On the decision support model for the patient admission scheduling problem with random arrivals and departures: A solution approach

Abstract

The focus of this work is the numerical application of a stochastic decision support model for the patient admission scheduling problem with random arrivals and departures. Here, we discuss the methodology for applying our model to real-world problems. We outline a solution approach for efficient computation, provide a numerical analysis of the model, and illustrate the methodology with examples. A key component of the model is an integer linear program which formulates the patient admission scheduling problem as an optimization of the total expected cost accumulated over a finite planning horizon. We rewrite some of the components of this integer linear program in order to improve numerical efficiency. We use Poisson processes and discrete phase-type distributions to model the random arrivals and departures, respectively. We argue that this stochastic component is essential for an accurate treatment of real-world problems which are stochastic in nature. We support our claim with simple numerical examples, and show that the optimal solutions obtained from deterministic models are inadequate when compared with the solutions of our stochastic model. We also construct more complex numerical examples for large-scale problems using heuristics that approximate the objective function, in order to demonstrate that our model can be efficiently applied to real-world problems, which typically involve large data sets.

Keywords:

• Integer programing
• patient admission scheduling
• phase-type distribution
• stochastic programing