A derivative-free approach for a simulation-based optimization problem in healthcare

In this work a simulation–based optimization model is considered in the framework of the management of hospital services. Given specific parameters which describe the hospital setting, the simulation model aims at reproducing the hospital processes and evaluating their efficiency. The use of a simulation–based optimization approach is necessary since the model can not be expressed as closed–form function. In order to obtain the optimal setting, we combine a derivative–free optimization method with a discrete event simulation model. The resulting framework has been tested on a real healthcare problem. More specifically, we study how to optimize the performance of an obstetric ward of a big Italian hospital, from both an economical and clinical point of view, taking into account some relevant constraints. The resulting optimization problem is a Mixed Integer Nonlinear Programming problem due to the presence of some variables constrained to be integer.