A new model of competitive location and pricing with the uniform split of the demand

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Abstract

In this paper, a new optimization model of competitive facility location and pricing is introduced. This model is an extension of the well-known (r|p)-centroid problem. In the model, two companies compete for the client’s demand. Each client has a finite budget and a finite demand. First, a company-leader determines a location of p facilities. Taking into account the location of leader’s facilities, the company-follower determines a location of its own r facilities. After that, each company assigns a price for each client. When buying a product, the client pays the price of the product and its transportation. A client buys everything from a company with lower total costs if their total costs do not exceed the budget of the client. If the cost of buying a product from both companies is the same, the demand of clients is distributed equally among them. The goal is to determine a location of leader’s facilities and set the prices in which the total income of the leader is maximal. Results about the computational complexity of the model are presented. Several special cases are considered. These cases can be divided into three categories: (1) polynomially solvable problems; (2) NP-hard problems; (3) problems related to the second level of the polynomial hierarchy. Finally, the complexity of the maxmin-2-Sat problem is discussed.

Original languageEnglish
Title of host publicationOptimization Problems and Their Applications - 7th International Conference, OPTA 2018, Revised Selected Papers
PublisherSpringer-Verlag GmbH and Co. KG
Pages16-28
Number of pages13
ISBN (Print)9783319937991
DOIs
Publication statusPublished - 1 Jan 2018
Event7th International Conference on Optimization Problems and Their Applications, OPTA 2018 - Omsk, Russian Federation
Duration: 8 Jun 201814 Jun 2018

Publication series

NameCommunications in Computer and Information Science
Volume871
ISSN (Print)1865-0929

Conference

Conference7th International Conference on Optimization Problems and Their Applications, OPTA 2018
CountryRussian Federation
CityOmsk
Period08.06.201814.06.2018

Keywords

  • Competitive location
  • Computational complexity
  • Pricing
  • Split demand

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