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.

Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic-Epidemiological Model.

We analyze the implications of strategic interactions between two heterogeneous groups (i.e., young and old, men and women) in a macroeconomic-epidemiological framework. The interactions between groups determine the overall prevalence of a communicable disease, which in turn affects the level of economic activity. Individuals may lower their disease exposure by reducing their mobility, but since changing mobility patterns is costly, each group has an incentive to free ride negatively affecting the chances of disease containment at the aggregate level. By focusing on an early epidemic setting, we explicitly characterize the cooperative and noncooperative equilibria, determining how the inefficiency induced by noncooperation (i.e., failure to internalize epidemic externalities) depends both on economic and epidemiological parameters. We show that long-run eradication may be possible even in the absence of coordination, but coordination leads to a faster reduction in the number of infectives in finite time. Moreover, the inefficiency induced by noncooperation increases (decreases) with the factors increasing (decreasing) the pace of the disease spread.

Sustainability, cooperation and mobility of workers within and between European countries: a two-stage goal programming model.

Facing multiple and often considered as conflicting stakes, either economical, migratory, or environmental, policy-making may struggle to identify and implement relevant policy action allowing for balanced and joint completion of such challenges. Addressing this important public issue, we develop a multi-criteria two-stage Goal Programming (GP) model to identify optimal policy paths towards the Europe 2020 strategy on economic growth, employment levels and environmental sustainability. The model is calibrated on current contributions of economic sectors in all European countries to each policy objective: contribution to economic output (GDP), emissions of Green House Gas, electric consumption and number of jobs. First, we study the optimal allocation of workers within economic sectors of each European country to maximize the joint achievement of Europe 2020 multi criteria sustainability targets. We then extend the model to allow cooperation between states, namely allowing internal migrations of workers between countries. We highlight how supranational allocation schemes of surplus workers improve the satisfaction of national sustainability objectives. Finally, we consider extra-European migrants regional integration and study the consequences of such opening over EU2020 targets satisfaction and per capita GDP. Simulation results highlight countries performance comparison, and sheds light on significant benefits from such cooperation for the majority of countries. Improved integration of internal and external workforce generally improves the achievement of EU2020 objectives, while keeping per capita GDP at least constant. Moreover, we expose the relevance of cooperative work-flows allocation strategies across Europe and emphasize the importance of workers mobility in order to ensure more sustainable common development.

Epidemics and macroeconomic outcomes: Social distancing intensity and duration.

We analyze the determination of the optimal intensity and duration of social distancing policy aiming to control the spread of an infectious disease in a simple macroeconomic-epidemiological model. In our setting the social planner wishes to minimize the social costs associated with the levels of disease prevalence and output lost due to social distancing, both during and at the end of epidemic management program. Indeed, by limiting individuals' ability to freely move or interact with others (since requiring to wear face mask or to maintain physical distance from others, or even forcing some businesses to remain closed), social distancing has on the one hand the effect to reduce the disease incidence and on the other hand to reduce the economy's productive capacity. We analyze both the early and the advanced epidemic stage intervention strategies highlighting their implications for short and long run health and macroeconomic outcomes. We show that both the intensity and the duration of the optimal social distancing policy may largely vary according to the epidemiological characteristics of specific diseases, and that the balancing of the health benefits and economic costs associated with social distancing may require to accept the disease to reach an endemic state. Focusing in particular on COVID-19 we present a calibration based on Italian data showing how the optimal social distancing policy may vary if implemented at national or at regional level.