Application of mixture distribution in the service sector

Intensive care units (ICUs) are one of the most crucial elements of hospitals. These units play a central role in the healthcare system and providing care to critically ill patients, so capacity planning in these units is of critical importance. Shortages of ICU beds and personnel can lead to irreversible consequences, including patient mortality. As a result, hospital administrators make efforts to determine the appropriate number of beds in these units. However, the inter-arrival time (IAT) of patients to the ICUs and the duration of their service time (ST) in these units are inherently stochastic. Consequently, capacity planning becomes a dynamic operational management problem. The inter-arrival time and service time often exhibit highly skewed distributions, making it difficult to fit a known probability distribution. In such cases, empirical distributions need to be constructed to define the inter-arrival time and service time. Nonetheless, empirical distributions have a small number of parameters and may not represent the structure of the data adequately. This thesis is based on the use of a mixture distribution approach to estimate the inter-arrival times and service time of patients in ICUs. It has been observed that the estimated parameters of the mixture distribution provide better predictions than empirical statistical distributions. The estimated parameters of the mixture distribution were included in a simulation model that helps determine the required number of beds to serve all incoming patients without any waiting time, and the ICU was analyzed accordingly.