Reallocating and Sharing Health Equipments in Sanitary Emergency Situations: The COVID-19 Case in Spain

Abstract

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipments between different units in emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipments or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipments at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where a given network structured set of units is given. The mathematical programming models that we provide are stochastic and multiperiod and we provide different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the data of the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.

Figures (13)

• Figure 1: Example of the graph structure involving different types of units and links in a health distribution system.
• Figure 3: Real demands of ventilators for Region of Andalucía (left) and Region of Madrid (right).
• Figure 4: Non-covered demand (red lines) and available stock (green lines) at each time period, if the real scenario occurs, with (continuous line) and without (dashed line) redistribution, in Madrid, for LC-graph and objective $\Phi_2^{\rm Regret}$ (left) and for C-graph and objective $\Phi_1$(right).
• Figure 5: Non-covered demand (red lines) and available stock (green lines) at each time period, if the real scenario occurs, with (continuous line) and without (dashed line) redistribution, in Andalucía, for LC-graph and objective function $\Phi_4$ (left) and for C-graph and objective function $\Phi_3^{\rm Regret}$(right).
• Figure 6: Amount of redistributed stock throught the LC-graphs, at each time period, for the objective function $\Phi_3$, for the region of Madrid (left) and the region of Andalucía (right).

Theorems & Definitions (2)

• Theorem 1
• proof