Zhen Liu, PhD

Zhen Liu, PhD

Assistant Professor

Phone: 630-829-6205
Office Location: Goodwin 366

BenU Faculty since 2017

Ph.D. – Northwestern University, 2007

Courses Taught
Analytical Tools for Management Decisions, Programming for Analytics, Business Analytics: Predictive/Prescriptive Analytics, Databases and Data Warehousing, Machine Learning, Analytics for Big Data.

Research Area
Quantitative Marketing, Revenue Management/Dynamic Pricing, Interface of Operations and Finance, Quantitative Finance


Current Research Projects:
Project 1 – Optimal Trials in Search for Product Information

A consumer can gain information of a product (a) prior to purchase by paying search costs, or (b) when actually owning a product, or (c) through trials (free or paid) for some period of time without and/or before purchasing the product in some industries. We consider a model where all of these three types of information gaining are available. The consumer decides (1) whether and when to start trials without paying search cost anymore, and then (2) whether and when to stop trials and purchase the product. By assuming consumers can subscribe services for some period of time, our work is an extension of Ning and Villas-Boas (2022).

Following the lines for Branco et al. (2012), we model the customer’s expected valuation as a (continuous time) Brownian motion and formulate the customer’s decision-making as a multiple optimal stopping problem. We characterize (1) the optimal stopping rules for either trial, or no trial, as a function of search costs, informativeness of each attribute, discount factor, and trial price, if any; and (2) characterize the optimal stopping rules for either purchase, or no purchase, as a function of informativeness of each attribute, discount factor, and trial and sales prices, if any. We find that optimal trial period is as a function of discount factor, and trial and sales prices, but is independent of search costs and informativeness. We discuss how the seller determines his optimal trial and sales prices, and how these prices affect the extent of the consumers’ trial and purchase decisions. We also consider discount factors, switching costs, and fremium pricing strategy (limited access to attributes but longer trial periods).

Our results justify current practice of fixed-time trial periods in SaaS (Software as a Service) industry, and allows a marketing manager in SaaS industry to infer the optimal pricing strategies.

Project 2 – Multiproduct Dynamic Pricing with Menu Costs

We consider a dynamic pricing problem where a firm which has inventories of multiple components that are used to produce multiple products over a finite time horizon. The firm is to optimally adjust the prices of its products to maximize the expected total revenue. However, menu cost, the cost associated with adjustments of prices, accounts for an important proportion of a firm’s total revenue and net margin, and therefore cannot be ignored in the context of dynamic pricing.

In this research, we model demand for each product as a price-sensitive point process whose intensity is a function of the vector of prices for the products and the time when the prices are offered. We extend Gallego and Ryzin (1997) by incorporating menu cost as fixed cost into the pricing problem following Alvarez and Lippi (2014).

Our work is the first attempt to incorporate economics literatures on menu cost, and include them in dynamic pricing. Second, our modified resolving heuristic leads to less frequency adjustments of prices, which are consistent with real-world observations (Brynjolfsson and Smith 2000, Kauffman and Lee 2004).