On the scheduling of operations in a chat contact center

Unlike calls, the chat channel allows a contact center agent to simultaneously work with many customers. The benefit of this flexibility can be however challenged by a new abandonment feature during service. In this context, new flow routing questions arise. How many chats should an agent serve? Which agent should be selected? Or may a chat be served by more than one agent? We aim to answer these questions so as to find the best trade-off between time spent in service, queueing delay and abandonment. For this purpose, we determine conditions under which the traditional Least Busy First or Most Busy First polities are optimal for agent selection. Using a dynamic programming analysis, we prove that a state-dependent threshold reservation policy is optimal when a chat can be handed to other agents without loss of efficiency. This analysis reveals that reservation is useful as it allows to maintain of sufficient agent productivity and abandonment from the queue which in turn reduce the system's congestion. In addition, we show the closeness between the optimal policy and the easier-to-implement fixed capacity policy if this fixed capacity is optimized. When a chat cannot be handed to other agents, we develop a dispatching policy improvement algorithm based on the explicit computation of the relative value function for an initial policy with fixed probabilities. The dispatching policy significantly outperforms non state-dependent ones, as it partly compensates the agents' inability to share a chat service. (C) 2018 Elsevier B.V. All rights reserved.