Safety-Stock: Predicting the demand for supplies in Brazilian hospitals during the COVID-19 pandemic

Abstract

Many challenges lie ahead when dealing with COVID-19, not only related to the acceleration of the pandemic, but also to the prediction of personal protective equipment sets consumption to accommodate the explosive demand. Due to this situation of uncertainty, hospital administration encourages the excess stock of these materials, over-stocking products in some hospitals, and provoking shortages in others. The number of available personal protective equipment sets is one of the three main factors that limit the number of patients at a hospital, as well as the number of available beds and the number of professionals per shift. In this scenario, we developed an easy-to-use expert system to predict the demand for personal protective equipment sets in hospitals during the COVID-19 pandemic, which can be updated in real-time for short term planning. For this system, we propose a naive statistical modeling which combines historical data of the consumption of personal protective equipment sets by hospitals, current protocols for their uses and epidemiological data related to the disease, to build predictive models for the demand for personal protective equipment in Brazilian hospitals during the pandemic. We then embed this modeling in the free Safety-Stock system, which provides useful information for the hospital, especially the safety-stock level and the prediction of consumption/demand for each personal protective equipment set over time. Considering our predictions, a hospital may have its needs related to specific personal protective equipment sets estimated, taking into account its historical stock levels and possible scheduled purchases. The tool allows for adopting strategies to control and keep the stock at safety levels to the demand, mitigating the risk of stock-out. As a direct consequence, it also enables the interchange and cooperation between hospitals, aiming to maximize the availability of equipment during the pandemic.

Keywords: COVID-19 pandemic; Easy-to-use free expert system; Healthcare supply chain; Outbreak; Stock-out mitigating risk.

Fig. 1

Overview of the structure used in the proposed modeling. The process adopted by the algorithm is to estimate the number of infected patients which will demand some kind of assistance and, combined with the hospital capacities and characteristics, predict the PPE consumption during the COVID-19 pandemic.

Fig. 2

Some possible behaviors of ${\mu }_t$ for fixed values of $a=1$, $e=20$ and $b=0.5,1.0,1.5,10$, $c=10,15,20,25$ and $d=2,3,4$.

Fig. 3

Safety-Stock information flow.

Fig. 4

Pandemic dynamic estimation for five Brazilian cities. The selected cities are Belo Horizonte (MG), Recife (PE), Curitiba (PR), Porto Alegre (RS) and São Paulo (SP). The top panel (a) represents the cumulative death rate per region, the middle panel (b) expresses the expected dynamics of the disease and the bottom panel (c) represents the market share fraction expected to be attended by the analyzed hospital from that city.

Fig. 5

Dynamic estimation towards a PPE, considering the simulated hospital. The black line and dots represent the consumption history available in the spreadsheet. The dashed lines (horizontal) in black represent possible consumption limits. Left-hand panel (a) displays the different PPE level demands based on the hospital capacities, meanwhile right-hand panel (b) displays the chosen option according, e.g. to the supply chain manager. These figures were taken directly from the online platform, which is available in Portuguese.

Fig. 6

Pandemic dynamic per region based on the analyzed hospital. Left-hand panel plots the death growth, center panel related to the region’s demand curve, and right-hand panel display the daily estimation demand of the hospital. Online platform print, which is available in Portuguese.