Robust model for discrete competitive facility location problem with the uncertainty of customer behaviors
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Robust model for discrete competitive facility location problem with the uncertainty of customer behaviors Wuyang Yu1 Received: 24 November 2018 / Accepted: 15 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Two customer behavior rules that commonly employed in the literature of competitive facility location problem are the binary rule and the proportional rule. Most of the research is based on the assumption that customers patronize facilities in accordance with one of the two customer behavior rules or their variants. But a basic problem behind this assumption is: can it be confirmed that all customers follow one of the behavior rules? Actually, the heterogeneity of customer behaviors is more common than homogeneity, at the same time, the uncertainty within customer behaviors may lead to worse results for the original optimal solutions. This is the motivation to study competitive facility location problem with customer behavior uncertainty. In this paper, a robust model for competitive facility location problem is presented at first, which is established to deal with the uncertainty within two customer behaviors. A sort-based algorithm for solving the inner sub-problem of the robust model is designed by proving its optimal solution form. Then the improved ranking-based algorithm is proposed to solve the robust model. Finally, a quasi-real case and some benchmark problems are used to demonstrate the effectiveness and efficiency of the model and algorithm. Keywords Competitive facility location · Customer behavior · Robust optimization · Ranking-based algorithm
1 Introduction Determining the locations of new facilities is a very important strategic decision for any firm that involved in a competitive market (see survey papers [1,2]). Many competitive facility location problem (CFLP) models are proposed in the literature to deal with this kind of strategic decision problems. Generally, these models can be categorized according to three features [3]: (1) competition type: static or with foresight
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Wuyang Yu [email protected] School of Management, Hangzhou Dianzi University, Zhejiang 310018, China
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W. Yu
competition; (2) location space: discrete, network, or plane space etc.; (3) customer behavior: binary, proportional, or some other customer behaviors etc. When similar goods or services offered by several facilities, the way that customers how to spend their buying powers (i.e. customer behavior) determines a facility’s success or failure. Hence, customer behavior is the foundation for an enterprise to estimate its market share in a competitive environment [4]. The two most common rules used to describe the customers’ behavior in the literature are the binary rule and the proportional rule [5]. The binary rule can be dated back to the duopoly model proposed by Hotelling [6] in a linear market, which assumes that the customer patronizes the most attractive facility. The proportional rule of customer behavior, first proposed by Huff [7], assumes that the customer splits
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