Oualid Jouini

Call Centers with Delay Information: Models and Insights

This section supports the paragraph “Effect of θ on the optimal announcement coverage β∗” in Section 5 of the main paper Jouini et al. (2011). We would like to see how the call center performance measures under the optimal announcement coverage β∗ are different from those under other β values. In other words, does it matter that a manager chooses a β that would be different from the optimal one, and to what extent? We consider Model 2 under the update case (θ = 0) with the same parameters as those in Table 1 of the main paper: μ = 1, γ = 0.5, α0 = 5%, (s, λ) = (3,3), (5,5), (20,20), and (100,100). We compute the performance measures of Model 2 for different β, β =10%, 20%, ..., 90%. Note from Table 1 of the main paper that for all call center sizes, β =90% is approximately optimal. The results are given in Table 1, and in Figures 1(a)-1(d). From Table 1, we see that there are considerable changes in the performance measures when we announce delays other than those under the optimal announcement coverage. These changes are particularly apparent when the pooling effect is absent. The pooling effect improves the performance measures thereby reducing the sensitivity to the choice of β. For s = 3, P is divided by around 10 when moving from β = 10% to β = 90%. However for s = 100, it is only divided by around 2. In summary, for all call center sizes, all

Analysis of the Impact of Team-Based Organizations in Call Center Management

We investigate the benefits of migrating from a call center, where all agents are pooled and customers are treated indifferently by any agent, toward a call center where customers are grouped into clusters with dedicated teams of agents. Each cluster is referred to as a portfolio. Customers of the same portfolio are always served by an agent of the corresponding team. There is no specialization involved in this organization in the sense that all customer portfolios as well as all agent teams have (statistically) identical behaviors. The reason for moving to this organization is that dealing with teams of limited size allows a much better workforce management than the situation usually encountered in large call centers. The purpose of this paper is to examine how the benefits of moving to this new organization can outweigh the drawbacks. The drawbacks come from the fact that there is less of a pooling effect in the new organization than in the original one. The benefits come from the better human resource management that results in a higher efficiency of the agents, both in terms of speed and quality of the answers they provide to customers. Our analysis is supported by the use of some simple queueing models and provides some interesting insights. In particular, it appears that for some reasonable ranges of parameters, the new organization can outperform the original organization. We then extend the analysis to the case where, in addition to the identified customer portfolios, there is an additional flow of calls called out-portfolio flow. It is shown that this feature makes the new organization even more efficient.

Performance indicators for call centers with impatience

An important feature of call center modeling is the presence of impatient customers. This article considers single-skill call centers including customer abandonments. A number of different service-level definitions are structured, including all those used in practice, and the explicit computation of their performance measures is performed. Based on data from different call centers, models are defined that extend the common Erlang A model. It is shown that the proposed models fit reality very well.

Staffing a call center with uncertain non-stationary arrival rate and flexibility

We consider a multi-period staffing problem in a single-shift call center. The call center handles inbound calls, as well as some alternative back-office jobs. The call arrival process is assumed to follow a doubly non-stationary stochastic process with a random mean arrival rate. The inbound calls have to be handled as quickly as possible, while the back-office jobs, such as answering emails, may be delayed to some extent. The staffing problem is modeled as a generalized newsboy-type model under an expected cost criterion. Two different solution approaches are considered. First, by discretization of the underlying probability distribution, we explicitly formulate the expected cost newsboy-type formulation as a stochastic program. Second, we develop a robust programming formulation. The characteristics of the two methods and the associated optimal solutions are illustrated through a numerical study based on real-life data. In particular we focus on the numerical tractability of each formulation. We also show that the alternative workload of back-office jobs offers an interesting flexibility allowing to decrease the total operating cost of the call center.

Moments of first passage times in general birth–death processes

We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 1. We also give an explicit condition for a birth–death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In particular, we compute for some non-standard Markovian queues, the moments of the busy period duration, the busy cycle duration, and the state-dependent waiting time in queue.

