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A piecewise linearization framework for retail shelf space management models

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  • Irion, Jens
  • Lu, Jye-Chyi
  • Al-Khayyal, Faiz
  • Tsao, Yu-Chung

Abstract

Managing shelf space is critical for retailers to attract customers and optimize profits. This article develops a shelf-space allocation optimization model that explicitly incorporates essential in-store costs and considers space- and cross-elasticities. A piecewise linearization technique is used to approximate the complicated nonlinear space-allocation model. The approximation reformulates the non-convex optimization problem into a linear mixed integer programming (MIP) problem. The MIP solution not only generates near-optimal solutions for large scale optimization problems, but also provides an error bound to evaluate the solution quality. Consequently, the proposed approach can solve single category-shelf space management problems with as many products as are typically encountered in practice and with more complicated cost and profit structures than currently possible by existing methods. Numerical experiments show the competitive accuracy of the proposed method compared with the mixed integer nonlinear programming shelf-space model. Several extensions of the main model are discussed to illustrate the flexibility of the proposed methodology.

Suggested Citation

  • Irion, Jens & Lu, Jye-Chyi & Al-Khayyal, Faiz & Tsao, Yu-Chung, 2012. "A piecewise linearization framework for retail shelf space management models," European Journal of Operational Research, Elsevier, vol. 222(1), pages 122-136.
  • Handle: RePEc:eee:ejores:v:222:y:2012:i:1:p:122-136
    DOI: 10.1016/j.ejor.2012.04.021
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    References listed on IDEAS

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    1. Amrouche, Nawel & Zaccour, Georges, 2007. "Shelf-space allocation of national and private brands," European Journal of Operational Research, Elsevier, vol. 180(2), pages 648-663, July.
    2. Reyes, Pedro M. & Frazier, Gregory V., 2007. "Goal programming model for grocery shelf space allocation," European Journal of Operational Research, Elsevier, vol. 181(2), pages 634-644, September.
    3. Yang, Ming-Hsien & Chen, Wen-Cher, 1999. "A study on shelf space allocation and management," International Journal of Production Economics, Elsevier, vol. 60(1), pages 309-317, April.
    4. Lotfi, M.M. & Torabi, S.A., 2011. "A fuzzy goal programming approach for mid-term assortment planning in supermarkets," European Journal of Operational Research, Elsevier, vol. 213(2), pages 430-441, September.
    5. Abbott, Harish & Palekar, Udatta S., 2008. "Retail replenishment models with display-space elastic demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 586-607, April.
    6. Murray, Chase C. & Talukdar, Debabrata & Gosavi, Abhijit, 2010. "Joint Optimization of Product Price, Display Orientation and Shelf-Space Allocation in Retail Category Management," Journal of Retailing, Elsevier, vol. 86(2), pages 125-136.
    7. Anderson, Evan E, 1979. "An Analysis of Retail Display Space: Theory and Methods," The Journal of Business, University of Chicago Press, vol. 52(1), pages 103-118, January.
    8. Hariga, Moncer A. & Al-Ahmari, Abdulrahman & Mohamed, Abdel-Rahman A., 2007. "A joint optimisation model for inventory replenishment, product assortment, shelf space and display area allocation decisions," European Journal of Operational Research, Elsevier, vol. 181(1), pages 239-251, August.
    9. repec:dau:papers:123456789/1757 is not listed on IDEAS
    10. CAMPO, Katia & GIJSBRECHTS, Els & GOOSSENS, T. & VERHETSEL, Ann, "undated". "The impact of location-specific factors on attractiveness and performance of product categories," Working Papers 1999012, University of Antwerp, Faculty of Business and Economics.
    11. Yang, Ming-Hsien, 2001. "An efficient algorithm to allocate shelf space," European Journal of Operational Research, Elsevier, vol. 131(1), pages 107-118, May.
    12. J Irion & J-C Lu & F A Al-Khayyal & Y-C Tsao, 2011. "A hierarchical decomposition approach to retail shelf space management and assortment decisions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1861-1870, October.
    13. Hansen, Pierre & Heinsbroek, Hans, 1979. "Product selection and space allocation in supermarkets," European Journal of Operational Research, Elsevier, vol. 3(6), pages 474-484, November.
    14. Hwang, Hark & Choi, Bum & Lee, Min-Jin, 2005. "A model for shelf space allocation and inventory control considering location and inventory level effects on demand," International Journal of Production Economics, Elsevier, vol. 97(2), pages 185-195, August.
    15. Gérard P. Cachon & Christian Terwiesch & Yi Xu, 2005. "Retail Assortment Planning in the Presence of Consumer Search," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 330-346, August.
    16. Andrew Lim & Brian Rodrigues & Xingwen Zhang, 2004. "Metaheuristics with Local Search Techniques for Retail Shelf-Space Optimization," Management Science, INFORMS, vol. 50(1), pages 117-131, January.
    17. Yuxin Chen & James D. Hess & Ronald T. Wilcox & Z. John Zhang, 1999. "Accounting Profits Versus Marketing Profits: A Relevant Metric for Category Management," Marketing Science, INFORMS, vol. 18(3), pages 208-229.
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    Citations

