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This paper investigates a new multi-objective order assignment and scheduling problem for personal protective equipment (PPE) production and distribution during the outbreak of epidemics like COVID-19. The objective is to simultaneously minimize the total cost and maximize the PPE supply timeliness. For the problem, we first develop a bi-objective mixed-integer linear program (MILP). Then an $\epsilon $ -constraint combined with logic-based Benders decomposition method is proposed based on some explored properties. We then extend the proposed model to handle dynamics and randomness. In particular, we design a predictive reactive rescheduling approach to address random order arrivals and manufacturer disruptions. Computational experiments on a real case from China and 100 randomly generated instances are conducted. Results show that the proposed algorithm significantly outperforms an adapted $\epsilon $ -constraint method combined with the proposed MILP and the widely used non-dominated sorting genetic (NSGA-II) in obtaining high-quality Pareto solutions. Note to Practitioners—The unprecedented outbreak of COVID-19 and its rapid spread caught numerous national and local governments unprepared. Healthcare systems faced a vital scarcity of PPEs. The urgency of producing and delivering PPEs increases as the number of infected cases rapidly increases. A key challenge in response to the epidemic is effectively and efficiently matching the demands and needs. Performing practical and efficient order assignment and scheduling for PPE production during the COVID-19 outbreak is critical to curbing the COVID-19 pandemic. This work first proposes a bi-objective mixed-integer linear program for optimal order assignment and scheduling for PPE production. The aim is to achieve an economical and timely PPE production and supply. A novel method that combines the $\epsilon $ -constraint framework and the logic-based Benders decomposition is proposed to yield high-quality Pareto solutions for practical-sized problems. Computational results indicate that the proposed approaches are practical and feasible, which can help decision-makers to perform acceptable order assignment and scheduling decisions. [ABSTRACT FROM AUTHOR]