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On a Profit Maximizing Location Model

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  • Shuzhong Zhang

Abstract

In this paper we discuss a locational model with a profit-maximizing objective. The model can be illustrated by the following situation. There is a set of potential customers in a given region. A firm enters the market and wants to sell a certain product to this set of customers. The location and demand of each potential customer are assumed to be known. In order to maximize its total profit, the firm has to decide: (1) where to locate its distribution warehouse to serve the customers; (2) the price for its product. Due to existence of competition, each customer holds a reservation price for the product. This reservation price is a decreasing function in the distance to the warehouse. If the actual price is higher than the reservation price, then the customer will turn to some other supplier and hence is lost from the firm's market. The problem of the firm is to find the best location for its warehouse and the best price for its product at the same time in order to maximize the total profit. We show that under certain assumptions on the complexity counts, a special case of this problem can be solved in polynomial time. Copyright Kluwer Academic Publishers 2001

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  • Shuzhong Zhang, 2001. "On a Profit Maximizing Location Model," Annals of Operations Research, Springer, vol. 103(1), pages 251-260, March.
    • Handle: RePEc:spr:annopr:v:103:y:2001:i:1:p:251-260:10.1023/a:1012963324046
    DOI: 10.1023/A:1012963324046
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    Cited by:

    1. Fattahi, Mohammad & Mahootchi, Masoud & Govindan, Kannan & Moattar Husseini, Seyed Mohammad, 2015. "Dynamic supply chain network design with capacity planning and multi-period pricing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 81(C), pages 169-202.
    2. Shu, Jia & Li, Zhengyi & Shen, Houcai & Wu, Ting & Zhong, Weijun, 2012. "A logistics network design model with vendor managed inventory," International Journal of Production Economics, Elsevier, vol. 135(2), pages 754-761.
    3. Fernandez, Pascual & Pelegrin, Blas & Garcia Perez, Maria Dolores & Peeters, Peter H., 2007. "A discrete long-term location-price problem under the assumption of discriminatory pricing: Formulations and parametric analysis," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1050-1062, June.
    4. Aboolian, Robert & Berman, Oded & Krass, Dmitry, 2007. "Competitive facility location and design problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 40-62, October.
    5. Pan, Feng & Nagi, Rakesh, 2013. "Multi-echelon supply chain network design in agile manufacturing," Omega, Elsevier, vol. 41(6), pages 969-983.
    6. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2015. "A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 238-255.
    7. Das, Kanchan, 2011. "Integrating effective flexibility measures into a strategic supply chain planning model," European Journal of Operational Research, Elsevier, vol. 211(1), pages 170-183, May.

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