This paper proposes a scheduling model for the washing step of medical device sterilization. After use in a surgery, medical devices pass through several steps where the washing is usually a bottleneck. We study the cases of external and internal sterilization services to minimize two objectives: makespan and flow time of washing operations. First, we study internal sterilization services considering jobs can have different or unit sizes. For these two cases, we provide a mixed integer linear model and a dynamic programming model, and integrate these methods in an -constraint model. For the case of external services, first we develop a simultaneous (2, 2) approximation algorithm and then derive an algorithmic scheme to generate a partial 2-approximation of the Pareto set. Several numerical experiments are conducted to demonstrate the strength of proposed solution methods.