Performance Evaluation of Small Call Centres in a Transient Regime

Abstract

This paper addresses a fundamental and practically significant problem in call centre operations -- determining optimal call allocation policies that meet client service targets while minimising staffing costs. Motivated by a problem presented by an industry partner, we examine a real-world setting involving a relatively small call centre with hierarchical structure among agents. It is natural to model the operation of such a centre as a continuous-time Markov chain. To gain insight into the structure of optimal policies, we first (i) apply backward induction based on Bellman's equation to a finite-horizon discrete-time model, and (ii) derive stationary policies for an infinite-horizon continuous-time model with discounting. Subsequently, we evaluate the performance of these policies in the original finite-horizon continuous-time setting by computing the expected number of abandonments and the waiting time distributions of customers. This is achieved using first-step analysis combined with Laplace transform methods. The effectiveness of the proposed approach is illustrated through numerical examples.