We develop a nonlinear integer programming model which minimizes the total cost with the optimal number of operators to hire and their optimal allocation to the tasks under the diverse constraints such as the weekly, daily, and hourly maximum allowable abandonment rates for the time-varying inbound call volume. We present a case study based on actual data at a call center, in order to prove the validity of applying the optimization method proposed. By the one-sample two-tailed t-test, we confirm that the expected abandonment rates resulting from the optimization method are identical with the ones from the discrete-event simulation within specified confidence intervals.