assumptions. It is one of the pluggable strategy components in this optimizer, which is used in conjunction with Abstract Factory and Builder architecture, dynamically assigning patients to services and integrated into the HMS. We provide illustrative examples using synthetic scenarios as well as using a real hospital dataset, to see the important reductions in the average waiting time. In the experiments, our PF-PD-Dk algorithm yields a higher algorithm quality and computational efficiency compared to a baseline algorithm consisting of a Genetic Algorithm (GA), an LSTM-based scheduler and a MILP solver. We perform in-depth ablations of major hyperparameters (fractional order γ, memory length M, learning rates α, β), and demonstrate the use of the optimizer strategy with the Abstract Factory and Builder patterns. When a design pattern driven architecture, combined with advanced optimization, is used, the resulting HMS is flexible, maintainable and performance-aware, the results show.