We propose a general modular approach to support decision‐makers' response in the early stages of a pandemic with resource expansion, motivated by the shortage of Covid‐19‐related intensive care units (ICU) capacity in 2020 in Italy. Our approach uses (1) a stochastic extension of an epidemic model for scenarios of projected infections, (2) a capacity load model to translate infections into scenarios of demand for the resources of interest, and (3) an optimization model to allocate this demand to the projected levels of resources based on different values of investment. We demonstrate this approach with the onset of the first and second Covid‐19 waves in three Italian regions, using the data available at that time. For epidemic modeling, we used a parsimonious stochastic susceptible‐infected‐removed model with a robust estimation procedure based on bootstrap resampling, suitable for a noisy and data‐limited environment. For capacity loading, we used a Cox queuing model to translate the projected infections into demand for ICU, using stochastic intensity to capture the variability of the patient arrival process. Finally, we used stochastic dynamic optimization to select the best policy (when and how much to expand) to minimize the expected number of patients denied ICU for any level of investment in capacity expansion and obtain an efficient frontier. The frontier allows a trade‐off between investment in additional resources and the number of patients denied intensive care. Moreover, in the panic‐driven early days of a pandemic, decision‐makers can also obtain the time until which they can postpone action, potentially reducing investment costs without increasing the expected number of denied patients.
This paper proposes a systemic model on the intertwined relations among managerialization, professionalization and firm economic performance, considering both business‐ and family‐specific features and issues. It sheds light on the role that, in the family business, the firm economic performance may play in favouring a positive development of both the business and the family itself. It aims at understanding how, in family businesses, the firm managerialization and professionalization may represent relevant drivers of firm performance. A Systems Thinking model based on causal loop diagrams was developed, to provide a clear framing of the interrelationships among the various aspects at stake. The conceptual model combines with systemic perspective all the variables and relationships that come into play when considering jointly the growth and development of the company and the family. This paper provides not only a conceptual background but also practical insights for family business' owners, managers and consultants.
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