Retailing with Opaque Products

40 Pages Posted: 11 Sep 2015 Last revised: 3 Oct 2018

See all articles by Adam N. Elmachtoub

Adam N. Elmachtoub

Industrial Engineering and Operations Research, Columbia University

Yehua Wei

Boston College - Carroll School of Management

Date Written: September 11, 2015


A product is said to be opaque when one or more attributes of the product are hidden until after it has been purchased. This study considers the management and value of opaque products in the context of online retail, where opaque products are commonly offered by hiding the color or style of a product. We present the first results on dynamic inventory management problems with opaque products, which features a new type of decision of which product to allocate to a customer who buys an opaque product. We consider a model where customers arrive dynamically and choose between two substitutable products and an opaque product. Ordering inventory incurs a joint replenishment cost while storing inventory incurs holding costs. We use average cost dynamic programming to analyze policies for opaque product allocation, and we use a Markov chain analysis to study the value that opaque products provide in comparison to a setting without opaque products. We also consider common discrete choice models to capture the joint effects on revenue and cost from opaque products.

Under symmetric demand, we show the optimal policy for opaque product allocation myopically balances the inventory levels of the two products. We also precisely characterize the cost savings benefit, which is on the order of the inverse of the square root of the reorder level when the opaque demand is above a relatively small threshold. Empirically, a simple ratio-matching heuristic achieves similar outcomes for scenarios with asymmetric demand. We also show that substantial cost savings can be achieved without sacrificing significant revenue to attract opaque product demand. Our results imply that selling opaque products can be done using simple policies and may yield sizable profit increases for online retailers. Moreover, this advantage only requires a relatively small fraction of customers to purchase opaque products, and does not require changing the inherent reorder and pricing policies.

Suggested Citation

Elmachtoub, Adam and Wei, Yehua, Retailing with Opaque Products (September 11, 2015). Available at SSRN: or

Adam Elmachtoub

Industrial Engineering and Operations Research, Columbia University ( email )

535F S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States


Yehua Wei (Contact Author)

Boston College - Carroll School of Management ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Register to save articles to
your library


Paper statistics

Abstract Views
PlumX Metrics

Under construction: SSRN citations while be offline until July when we will launch a brand new and improved citations service, check here for more details.

For more information