Exercise of robotics in many applications brings in concerns of human-robot interaction. This paper offers a mathematical model-based mission planning tool for optimizing operator workload and platform utilization in human/multi-robot (H/M-R) teams. None of the earlier methods consistently predicts fan-out (number and configuration of robots that can be operated simultaneously and effectively, a critical H/M-R design decision). In this research, a mixed integer programming (MIP) model and solution framework are proposed to provide better estimates of fan-out while explicitly considering the performance, mission characteristics, objective and task/environment complexity. The extent of each robot's waiting time is restricted by a utilization threshold in the MIP model. The effect of environment's complexity on the task effectiveness is considered, where robots' performances deteriorate during switch and neglect times. Simulation results show that fan-out effect is dependent on interaction efficiency, neglect tolerance, as well as other parameters. Performance is most sensitive to environment's complexity and least sensitive to utilization threshold. In addition, the MIP model reveals optimal control sequence of robots to prevent switching confusions and maximize team performance. Empirical evaluations show that this approach holds great promise for real-world scenarios.