Call Centers with Delay Information: Models and Insights

This section supports the paragraph “Effect of θ on the optimal announcement coverage β∗” in Section 5 of the main paper Jouini et al. (2011). We would like to see how the call center performance measures under the optimal announcement coverage β∗ are different from those under other β values. In other words, does it matter that a manager chooses a β that would be different from the optimal one, and to what extent? We consider Model 2 under the update case (θ = 0) with the same parameters as those in Table 1 of the main paper: μ = 1, γ = 0.5, α0 = 5%, (s, λ) = (3,3), (5,5), (20,20), and (100,100). We compute the performance measures of Model 2 for different β, β =10%, 20%, ..., 90%. Note from Table 1 of the main paper that for all call center sizes, β =90% is approximately optimal. The results are given in Table 1, and in Figures 1(a)-1(d). From Table 1, we see that there are considerable changes in the performance measures when we announce delays other than those under the optimal announcement coverage. These changes are particularly apparent when the pooling effect is absent. The pooling effect improves the performance measures thereby reducing the sensitivity to the choice of β. For s = 3, P is divided by around 10 when moving from β = 10% to β = 90%. However for s = 100, it is only divided by around 2. In summary, for all call center sizes, all