|
Article Excerpt
1. Introduction
The proliferation of call and service centers within the rapidly expanding service economy has elevated interest in their efficient design and management. A practice that is well suited to improving call centers is agent cross-training. Cross-training can improve customer service by offering more choices for matching agents to customer service requests and enhance efficiency by utilizing the existing workforce more effectively to handle a given call load. Effective use of cross-training requires two steps: (i) a design that determines which agents are trained to handle which customer types; and (ii) a control mechanism that dynamically assigns customers to agents. In this paper, we concentrate primarily on the design step by considering situations in which the control step is straightforward due to the structure of the system.
A call center has a departmental structure if the agents can be divided into groups such that each customer type is unambiguously assigned to a single group (department) for service. The customer type to group assignment can be one-to-one, or if agents are cross-trained to serve more than one type, many-to-one. For example, in a multilingual call center, departments could correspond to groups of agents that handle customers from a specific set of languages (Brigandi etal, 1994). If all French-speaking agents also speak English and vice versa, then we could pool the French and English departments and route both call types to the combined department. However, if some, but not all French speakers speak English, then the system no longer has a departmental structure, since French/English agents cannot be assigned to a unique department. When the cross-training pattern follows a non-departmental structure, the control problem of assigning customers to agents become more complex (see Gans et al. (2003) for a discussion). However, in many call centers, such as financial services support, where customers can be typed according to the products about which they are calling, grouping agents into merged departments is a common practice (Evenson et al., 1999). In such environments, it is important to know which departments to pool via crosstraining of agents. This paper provides insight into this problem.
To understand call centers with departmental structures, we consider environments in which agents are initially grouped into departments based on the customer type(s) they are assigned. We assume that departments differ with respect to parameters such as arrival rate, mean service time, variability in service time and number of agents. Then we examine the impact of pooling, namely combining two or more departments into a larger department with the agents in the pooled department cross-trained to handle all of the call types of those departments. This involves two fundamental issues: (i) how many departments to pool; and (ii) which departments to pool. The specific focus of this paper is to determine how the various system parameters--arrival rates, mean service times, variability in service times and the number of agents--affect these pooling decisions.
Pooling has been widely studied in the literature (for example, see Mandelbaum and Reiman (1998)), usually by comparing the two extreme scenarios of a dedicated system versus a fully pooled system. In a dedicated system, each group of servers is responsible for a specific customer type, whereas in a fully pooled system all servers are merged into a single group that serves all customer types. However, in many real-life situations, and particularly in call centers, cross-training all agents to handle all call types may not be feasible due to cost and/or quality penalties arising from cross-training, excessive agent stress and/or scarcity of agents capable of handling all of the call types. Therefore, while we consider fully pooled systems in this paper, we are particularly interested in partial pooling scenarios consisting of a mixture of pooled and dedicated departments. Specifically, we consider a call center that initially consists of N dedicated departments, and seek to pool k [less than or equal to] N departments into a larger department so as to minimize the expected waiting time of customers in the queue. However, because we recognize that using expected waiting time as the objective can lead to policies that degrade service to some customer types, we also derive sufficient conditions for pooling to reduce expected waiting of all customer types. Our results show that mean service times and the service time coefficient of variations are the major factors that affect the decision on what departments to pool when the utilization is the same across all departments.
The remainder of this paper is organized as follows: Section 2 presents a literature review. Section 3 develops models of the pooling strategies we consider. Section 4 evaluates the relative effectiveness of these strategies and draws simple principles on the structure of the pooling decisions. In Section 5, we present a numerical analysis that addresses the impact of the simple principles derived in Section 4 for general systems. Section 6 concludes the paper. All proofs are given in the online Appendix.
2. Literature review
The literature on call centers has grown rapidly in recent years. Gans et al. (2003) and Aksin et al. (2007) provide excellent surveys of this literature. Most of the analytic call center literature has been based on queueing models where the customers and agents are homogenous (see Koole and Mandelbaum (2002) for a thorough review).
A large body of the queueing literature on call centers has focused on dynamic routing of calls to available agents with the right skills. Perry and Nilsson (1992) considered a system in which two classes of calls are served by a single pool of agents (V-design) and determined both the number of agents and the assignment policy needed to yield specified expected waiting times. Bhulai and Koole (2003) also modeled a variant of this system. Stanford and Grassman (2000) considered a call center with two call types and two agent groups where one group can handle both call types and the other can handle only one of them (N-design), and used fixed priority policies and matrix-geometric methods for performance and staffing analysis. Shumsky (2004) considered the same problem and proposed an approximate analysis. Borst and Seri (2000) proposed a dynamic routing rule that prioritizes the call type that is farthest behind schedule, and determined bounds on the number of fully cross-trained agents needed to provide a given service level. Koole and Talim (2000) modeled a multi-skill call center as a network of queues and approximated each queue as an M/M/r loss system to minimize the number of unanswered calls. Gans and Zhou (2003) studied a call routing problem with two call types where one call always has priority over the other and used a Markov decision process model to achieve service level constraints.
