During the COVID-19 pandemic, allocation plan of ventilators is reinforced for fulfilling its critical needs to the hospitals. The death rate caused by COVID-19 could have been diminished globally if the proposed medical logistics network is possible to be timely deployed between suppliers and demand regions. Owing to operate and organize medical logistics network and to minimize the total delivery time (TDT), we have formulated a mathematical model based on mixed-integer non-linear programming (MINLP). The application of the proposed model is considered employing the real-life pandemic data, which is alarmed to the severely affected regions in India. The results denote that the anticipated model of medical logistics network efficiently performs in a pandemic demand scenario. The responsiveness of the developed model is also examined under three demand scenarios based on Covid-19 pandemic wave-1, wave-2, and wave-3. Lastly, the sensitivity analyses are done to examining the impact of the critical parameters of the model, and findings are discussed.