A Model for Supply-Chain Decisions for Resource Sharing with an Application to Ventilator Allocation to Combat COVID-19

Sanjay Mehrotra; Hamed Rahimian; Masoud Barah; Fengqiao Luo; Karolina Schantz

where t denotes a day that the worst expected shortage happens, i.e., t ∈ arg max t∈T n∈N w n,t . Moreover, quantity "Worst day-state" in column "Worst day-state (t)" denotes the expected shortage in the worst day and state, and is calculated as where (t, n) ∈ arg max t∈T arg max n∈N w n,t . The results in Tables 1-3 suggest that when up to 60% of a state's ventilator inventory is used for non-COVID-19 patients, FEMA's current stockpile of 20,000 ventilators is nearly sufficient to meet the demand imposed by COVID-19 patients in mild cases (i.e., Cases I-III). The ventilator availability situation gets worse in the case where 75% (or greater %) of the available ventilators must be used for non-COVID-19 patients and states' risk-aversion parameter to send the idle ventilators to FEMA to be used in a different state is 3. In this case, if states are willing to share up to 50% of their excess inventory with other states, then 12,700 number of ventilators will be required beyond FEMA's current stockpile to meet demand in Cases I-IV. However, if no such sharing is considered, then the need for ventilators would increase to 14,200. This situation gets even worse for Cases V and VI, where the inventory shortfall on the worst day (04/19/2020) is between 17,200-30,600. This shortfall decreases moderately to 15,900-28,000 if states are willing to share part of their initial ventilator inventory. If parameter ρ goes down to 1.25, the inventory shortfall on the worst day (04/19/2020) is between 13,800-22,800. This shortfall decreases moderately to 12,800-21,300 if states are willing to share part of their initial ventilator inventory.