Production optimisation in a pandemic context

Abstract

A pandemic can wreak havoc in supply chains, as witnessed in the COVID-19 context. As workers get infected, production level drops and demand from customers goes unfulfilled. Combining in a novel way an epidemic model with optimal control theory, our model provides a plant manager with the optimal level of prophylactic effort she needs to deploy over a planning horizon to protect the workforce from a pandemic in its early stage and so maintain production levels. Given the production planning problem, the effort in terms of prophylactic measures can be optimally determined in closed form, balancing worker protection against production requirements in a single step. The manager must initially implement the strictest measures before relaxing them in time. Three extensions are presented:, (1) determine the optimal period of time over which the prophylactic measures should be maintained; (2) determine the optimal effort in terms of prophylactic measures in the case of an endemic disease; and (3) assess the effect of a stochastic exogenous shock on the total number of infected. This research provides a production planning model that allows a decision-maker to mitigate the impact of worker absenteeism at the onset of a pandemic, thus improving supply chain resilience.