Production optimization in the time of pandemic: an SIS-based optimal control model with protection effort and cost minimization

The COVID-19 pandemic wreaks havoc in supply chains by reducing the production capacity of some essential suppliers, closure of production facilities or the absence of infected workers. In this paper, we present three decision support models for a plant manager to help in deciding on (a) the level of protection of the workforce against the spread of the virus in the absence of regional protection measures, (b) on the duration of the protection, and (c) the level of protection of the workforce with regional protection measures enforced by health authorities. These decision models are based on a SIS epidemiological model which takes into account the possibility that a worker can infect others but also that even when recovered can be infected again. The first and third models prescribe how, in time, the protection effort in terms of prophylactic measures must be deployed. The second model extends the first one as it also determines the length the protection effort must be deployed. The proposed models have been applied to the case of a meat processing plant that must satisfy the demand of a large-scale retailer. Clearly, to achieve production targets and satisfy customers' demand, plants in this labor-intensive industry rely on the number of healthy workers and the service level of suppliers. Our results indicate that these models provide managers with the tools to understand and measure the impact of an infection on production and the corresponding cost. Along the way, this work illustrates the ripple effect as suppliers affected by the pandemic are unable to fulfill the processing plant requirements and so the retailer's orders. Our findings provide normative guidance for supply chain decision support systems under risk of pandemic induced disruptions using a quantitative model-based approach.