A dynamic supply chain network for PPE during the COVID-19 pandemic

In this paper, we present an optimization model consisting of a dynamic supply chain network related to Personal Protective Equipment (PPE). We suppose that the variables in the model, namely flows on arcs and additional capacities on arcs, depend both on time and on a delay function. The aim of the firm is to find the optimal flows and the optimal additional capacities on arcs to satisfy the huge and immediate increasing request in the demand markets due to the spread of the COVID-19 disease, minimizing, simultaneously, its total costs. We obtain a minimization problem and the related “retarded” evolutionary variational inequality (rEVI). We introduce the associated infinite-dimensional projected dynamical system to obtain a computational procedure to find the optimal solution to the rEVI associated with our minimization problem and, finally, we propose some numerical examples based on real scenarios.