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The retail space-exchange problem with pricing and space allocation decisions
Production and Operations Management
  • Mingming LENG, Department of Computing and Decision Sciences, Faculty of Business, Lingnan University
  • Mahmut PARLAR, McMaster University
  • Dengfeng ZHANG, Shenzhen Development Bank, Shenzhen
Document Type
Journal article
Publication Date
Wiley-Blackwell Publishing, Inc.
  • retail space-exchange; price; space allocation; Hotelling model; Nash equilibrium

We consider retail space-exchange problems where two retailers exchange shelf space to increase accessibility to more of their consumers in more locations without opening new stores. Using the Hotelling model, we find two retailers’ optimal prices, given their host and guest space in two stores under the space-exchange strategy. Next, using the optimal space-dependent prices, we analyze a non-cooperative game, where each retailer makes a space allocation decision for the retailer's own store. We show that the two retailers will implement such a strategy in the game, if and only if their stores are large enough to serve more than one-half of their consumers. Nash equilibrium for the game exists, and its value depends on consumers’ utilities and trip costs as well as the total available space in each retailer's store. Moreover, as a result of the space-exchange strategy, each retailer's prices in two stores are both higher than the retailer's price before the space exchange, but they may or may not be identical.

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Copyright © 2012 Production and Operations Management Society. Access to external full text or publisher's version may require subscription.
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Citation Information
Leng. M., Parlar, M., & Zhang, D. (2013). The retail space-exchange problem with pricing and space allocation decisions. Production and Operations Management, 22(1), 189-202. doi: 10.1111/j.1937-5956.2012.01335.x