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Article Excerpt
Cross-selling is becoming an increasingly prevalent practice in call centers, due, in part, to its unique capability to allow firms to dynamically segment their callers and customize their product offerings accordingly. This paper considers a call center with cross-selling capability that serves a pool of customers that are differentiated in terms of their revenue potential and delay sensitivity. It studies the operational decisions of staffing, call routing, and cross-selling under various forms of customer segmentation. It derives near-optimal controls in each of the settings analyzed, and characterizes the impact of a more refined customer segmentation on the structure of these policies and the center's profitability.
Subject classifications: call centers; cross-selling; queueing systems; revenue management; pricing.
Area of review: Manufacturing, Service, and Supply Chain Operations.
History: Received September 2006; revisions received May 2007, September 2007, December 2007; accepted December 2007. Published online in Articles in Advance January 5, 2009.
1. Introduction
Many organizations consider their call centers to be one of the most important channels of interaction with their customers, acting both as a service center and a point of sales--an opportunity for the firm to generate extra revenue by offering new or existing products to their customers. The significant revenue potential of this cross-selling strategy is underscored by the nature of the interaction that takes place in a call center and the wealth of information that is available through state-of-the-art customer relationship management (CRM) systems. Together, they enable firms to segment their customer pools effectively and to tailor their product offerings to each such segment to increase the likelihood of purchase and the associated expected revenue. A familiar and successful example of cross-selling practice is in the financial services industry, where customers who call for service, such as for account balance inquiries, are often offered new financial products. (1)
Alongside its potential benefits, cross-selling may substantially increase the total workload that needs to be handled by the call center's agents, (2) which may degrade the system's quality of service and, in turn, have an adverse effect on the overall customer experience, as well as the effectiveness of cross-selling itself. It is important to carefully select which cross-selling opportunities to pursue and when to do so, and to account for the impact of these decisions in determining the staffing level of the call center. This paper considers a call center with cross-selling capabilities that serves a heterogenous pool of customers, and studies the operational decisions of staffing, call routing, and cross-selling under various forms of customer segmentation. It derives near-optimal controls in each of the settings analyzed, and characterizes the impact of more refined customer segmentation on the structure of these policies and the center's profitability.
In more detail, we consider a call center with a single pool of fully flexible agents that first handle inbound call service requests, and subsequently decide whether or not to attempt to cross-sell to some of these customers a certain product or service whenever such an opportunity arises. Cross-selling attempts are handled by the same agent that has served the customer's original request, upon completion of that task. Each cross-selling attempt is preceded by an instantaneous step that captures the customer's decision of whether or not to agree to listen to the cross-selling offer. The processing times for the original service request and the cross-selling phase are exponentially distributed with potentially different parameters. Finally, the heterogeneous pool of potential customers comprises a discrete set of types or segments. (The terms "type" and "segment" are used in this paper interchangeably.) Types differ in terms of their delay sensitivity and revenue potential. These are captured through the probability that a customer will agree to listen to a cross-selling offer as a function of the waiting time that he encountered, and through a demand relation that specifies the probability that a customer decides to buy the offered product as a function of the quoted price and the waiting time.
The ability to segment the caller population allows the call center to customize the product offered to each caller segment. In this paper, we assume that the degree of segmentation is exogenously specified, for example, as the output of an upstream marketing analysis. Depending on the application setting at hand, product customization may involve charging a different price to different segments for the same product, or could involve changing the attributes, as well as the price of the product offered to each segment. In both settings, the goal is to better exploit the preferences of each caller segment so as to increase the expected profitability from cross-selling. The output of this pricing and/or product attribute customization process is summarized by the segment-specific expected revenue per cross-selling attempt. As we show, the latter is crucial in deciding to whom to cross-sell and how to staff the call center. For purposes of the analysis in this paper, we consider the simpler of the two settings mentioned above, in which the call center only customizes the price of the product offered to each segment, keeping all other characteristics of that product common across segments. We acknowledge this fact by using the term price customization as opposed to product customization, again keeping in mind that the essential consequence of the customization capability is that it leads to different expected revenues per cross-selling attempt for each segment.
As an example of price customization, one may consider the pricing of CD (certificate of deposit) products offered by banks to different customers. It is natural to think of the price of the CD as its associated interest rate, although two important product attributes are the minimum capital contribution and the length of the time over which the promised interest rate is guaranteed. An increasingly important application of quantitative pricing and revenue management tools in the financial services industry is in deciding the terms, and more importantly the interest rate, of the CD product that is offered to existing customers to entice them to roll their expiring CD contribution from one product to another. Although pricing to initially attract customers who may be "shopping around" for such a product is quite competitive, the subsequent repricing decisions tend to be less constrained and, indeed, an area of intense activity in that industry.
