Approximate Linear Program for Multi-Type Inpatient Allocation Admission Scheduling Problem

This paper studies an inpatient allocation admission scheduling problem by considering the sharing of inpatient beds among patients from different medical departments. Hospital managers need to make admission control decision each day to minimize operational costs. Considering the uncertainty of patients' arrival and length of stay, we propose a Markov decision process (MDP) model with the objective to minimize patients' waiting cost, diversion cost and overcapacity cost. Due to the curse of dimensionality, the MDP is difficult to solve. To address the problem, an approximate linear programming (ALP) approach is developed by firstly transforming the MDP model into an equivalent linear program and then approximating the value function by a linear combination of basis functions with a set of parameters. The optimal parameters in the approximate value function can be obtained by solving the dual problem of the approximate linear program using column generation. Managers can make admission decision using the approximate value function. Numerical experiments show the effectiveness of ALP compared with other policies.