Price and Quantity Promotions for Clearance Sales

34 Pages Posted: 6 Jan 2021 Last revised: 29 Mar 2021

See all articles by Fang Liu

Fang Liu

University of Chinese Academy of Sciences; Chinese Academy of Sciences

Arvind Sainathan

Nanyang Technological University (NTU) - Nanyang Business School

Date Written: November 10, 2020


Retailers often offer price and quantity promotions to customers during clearance sales. In a price promotion, they offer discounted unit prices. In a quantity promotion, they usually offer a buy-one-get-one free (BOGO) or buy-two-get-one free (BTGO) policy. Under BOGO, customers buying one unit get the second unit free while under BTGO, those who buy two units get the third unit free. Customers may purchase multiple units and have decreasing valuations for each additional unit. We analyze which promotion policy --- unit pricing, BOGO, or BTGO --- a retailer should select. We focus on how the optimal promotion policy (OPP) changes with the quantity available for clearance. In a homogeneous market where customers have identical valuations, the retailer prefers unit pricing when the quantity is low but prefers BOGO first and then possibly BTGO as the quantity increases. In a heterogeneous market where customer valuations differ, OPP may follow similar trends as those in a homogeneous market. However, we also find two new trends: as quantity increases, OPP may either shift from (i) unit pricing to BTGO thereby making BOGO sub-optimal for any quantity, or (ii) unit pricing to BTGO first, then to BOGO, and finally again to BTGO. They occur because some customers under BTGO may get just a single unit while others get three units. The customer differentiation enables BTGO to be optimal in a heterogeneous market even for relatively lower quantities. We derive conditions under which the different trends occur in both markets. We also develop managerial insights by examining how (i) OPP is impacted by customer valuations for additional units, and (ii) inventory clearance is affected by different parameters.

Keywords: buy-one-get-one-free, quantity promotion, heterogeneous, inventory clearance

JEL Classification: M11, M21, M31

Suggested Citation

Liu, Fang and Sainathan, Arvind, Price and Quantity Promotions for Clearance Sales (November 10, 2020). Nanyang Business School Research Paper No. 21-05, Available at SSRN: or

Fang Liu

University of Chinese Academy of Sciences ( email )

No.80, Zhongguancun East Road, Haidian District
15311858853 (Phone)

Chinese Academy of Sciences ( email )

Beijing, 100190
+8615311858853 (Phone)

Arvind Sainathan (Contact Author)

Nanyang Technological University (NTU) - Nanyang Business School ( email )

Singapore, 639798

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