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Article Excerpt
1. Introduction
Over the past two decades, businesses worldwide have vigorously worked to implement new operational approaches to deal with the difficult demands of the global economy. This has resulted in a rethinking of labor management practices. For a growing number of companies, this has meant a shift from workers trained only for one task to workforces trained for multiple tasks and, in some cases, dynamic worksharing (see Hopp and Van Oyen 2004). A vivid illustration of this change can be found in call centers, a large service industry employing roughly three to four million Americans, according to Datamonitor. Critical emergency services such as the police, ambulance services, and fire services depend on inbound call centers (such as 911 in North America) for dispatching; therefore, much more than convenience and profit are at stake.
Call centers have found that careful attention to the management of the workforce (staffing, rostering, training, performance measurement, skills-based routing, etc.) can help avoid lost calls and reduce long waiting times. Competitive marketplace pressures (including increased pressure to outsource operations to nations with low-wage labor markets), increasing customer service level expectations, and the recent advent of skills-based routing technologies have expanded the cross-training of customer sales representatives (CSRs) in inbound call centers. That is to say, some or all of the agents are (cross-)trained to provide two or more types of service during a work shift. For example, a CSR may be trained for sales, and also for customer service, repairs, complaints, etc.
Among the possible reasons for cross-training (e.g., motivation, providing a career path, improving the probability of service resolution on the first call, reducing the number of agents with whom a customer must speak, etc.), we focus on the operational benefits of cross-training in reducing the average number of customers in queue (and thus, by Little's law, the average customer waiting time). In a nutshell, cross-training allows labor capacity to be dynamically reallocated to the services required by customers as call volumes shift and the mix across service types changes. Even when trends in the environment are absent, cross-training reduces the frequency with which agents starve for lack of calls due to intrinsic variability in the demand process and service times. The effect of cross-trained agents can result in, for example, callers experiencing a shorter wait to reach an agent and offering the same quality of service with a smaller workforce. These operational benefits alone may be sufficient to justify agent cross-training.
It is obvious that full cross-training of every agent for every call type is very costly, and sometimes impossible (e.g., call centers that serve clients in several languages). Therefore, an important question becomes: which type(s) of calls should each call-center agent be (cross-)trained to handle? In many applications, there will be a range of choices available in determining worker skill sets, and there is no easy way to tell which choices are better than others. We illustrate this with the following simple example to describe the critical issue of workforce cross-training in call centers.
Consider a call center that receives 12 different types of calls, namely, call types A, B, C,..., L. Calls of type i arrive randomly with a rate specified by the ith element of the demand rate vector D = (0.5, 0.5, 0.5, 0.75, 0.75, 0.5, 1.167, 0.667, 0.667, 0.333, 0.333, 0.333). For simplicity, suppose that the call center has seven agents. We assume that call-handling/service times are stochastic with an average of 0.9 units of time (which corresponds to a system utilization of 90% under an aggregate arrival rate of seven calls per unit time). Associated with every agent is a nonempty set, called a skill set, defining the type(s) of calls the agent is (cross-)trained to serve. Figure 1 shows two agent cross-training structures, in which an arrow from a call type to an agent indicates that the agent is trained to respond to that call type (i.e., this type of call is in the agent's skill set). For example, in Structure 1, Call-Center Agent 5 is trained to respond to call types {G, H, I}, while in Structure 2, the skill set of that agent is {G, I, J}. Both structures are easily capable of handling demand vector D because each worker can spend an equal fraction of effort on each skill in their skill set. All call types receive enough capacity, so the number of customers in the queues will not grow to infinity. However, the question is, which cross-training structure is more flexible, yielding a smaller average customer waiting time over a range of operating conditions? If there exists some property in a cross-training structure that impacts the relative performance of the corresponding stochastic queueing system over a broad operating range, then we are facing the interesting question of how to quantify this property with a computationally lightweight algorithm.
A simple and intuitive way to capture the effectiveness of a cross-training structure is to simply use the total number of skills of a structure as an index. The number of arcs index of a system is defined to be the sum of the number of skills (arcs in the structure graph) of all agents. The intuition is clear: Every additional skill serving a call type provides more capacity that (as needed) can be used to serve that call type. In other words, every additional skill corresponding to a call type pools more capacity to serve that call type. As Figure 1 shows, the total number of skills in Structure 1 is 27, while the total number of skills in Structure 2 is only 25. Thus, the number of arcs index would select Structure 1 as a more effective cross-training structure.
[FIGURE 1 OMITTED]
To identify which structure yields the lowest average customer waiting time, we developed a discrete-event computer simulation program and estimated the average customer waiting times under each cross-training structure. The system model is a queueing network with parallel, infinite-buffer...
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