This paper presents a multi-objective modeling process that formulates a system under various constraints so that its performance can be optimized. In this approach, different objectives are formulated individually first and combined with (priority parameters) together into a single objective function that serves as the main part of an optimization problem. Operational constraints are identified to further restrict the solution space into a finite set of feasible solutions that can be searched and evaluated in a reasonable timeframe. The workability of this multi-objective modeling process is demonstrated in the hospital system in Chile where efficiency is modeled under the constraints of operational capability that relies on available supply and the replenishing behavior. The operational data are collected and used as inputs to the modeling process, and the optimized replenishing behavior is determined so that the efficiency of having as many patients as possible under the availability of necessary supplies can be obtained for automating the operational process.