Decision support model for the patient admission scheduling problem with random arrivals and departures

The patient admission scheduling (PAS) problem is a class of scheduling problems that must be handled by the managers of the hospital admission systems. The problem arises when patients arriving at the hospital need to be allocated to beds in an optimal manner, subject to the availability of beds and the needs of patients.

The PAS problem in a dynamic context, as analysed in Ceschia and Schaerf [2] and Lusby et al. [6], considers a scenario in which random arrivals and unknown departures of patients are gradually revealed over the planning horizon. The problem was formulated as an integer programming model, and various procedures for computing the optimal solution were proposed. Ceschia and Schaerf [2] developed a metaheuristic algorithm based on simulated annealing and neighborhood search. Lusby et al. [6] developed an adaptive large neighbourhood search procedure to solve the problem.

Although the arrivals and departures of patients are in general random, the models in [2, 6] assumed deterministic inputs such as a fixed length of stay for each patient, and a fixed number of arrivals at the start of each day. Here, we build on the analysis in Lusby et al. [6], and develop a model for the PAS problem in a dynamic context, which captures the random dynamics of the flow of the patients. Our aim here is to develop an improved mathematical model to solve the PAS problem in a dynamic environment with random arrivals and departures. At the start of each with random arrivals and departures. At the start of each day we record new information about the registered patients, newly arrived patients and future arrivals (including emergency patients and scheduled arrivals), and then determine an optimal assignment of patients to beds. Our goal is to provide a decision support tool for the patient scheduling process to be used by hospital administrators and planners.