A controlled Markov chain model for nursing homes

Abstract

This paper deals with the modeling of the patient admission policy in a nursing home as a Markov deci sion process. There are two different charges for care in the home, i.e., two kinds of patients k₁ and k₂; patients arrivals follow a Poisson process; lengths of stay are exponential or Erlang; and, finally, the home decides whether or not to admit a patient on the basis of maximizing its expected dis counted returns. Computer simulation experiments show interesting results: the optimal policy is not very sensitive to different discount rates, average length of stay, home size, charges for care, or k₁ to-k₂ arrival ratios. To investigate the validity of the model, computer experiments for a system of several nursing homes in a competitive situation were run, using real data from homes in Rhode Island. These experiments included comparisons of real length-of-stay distributions with assumed distribu tions and analyses of statistics such as backlog in hospitals and average occupancy of nursing homes for different values of the system's utilization factor.