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    Cited by:

    1. Mowrey, Corinne H. & Parikh, Pratik J. & Gue, Kevin R., 2018. "A model to optimize rack layout in a retail store," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1100-1112.
    2. Rovatti, Riccardo & D’Ambrosio, Claudia & Lodi, Andrea & Martello, Silvano, 2014. "Optimistic MILP modeling of non-linear optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 32-45.
    3. Hübner, Alexander & Kuhn, Heinrich & Kühn, Sandro, 2016. "An efficient algorithm for capacitated assortment planning with stochastic demand and substitution," European Journal of Operational Research, Elsevier, vol. 250(2), pages 505-520.
    4. Kuo, Chia-Wei & Yang, Shu-Jung Sunny, 2013. "The role of store brand positioning for appropriating supply chain profit under shelf space allocation," European Journal of Operational Research, Elsevier, vol. 231(1), pages 88-97.
    5. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    6. Hübner, Alexander & Schaal, Kai, 2017. "A shelf-space optimization model when demand is stochastic and space-elastic," Omega, Elsevier, vol. 68(C), pages 139-154.
    7. Alexander Hübner & Kai Schaal, 2017. "Effect of replenishment and backroom on retail shelf-space planning," Business Research, Springer;German Academic Association for Business Research, vol. 10(1), pages 123-156, June.
    8. Moon, Ilkyeong & Park, Kun Soo & Hao, Jing & Kim, Dongwook, 2017. "Joint decisions on product line selection, purchasing, and pricing," European Journal of Operational Research, Elsevier, vol. 262(1), pages 207-216.
    9. Leng, Mingming & Parlar, Mahmut & Zhang, Dengfeng, 2014. "Cooperative game analysis of retail space-exchange problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 393-404.
    10. Zhao, Ju & Zhou, Yong-Wu & Wahab, M.I.M., 2016. "Joint optimization models for shelf display and inventory control considering the impact of spatial relationship on demand," European Journal of Operational Research, Elsevier, vol. 255(3), pages 797-808.
    11. Amit, R.K. & Mehta, Peeyush & Tripathi, Rajeev R., 2015. "Optimal shelf-space stocking policy using stochastic dominance under supply-driven demand uncertainty," European Journal of Operational Research, Elsevier, vol. 246(1), pages 339-342.
    12. Hübner, Alexander & Schaal, Kai, 2017. "An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity effects," European Journal of Operational Research, Elsevier, vol. 261(1), pages 302-316.
    13. Schaal, Kai & Hübner, Alexander, 2018. "When does cross-space elasticity matter in shelf-space planning? A decision analytics approach," Omega, Elsevier, vol. 80(C), pages 135-152.

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