The Authors present a new methodological approach in stochastic regime to determine the actual costs of an healthcare process. The paper specifically shows the application of the methodology for the determination of the cost of an Assisted reproductive technology (ART) treatment in Italy. The reason of this research comes from the fact that deterministic regime is inadequate to implement an accurate estimate of the cost of this particular treatment. In fact the durations of the different activities involved are unfixed and described by means of frequency distributions. Hence the need to determine in addition to the mean value of the cost, the interval within which it is intended to vary with a known confidence level. Consequently the cost obtained for each type of cycle investigated (in vitro fertilization and embryo transfer with or without intracytoplasmic sperm injection), shows tolerance intervals around the mean value sufficiently restricted as to make the data obtained statistically robust and therefore usable also as reference for any benchmark with other Countries. It should be noted that under a methodological point of view the approach was rigorous. In fact it was used both the technique of Activity Based Costing for determining the cost of individual activities of the process both the Monte Carlo simulation, with control of experimental error, for the construction of the tolerance intervals on the final result.

The aim of the Response Surface Methodology (RSM), originally designed for chemical, physical and biological applications and experiments, but then extended also to simulations in the industrial field, is the construction of reliable response surfaces characterized by high adherence to the experimental data describing the reality being studied [1]-[2]-[11]. In order to achieve this result the most important scholars in this fields focus their attention on experimental projects capable of providing regression meta-models, that fit well the initial experimental data and have a sort of stability of the width of the confidence intervals on the average response and the prediction intervals [11]. At the same time it is also necessary to choose experimental projects allowing a good estimate of the Experimental Error divided into the two components called pure error and lack of fit by the literature on this subject. One of the key assumptions of the conventional RSM approach is that the Experimental Error strictly linked to the system under examination is fixed and it cannot be controlled by experimenters. Nevertheless, for applications in complex industrial plants, it is not possible to carry out the experimental phase directly on the real system and the object of study needs to be transferred into a simulation model [3]-[8]. Therefore, this assumption becomes meaningless. The transfer of the real physical model into a simulation model implies a substantial change in the nature of the Experimental Error, which, compared to the one in the conventional experiments, changes from fixed to dependent on the length of the simulation run and hence time-variant [4]-[6]-[7]-[9]-[10]. Therefore, it is no longer enough to try to improve the quality of the response surface using the traditional RSM concepts of Optimal Variance, Orthogonality and Rotatability, as these are strictly dependent on the value of the experimental error. In the applications on the discrete and stochastic simulation models experimenters must hence try to reduce, each time it is possible, the magnitude of the simulation model's outgoing Experimental Error extending the simulation run and consequently the computation time. Only once this has been done will it be possible to fine-tune the study examining the response surface to find the aforementioned properties whose influence on the quality of the outgoing surface is substantially lower compared to the reduction of the Experimental Error. This article illustrates an application to an industrial case that not only shows the validity of what is affirmed, but also highlights other limits linked to the use of the conventional RSM approach to simulation experiments on complex industrial plants. These limits challenge the efficacy of linear regression meta-models as descriptors of the relation between the independent and dependent variables considered.

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In Italian hospitals equipped with an Emergency Department (ED), it is possible that patients coming from such a structure occupy beds that had previously been scheduled for other patients. This happens because of some law regulations that give these kind of patients preferential access to hospitalization, and it may cause reduction in, or even stop, scheduled surgery activities. For such a reason operating theaters, surgery teams, sterilization structure, etc., are often unable to operate in an efficient way. Regarding costs and hospital management, this issue become considerable, and maybe even more unpleasant for patients on the waiting list since their scheduled surgery date generally is delayed by a long time. Studying an ED, the authors decided to build a System Dynamics model to analyze the impact of the admission from ED on other hospital structures, and thus identify the critical threshold. Some "non trivial" corrective actions have been evaluated in order to suggest how to address the problem which is currently causing internal conflicts and, if not managed, is destined to grow over time.