Another stream of queueing-based call center research has relied on heavy traffic analysis to obtain asymptotic results. Harrison and Lopez (1999) considered the optimal dynamic assignment of n non-identical servers working in parallel to serve m types of customers with minimal waiting costs. They showed that if server skills overlap in an appropriate manner, then in the limiting Brownian control problem all servers merge into a single service pool. Bell and Williams (2001) proved the asymptotic optimality of threshold controls for the N-design discussed above. In contrast, Van Mieghem (1995) proved the asymptotic optimality of a simple generalized c[micro] rule for a V-design with convex waiting costs. Harrison and Zeevi (2005) studied the problem of staffing large call centers using stochastic fluid models. Armony and Maglaras (2004a, 2004b) considered multi-class, multi-server call centers with a call-back option, and proposed asymptotically optimal routing and staffing policies. Bassamboo et al (2006) investigated a similar problem with abandonments for large call centers and proposed a method for staffing and routing based on linear programming. It is important to note that our scope does not restrict attention solely to highly utilized systems and also we do not restrict attention to systems with a large number of servers.
The literature most closely related to this paper has focused on choosing appropriate skill sets for servers, usually by comparing dedicated and fully pooled systems. The basic pooling models on which this work is based are described in Kleinrock (1976, pp. 272-290). Smith and Whitt (1981) and Benjaafar (1995) showed that pooling reduces the average delay if arrivals and service times have the same distribution, but it can increase the average delay when different classes of customers require different service times. Buzacott (1996) considered a serial system with n stages where each customer is served by a distinct server at each stage, and transformed this system into a parallel system with n servers in which each server can perform the operations required for all n stages. He showed that the pooled system where all servers can perform all tasks is superior to the unpooled alternative, and the higher the task variability the greater the advantage. Mandelbaum and Reiman (1998) considered pooling of a Jackson network into an M/PH/1 queue. They compared the pooled and unpooled systems in terms of the steady-state mean sojourn times and showed that depending on the system parameters, pooling can be either good or bad. Argon and Andradottir (2006) studied the effects of pooling several adjacent stations in tandem lines where servers are cross-trained and two or more servers can work on the same job simultaneously. They showed that the benefits of pooling can be substantial and that the bottleneck station should be among the pooled stations to obtain the greatest improvement. Our research differs from this literature in that: (i) we consider parallel service environments (e.g., call centers); and (ii) by comparing the performance of many (partially) pooled systems we provide insights for managerial decision making.
Finally, some researchers have proposed alternatives to pooling. For example, Sheikhzadeh et al. (1998) and Jordan et al. (2004) studied chaining of servers where each customer can be routed to one of two
adjacent servers and each server can process customers from two adjacent classes. These studies showed that chaining has the potential to achieve most of the benefits of pooling with respect to performance measures such as the expected time spent in the system and throughput. Hopp et al. (2004) investigated the value of chaining in CONWIP serial production lines, and showed that the impact of forming a complete chain of skills sets can be substantial in increasing throughput. Iravani et al. (2005) developed a structural flexibility index for systems with cross-trained servers that quantifies the flexibility inherent in an arbitrary systems structure and also elucidated the virtues of changing. Wallace and Whitt (2005) addressed routing and staffing problems in call centers under limited cross-training of agents (e.g., chaining) and demonstrated that when each agent has only two skills, in appropriate combinations, the performance is almost as good as when each agent has all skills.
3. Pooling strategies
We consider a call or service center that services N customer types. We assume that the system initially has a departmental structure, in which customers of type i are served by agents in department i with [c.sub.i] servers, i = 1, 2,..., N. We further assume that type i customers arrive according to a Poisson process with rate [[lambda].sub.i], and require a service time drawn from an independent and identicaly distributed (i.i.d.) sequence with finite mean [T.sub.i] and squared coefficient of variation (SCV) [v.sub.i.sup.2]. Hence, the initial system can be modeled as N parallel M/G/c queues. We assume that this original system is stable, which requires [[rho].sub.i] = [[lambda].sub.i] 1 [T.sub.i]/[c.sub.i] < 1 for i = 1,..., N. We define a pooling strategy by a set [KAPPA], which represents the set of departments where all servers are cross-trained to handle all customer types in [KAPPA] (see Fig. 1 for an illustration of a case where N = 3 and [KAPPA] = 11. 2)). Our objective...
|
