Simulation Optimization for Inpatient Bed Allocation with Sharing

The inpatient bed allocation that allows beds shared among different departments is an important and challenging problem for a healthcare system. When the objective function(s) and (some) constraints need to be estimated via expensive and noisy stochastic simulation, a simulation optimization algorithm is required to solve this problem. In literature, there is a heuristic algorithm highly customized for one specific inpatient bed allocation problem, and it performs quite well on that problem. However, its lack of theoretical convergence and high specialization may not give practitioners enough confidence to apply it on real inpatient bed allocation problems. To mitigate such issues, this paper proposes to use the empirical stochastic branch-and-bound (ESB&B) algorithm, which is theoretically convergent and suitable for relatively general problems. A modest improvement for the original ESB&B algorithm is made and how to adapt the ESB&B algorithm to inpatient bed allocation problems is presented. Numerical experiments reveal the generality and fairly satisfying performance of the ESB&B algorithm, and the superiority of the improved ESB&B algorithm over the original one.