In this work, we present a novel problem and its solution coined multi-agent, multi-objective, multi-mode routing and scheduling (M3RS). The formulation for M3RS is introduced for time-bound multi-agent, multi-objective routing and scheduling missions where each task has multiple execution modes. Different execution modes have distinct resource consumption, associated execution time, and quality. M3RS assigns an optimal sequence of tasks and the execution modes to each agent. The routes and associated modes are dependent on user preferences for different objective criteria. The need for M3RS comes from multi-robot applications in which a trade-off between multiple criteria arises from different task execution modes. We use M3RS for the application of multi-robot disinfection in public locations. The objectives considered for disinfection application are disinfection quality and number of tasks completed. A mixed-integer linear programming model is proposed for M3RS. Then a time-efficient column generation scheme is presented to tackle the issue of computation times for larger problem instances. The advantage of using multiple modes over fixed execution mode is demonstrated using experiments on synthetic data. The results suggest that M3RS provides flexibility to the user in terms of available solutions and performs well in joint performance metrics. The application of the proposed problem is shown for a team of disinfection robots.