COVID-19 pandemic has imposed many threats. One among them is the accumulation of waste in hospitals. Waste should be disposed regularly and safely using sustainable methods. Sustainability is self development with preser-vation of society and its resources. The main objective of this research is to achieve sustainability in waste collection by minimizing the cost factor. Minimi-zation of sustainable-cost involves minimization of three sub-components – total travel-cost representing economical component, total emission-cost representing environmental component and total driver-allowance-cost representing social component. Most papers under waste collection implement Tabu search algorithm and fail to consider the environmental and social aspects involved. We propose a mathematical model, a novel algorithm called grouping algorithm, a combination of Nearest Neighbor algorithm and Simulated Annealing algorithm to achieve sustainable transportation in waste collection during pandemics. All these algorithms are run on Solomon’s and Gehring and Homberger’s benchmark dataset. The sustainable-cost obtained from the output routes of the proposed grouping algorithm is found to perform effectively for all the instances with minimized solution. The results are verified using computational techniques such as Integrated Ranking and Relative Percentage Deviation and statistical techniques such as Descriptive Statistics.