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

Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters

Modeling And Optimization Of Non-Profit Hospital Call Centers With Service Blending

This dissertation focuses on the operations problems in non-profit hospital call centers with inbound and outbound calls service blending. First, the routing policy for inbound and outbound calls is considered. The objective is to improve the system utilization under constraints of service quality and operators\u27 quantity. A collection of practical staffing assignment methods, separating and mixing staffing policy are evaluated. Erlang C queuing model is used to decide the minimum number of operators required by inbound calls. Theoretical analysis and numerical experiments illustrate that through dynamically assigning the inbound and outbound calls to operators under optimal threshold policy, mixing staffing policy is efficient to balance the system utilization and service quality. Numerical experiments based on real-life data demonstrate how this method can be applied in practice. Second, we study the staffing shift planning problem based on the inbound and outbound calls routing policies. A mathematical programming model is developed, based on a hospital call center with one kind of inbound calls and multiple kinds of outbound calls. The objective is to minimize the staffing numbers, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments based on actual operational data are included. Results show that the model is effective to optimize the shift planning and hence reduce the call centers\u27 cost. Third, we model the staffing shift planning problem for a hospital call center with two kinds of service lines. Each kind of service is delivered through both inbound calls and outbound calls. The inbound calls can be transferred between these two service lines. A mathematical programming model is developed. The objective is to minimize the staffing cost, by deciding the shift setting and workload allocation. The inbound calls service level and staffing utilization are taken into consideration in the constraints. Numerical experiments are carried out based on actual operational data. Results show that the model is effective to reduce the call centers\u27 labor cost

Stationary analysis of a single queue with remaining service time dependent arrivals

We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$ of the current customer being served. We derive a natural stability condition and provide a stationary analysis under it both at service completion times (of the queue length process) and in continuous time (of the queue length and the residual service time). In particular, we show that the stationary measure of queue length at service completion times is equal to that of a corresponding $M/G/1$ system. For $f > 0$ we show that the continuous time stationary measure of the $rM/G/1$ system is linked to the $M/G/1$ system via a time change. As opposed to the $M/G/1$ queue, the stationary measure of queue length of the $rM/G/1$ system at service completions differs from its marginal distribution under the continuous time stationary measure. Thus, in general, arrivals of the $rM/G/1$ system do not see time averages. We derive formulas for the average queue length, probability of an empty system and average waiting time under the continuous time stationary measure. We provide examples showing the effect of changing the reshaping function on the average waiting time.Comment: 31 pages, 3 Figure