The given problem involved designing a supply purchase plan for multiple hospitals based on historical data. Initially, we delved into isolating and analyzing relevant variables. However, treating products and hospitals separately proved challenging, revealing a lack of correlation and crucial missing data, particularly in terms of inventory.
Adapting to these unexpected challenges, we pivoted our strategy, choosing to treat hospital restocking collectively and assuming a consistent approach to stocking without monthly overstocking. This strategic shift was crucial in navigating towards a viable solution.
Key assumptions played a vital role in reshaping our analytical framework. We assumed simultaneous restocking of all hospitals and considered the monthly amount purchased for a product as a pivotal variable, altering the dynamics of our problem-solving approach.
To effectively address the problem, we employed two models. The first model focused on studying the differentiated time series, leading us to adjust the series using an ARMA(p,q)/GARCH(P,Q) model. Our results indicated the successful fitting of the ARMA/GARCH model to a substantial portion of the dataset, enabling us to predict the amount to be purchased monthly in 2023. This outcome formed the foundation of our proposed purchase plan.
To conclude, we would like to add that given more time, we would be interested in predicting product demand for each hospital, optimizing purchase prices, investigating cases not fitted with ARMA/GARCH, and refining the variance of the white noise component.
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