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Integrating the Number and Location of Retail Outlets on a Line with Replenishment Decisions

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  • Hussein Naseraldin

    (Joseph L. Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

  • Yale T. Herer

    (Faculty of Industrial Engineering and Management, Technion-Israel Institute of Technology, Technion City, 32000 Haifa, Israel)

Abstract

We research the management approach that quantitatively combines decisions that affect different planning horizons--namely, the strategic and operational ones--and simultaneously derive the optimal values of these decisions. The system we investigate comprises retail outlets and customers in an infinite-horizon setting. Both retail outlets and customers are located on a finite homogenous line segment. The total demand posed by customers is normally distributed with known mean and variance. To optimally design and operate such a system, we need to determine the optimal values of the number of retail outlets, the location of each retail outlet, and the replenishment inventory levels maintained at each retail outlet. We analyze the system from an expected cost point of view, considering the fixed costs of operating the retail outlets, the expected holding and shortage costs, and the expected delivery costs. We show that all decisions can be represented as a function of the number of retail outlets. Moreover, we show that the system's expected cost function is quasi-convex in the number of retail outlets. We compare our model to a model that does not integrate these decisions at once. We show the advantage of our approach on both the solution and objective spaces. We propose an exact quantification of this advantage in terms of the cost and problem parameters. In addition, we point out several managerial insights.

Suggested Citation

  • Hussein Naseraldin & Yale T. Herer, 2008. "Integrating the Number and Location of Retail Outlets on a Line with Replenishment Decisions," Management Science, INFORMS, vol. 54(9), pages 1666-1683, September.
  • Handle: RePEc:inm:ormnsc:v:54:y:2008:i:9:p:1666-1683
    DOI: 10.1287/mnsc.1070.0850
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    References listed on IDEAS

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    Cited by:

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    2. Granot, Daniel & Granot, Frieda & Raviv, Tal, 2010. "On competitive sequential location in a network with a decreasing demand intensity," European Journal of Operational Research, Elsevier, vol. 205(2), pages 301-312, September.
    3. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.
    4. Tsao, Yu-Chung & Lu, Jye-Chyi, 2012. "A supply chain network design considering transportation cost discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 401-414.
    5. Huang, Rongbing & Menezes, Mozart B.C. & Kim, Seokjin, 2012. "The impact of cost uncertainty on the location of a distribution center," European Journal of Operational Research, Elsevier, vol. 218(2), pages 401-407.
    6. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    7. Hussein Naseraldin & Yale T. Herer, 2011. "A location‐inventory model with lateral transshipments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 437-456, August.
    8. Michael K. Lim & Ho-Yin Mak & Zuo-Jun Max Shen, 2017. "Agility and Proximity Considerations in Supply Chain Design," Management Science, INFORMS, vol. 63(4), pages 1026-1041, April.

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