We study three variants of this model with an increasing availability of information regarding customer segmentation and, as a result, increasing flexibility in terms of the aforementioned operational and pricing decisions. The simplest model is one where customers are not segmented, or equivalently, where their types are not observable. In this case, the manager is limited to making the cross-selling decisions based solely on the aggregate load in the system, and charging all customers the same price. The second model is one where types are observed sometime during their service, and this information can therefore be used together with the actual waiting time experienced by the customer in deciding whether to cross-sell to a customer, and if so, what price to charge. The third model is one where customer types are observable upon arrival, in which case the manager can also decide how to route customers of different types to the available agents. For each of these models, the call center manager's problem is to select its staffing, routing, cross-selling, and pricing policies to maximize the center's expected profit rate, given by its revenues minus the staffing cost minus a linear waiting time cost that is experienced by all customers and is incurred by the center.
The controlled two-stage service sequence of each customer and the dependence of the cross-selling phase on dynamic waiting time information makes an exact analysis of this model cumbersome and difficult, even if customers are treated as one segment. Our approach considers a deterministic relaxation of this problem, which is solved in closed form. Its solution suggests different staffing and cross-selling policies for each of the model variants listed above. In each case, we show that our proposed policy is asymptotically optimal in systems with increasing call volume, and as such is appropriate for call centers with high demand volumes.
Our contribution is twofold: From a practical view-point--we propose a concrete, simple, and provably near-optimal solution for the complex problem of cross-selling in environments with multiple customer classes. Our solution will allow firms to extract the revenue potential embedded in their CRM systems through smart operational management of their marketing interface. From a managerial viewpoint--our tractable deterministic analysis and the asymptotic performance guarantees of the proposed policies lead to several insights. The first one is that the marketing decisions of customer segmentation and price customization are effectively decoupled from the operational decisions of staffing, routing, and cross-selling. Specifically, once the set of customer segments has been identified through an appropriate marketing and statistical analysis, and their respective characteristics have been identified using observed data, (3) the firm can precompute its price customization strategy ahead of time, instead of dynamically choosing the price charged to each customer. In particular, the prices are static and are identical across customers of the same type. These prices are then fed into the operational control problem that involves staffing, routing, and cross-selling decisions.
The availability of information on customer segmentation has many important consequences, which can also be easily seen from our deterministic relaxation. To start with, roughly speaking, the center will only cross-sell to customers that generate an expected revenue that exceeds the capacity cost involved in pursuing this attempt; the expected revenue is equal to the quoted price times the probability that this customer will buy the offered product, provided that his waiting time was zero. If the center can segment its customers, then it will only cross-sell to its profitable types; if no segmentation capability is in place, then it will either cross-sell to all customers or to none, depending again on the expected profitability of these cross-selling attempts. In each case, the center will staff so as to handle all regular service requests plus the additional nominal workload generated by its expected cross-selling activities. Because the cross-selling is controllable, it can provide enough flexibility in the use of the center's capacity, which eliminates the need to add "safety staffing" as is typically done according to the "square-root" rule to stabilize the system and guarantee moderate congestion. It is possible that even though it is profitable to cross-sell in a system that segments its customers, this is not the case without segmentation. Our analysis outlines such cases. Overall, customer segmentation increases the center's profitability in two ways: first, through a more efficient use of capacity achieved by reducing the volume of cross-selling attempts that are unlikely to be profitable, and second, by customizing the price for each customer type so as to maximize the resulting expected revenue. Finally, we note that the effect of observing the customer type upon arrival, as opposed to after service has commenced, is small. This is explained by the fact that even when the system does not differentiate between types in its routing decisions and handles all external calls through a common first-come-first-served (FCFS) queue for all these types, the resulting waiting times are small; these are moderated through the dynamic cross-selling decisions of the call center and are reinforced by the customers' delay averseness.
The remainder of this paper is organized as follows. This section concludes with a brief literature survey. Section 2 describes the two models with observable types, emphasizing mostly the model where customer type is revealed once his service starts. These two models are analyzed in [section]3. Section 4 shows how the pricing problem can be treated separately from all other decisions, which is then used in [section]5 to analyze a model with no customer segmentation. Section 6 provides results from our numerical experiments. Section 7 contains concluding remarks. The electronic companion contains all of...
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