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　algorithm　II　(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.