Solving two-dimensional Markov chain model for call centers

The purpose of this paper is to develop a novel model of a call center that must treat calls with distinctly different service depending on whether they orginate from VIP or regular customers. VIP calls must be responded to immediately but regular calls can be routed to a retrial queue if the operators are busy.

This study’s proposed model can easily reveal the optimal arrangement of operators while minimizing computational time and without losing any precision of the performance measure when dealing with a call center with more operators.

Based on the results of the comparison between the exact method and the proposed approximation method, the approach shows that the larger the number of operators or inbound calls, the smaller the error between the two methods.

This investigation presents a computational method and management cost function intended to identify the optimal number of operators for a call center. Because of computational limitations, many operators could not be easily analyzed using the exact method. For the manager of a call center, the sooner the optimal solution is found, the faster business strategies are deployed. This study develops an approximation method and compares it with the exact method.