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Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. The aim of this research is to propose a novel inventory pooling model to help determine order sizes and safety inventories in local hospital warehouses. The current study attempts to portray the availability of pharmaceutical items in public hospitals facing COVID-19 challenges. Different from previous studies, this research builds upon the consecrated theory of inventory pooling, extending it to pandemic circumstances where the intractability of kurtosis and skewness in inventory models are critical issues for making sure that medicines have high availability at a low cost. These effects on the total cost of inventory are explored and compared to a supply system with no consolidation. A continuous-review model is assumed with allocation rules for centralization and regular transshipment given different skewness and kurtosis structures for the demand, describing them by the copula method. This method models a multivariate demand considering that the marginal distributions of the demand can be specified by the Generalized Additive Model for Location, Scale and Shape, which offers advantages to model demands considering virtually any marginal statistical distribution. Numerical simulations and an illustrative example show that distributions of demands with more negative skewness and high kurtosis favor to a greater extent obtaining lower total costs with regular supply transshipment systems. Our study points out important considerations for supply chain decision makers when having demands with skewness and kurtosis patterns.