Call centers with a postponed callback offer

We study a call center model with a postponed callback option. A customer at the head of the queuewhose elapsedwaiting time achieves a given threshold receives a voice message mentioning the option to be called back later. This callback option differs from the traditional ones found in the literature where the callback offer is given at customer’s arrival.We approximate this system by a two-dimensionalMarkov chain, with one dimension being a unit of a discretization of the waiting time. We next show that this approximation model converges to the exact one. This allows us to obtain explicitly the performancemeasureswithout abandonment and to compute them numerically otherwise. From the performance analysis, we derive a series of practical insights and recommendations for a clever use of the callback offer. In particular, we show that this time-based offer outperforms traditional ones when considering the waiting time of inbound calls. B Sihan Ding [email protected] Benjamin Legros [email protected] Rob van der Mei [email protected] Oualid Jouini [email protected] 1 Laboratoire Métis, EM Normandie, 64 Rue du Ranelagh, 75016 Paris, France 2 Stochastics Group, Center for Mathematics and Computer Science (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands 3 Laboratoire Genie Industriel, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92290 Chatenay-Malabry, France