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 queue whose elapsed waiting 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-dimensional Markov 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 performance measures without 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

Front-office multitasking between service encounters and back-office tasks

International audienceWe model the work of a front-line service worker as a queueing system. The server interacts with customers in a multi-stage process with random durations. Some stages require an interaction between server and customer, while other stages are performed by the customer as a self-service task or with the help of another resource. Random arrivals by customers at the beginning and during an encounter create random lengths of idle time in the work of the server (breaks and interludes respectively). The server considers treatment of an infinite amount of back-office tasks, or tasks that do not require interaction with the customer, during these idle times. We consider an optimal control problem for the server's work. The main question we explore is whether to use the interludes in service encounters for treating back-office, when the latter incur switching times. Under certain operating environments, working on back-office during interludes is shown to be valuable. Switching times play a critical role in the optimal control of the server's work, at times leading the server to prefer remaining idle during breaks and interludes, instead of working on back-office, and at others to continue back-office in the presence of waiting customers. The optimal policy for use of the interludes is one with multiple thresholds depending on both the customers queueing for service, and the ones who are in-service. We illustrate that in settings with multiple interludes in an encounter, if at all, the back-office work should be concentrated on fewer, longer and later interludes

Control policies for single-stage production systemls with perishable inventory and customer impatience

International audienceWe consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance