Candidate for the Lee B. Lusted Student Prize Competition
Purpose: Many teaching hospitals with strained inpatient bed capacity struggle to maintain a mix of patients that satisfies their teaching, research, and financial needs. Even an increase in bed capacity is unlikely to address the patient mix problem. We investigate one such hospital that received special dispensation from the government to partition its inpatient beds into wings. Each wing is allocated a fixed number of beds and is restricted to a fixed set of clinical specialties. An admission request is granted only if a bed is available in the appropriate wing. We develop a modeling framework to investigate how best to form wings so as to optimize some function of patient mix.
Method: A dynamic programming (DP) model is formulated to optimize the wing configurations from the perspective of the hospital administrator. The model assumes a heterogeneous patient population that demands hospital services in a stochastic manner. The model maximizes the average DRG (Diagnosis Related Grouping) relative weights of admitted patients. Parameters are calibrated with data from the hospital and from national databases. In addition, we model length-of-stays as decreasing when a wing becomes more heavily demanded. This model of length-of-stays is supported with empirical evidence. The associated DP is too large to solve using standard methods. However, we are able to exploit special structures of the model that enables us to obtain near optimal solutions very quickly.
Result: If the total demand for hospital beds per day is, on average, sufficiently less than bed capacity, then the optimal solution is to avoid forming specialized wings. As average total demand for beds increases it becomes more advantageous to form multiple wings. In particular, our model shows that forming wings when the hospital services are heavily demanded will increase the average DRG relative weight, decrease the average overall occupancy, yet increase the number of patients admitted. The increase in patient flow is due to a decrease in length-of-stays for highly utilized wings.
Conclusion: Forming wings can be an effective strategy to deal with strained bed capacity. Our dynamic programming model informs hospital administrators about how to form wings that achieve a patient mix that better matches the mission of the hospital. The solutions are fast to obtain and easy to communicate.