Online scheduling policies for multiclass call centers with impatient customers

We consider a call center with two classes of impatient customers: premium and regular classes. Modeling our call center as a multiclass GI/GI/s+M queue, we focus on developing scheduling policies that satisfy a target ratio constraint on the abandonment probabilities of premium customers to regular ones. The problem is inspired by a real call center application in which we want to reach some predefined preference between customer classes for any workload condition. The motivation for this constraint comes from the difficulty of predicting in a quite satisfying way the workload. In such a case, the traditional routing problem formulation with differentiated service levels for different customer classes would be useless. For this new problem formulation, we propose two families of online scheduling policies: queue joining and call selection policies. The principle of our policies is that we adjust their routing rules by dynamically changing their parameters. We then evaluate the performance of these policies through a numerical study. The policies are characterized by simplicity and ease of implementation.

Optimal scheduling in call centers with a callback option

Abstract We consider a call center model with a callback option, which allows to transform an inbound call into an outbound one. A delayed call, with a long anticipated waiting time, receives the option to be called back. We assume a probabilistic customer reaction to the callback offer (option). The objective of the system manager is to characterize the optimal call scheduling that minimizes the expected waiting and abandonment costs. For the single-server case, we prove that non-idling is optimal. Using a Markov decision process approach, we prove for the two-server case that a threshold policy on the number of queued outbound calls is optimal. For the multi-server case, we numerically characterize a switching curve of the number of agents reserved for inbound calls. It is a function of the number of queued outbound calls, the number of busy agents and the identity of jobs in service. We also develop a Markov chain method to evaluate the system performance measures under the optimal policy. We next conduct a numerical study to examine the impact of the policy parameters on the system performance. We observe that the value of the callback offer is especially important for congested situations. It also appears that the benefits of a reservation policy are more apparent in large call centers, while they almost disappear in the extreme situations of light or heavy workloads. We moreover observe in most cases that the callback offer should be given upon arrival to any delayed call. However, if balking and abandonment are very high (which helps to reduce the workload) or if the overall treatment time spent to serve an outbound call is too large compared to that of an inbound one, there is a value in delaying the proposition of the callback offer.

A comprehensive simulation modeling of an emergency department: a case study for simulation optimization of staffing levels

We propose a Discrete Event Simulation (DES) model for an emergency department (ED). The model is developed in close collaboration with the French hospital Saint Camille, and is validated using real data. The objective of this model is to help ED managers better understand the behavior of the system and to improve the ED operations performance. The most essential features of an ED are considered in the model. A case study is conducted in order to allow decision makers select the most relevant investment in the human staffing budget. A simulation-based optimization algorithm is adopted to minimize the average Length of Stay (LOS) under a budget constraint. We conduct a sensitivity analysis on the optimal average LOS as a function of the staffing budget, and derive useful recommendations to managers on how the budget can impact the performance of the system.

On Multiple Priority Multi-Server Queues with Impatience

We consider Markovian multi-server queues with two types of impatient customers: high- and low-priority ones. The first type of customer has a non-preemptive priority over the other type. After entering the queue, a customer will wait a random length of time for service to begin. If service has not begun by this time he or she will abandon and be lost. We consider two cases where the discipline of service within each customer type is first-come first-served (FCFS) or last-come first-served (LCFS). For each type of customer, we focus on various performance measures related to queueing delays: unconditional waiting times, and conditional waiting times given service and given abandonment. The analysis we develop holds also for a priority queue with mixed policies, that is, FCFS for the first type and LCFS for the second one, and vice versa. We explicitly derive the Laplace–Stieltjes transforms of the defined random variables. In addition we show how to extend the analysis to more than two customer types. Finally we compare FCFS and LCFS and gain insights through numerical experiments.

Control Policies for Single-Stage Production Systems with Perishable Inventory and Customer Impatience

We 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.