When Promotions Meet Operations: Cross-Selling and Its Effect on Call Center Performance

Abstract

We study cross-selling operations in call centers. The following question is addressed: How many customer-service representatives are required (staffing) and when should cross-selling opportunities be exercised (control) in a way that will maximize the expected profit of the center while maintaining a pre-specified service level target. We tackle this question by characterizing control and staffing schemes that are asymptotically optimal in the limit, as the system load grows large.Our main finding is that a threshold priority (TP) control, in which cross-selling is exercised only if the number of callers in the system is below a certain threshold, is asymptotically optimal in great generality. The asymptotic optimality of TP reduces the staffing problem to a solution of a simple deterministic problem, in one regime, and to a simple search procedure in another. We show that our joint staffing and control scheme is nearly optimal for large systems. Furthermore, it performs extremely well even for relatively small systems.

Cross-Selling in a Call Center with a Heterogeneous Customer Population

“…Moreover, when the queue is above η Λ 1 the delay sensitivity does not play any role as by the control mechanism (C), no cross-selling will be attempted until the queue goes below η Λ 1 . The proof of this result will then follow some of the results in [1]. A detailed proof of Proposition 5 would be obtained by expanding the proofs of Lemma B.1 and Proposition B.1 in [1] with the unique threshold there replaced by η Λ 1 .…”

“…The proof of this result will then follow some of the results in [1]. A detailed proof of Proposition 5 would be obtained by expanding the proofs of Lemma B.1 and Proposition B.1 in [1] with the unique threshold there replaced by η Λ 1 . We postpone the proof of this result to §E.…”

“…Note that with the exception of the customer cross-selling probability being delay sensitive, whenever the queue-length process exceeds the greatest threshold, η Λ 1 , it behaves just as the queue length process in the single class model of Armony and Gurvich [1] when it exceeds the unique threshold there. Moreover, when the queue is above η Λ 1 the delay sensitivity does not play any role as by the control mechanism (C), no cross-selling will be attempted until the queue goes below η Λ 1 .…”

“…The similar parts will be abbreviated and the reader will be referred to the technical appendix of [1] for the details. The first step is the following Lemma, the first part of which is an analogue of Lemma B.1 in [1].…”

“…Proof: The first part of the Lemma is proved just as in [1] and its proof is omitted. Since the bound is independent of the initial state, we can in particular initialize the system with its steady state distribution in which case we get the bound on this steady state distribution.…”