Multi-product Dynamic Pricing with Limited Inventories under Cascade Click Model

48 Pages Posted: 1 May 2019 Last revised: 5 Jun 2019

See all articles by Sajjad Najafi

Sajjad Najafi

University of Michigan, Stephen M. Ross School of Business

Izak Duenyas

University of Michigan, Stephen M. Ross School of Business

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Joline Uichanco

University of Michigan, Stephen M. Ross School of Business

Date Written: March 30, 2019

Abstract

We consider a multi-product dynamic pricing problem with limited inventories under the so-called Cascade Click model, which is one of the most popular click models used in practice for analyzing customers' click-and-search behavior in large-scale web analytic applications. We present three fundamental results. First, despite the highly non-linear structure of the problem, we derive a sufficiently general characterization of the optimal pricing policy and show that it has a different structure than the optimal policy under the standard pricing model. Second, we show that the optimal expected total revenues under the Cascade Click model can be upper-bounded by the objective value of an approximate deterministic pricing problem, and that this deterministic problem can be efficiently solved. This result is reminiscent of the classic upper-bound result in the standard Revenue Management (RM) setting, whose importance and impact on RM research in the past two decades cannot be overstated. Third, we show that two heuristic policies that are known to have strong performance guarantees in the standard RM setting can be properly adapted to the setting with Cascade Click model and retain their strong performance guarantees. Altogether our results show how classic results in the standard RM setting differ from that of, or can be extended to, the setting with Cascade Click model.

Suggested Citation

Najafi, Sajjad and Duenyas, Izak and Jasin, Stefanus and Uichanco, Joline, Multi-product Dynamic Pricing with Limited Inventories under Cascade Click Model (March 30, 2019). Available at SSRN: https://ssrn.com/abstract=3362921 or http://dx.doi.org/10.2139/ssrn.3362921

Sajjad Najafi

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Ave
Ann Arbor, MI 48109
United States

Izak Duenyas

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Stefanus Jasin (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Joline Uichanco

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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