The Follower Competitive Location Problem with Comparison-Shopping

A medianoid problem is a competitive location problem that determines the locations of a number of new service facilities that are competing with existing facilities for service to customers. This paper studies the medianoid problem on the plane with Manhattan distance. For the medianoid problem with binary customer preferences, i.e., a case where customers choose the closest facility to satisfy their entire demand, we show that the general problem is NP-hard and present solution methods to solve various special cases in polynomial time. We also show that the problem with partially binary customer preferences can be solved with a similar approach we develop for the model with binary customer preferences.

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Using NSGA-II to solve multi-objective competitive location problem with cooperative coverage for distance-based attractiveness

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-189592 ◽

2021 ◽

pp. 1-12

Author(s):

Sheng-Chuan Wang ◽

Ta-Cheng Chen

Keyword(s):

Genetic Algorithms ◽

Optimization Model ◽

Location Problem ◽

Solution Procedure ◽

Competitive Location ◽

Multi Objective Optimization ◽

Demand Point ◽

Nsga Ii ◽

Solution Sets ◽

Multi Objective

Multi-objective competitive location problem with cooperative coverage for distance-based attractiveness is introduced in this paper. The potential facilities compete to be selected to serve all demand points which are determined by maximizing total collective attractiveness of all demand points from assigned facilities and minimizing the fixed and distance costs between all demand points and selected facilities. Facility attractiveness is represented as a coverage of the facility with full, partial and none coverage corresponding to maximum full and partial coverage radii. Cooperative coverage, which the demand point is covered by at least one facility, is also considered. The problem is formulated as a multi-objective optimization model and solution procedure based on elitist non-dominated sorting genetic algorithms (NSGA-II) is developed. Experimental example demonstrates the best non-dominated solution sets obtained by developed solution procedure. Contributions of this paper include introducing competitive location problem with facility attractiveness as a distance-based coverage of the facility, re-categorizing facility coverage classification and developing solution procedure base upon NSGA-II.

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The multiple markets competitive location problem

Kybernetes ◽

10.1108/k-09-2014-0191 ◽

2016 ◽

Vol 45 (6) ◽

pp. 854-865 ◽

Cited By ~ 8

Author(s):

Tammy Drezner ◽

Zvi Drezner ◽

Pawel J Kalczynski

Keyword(s):

Return On Investment ◽

Design Methodology ◽

Location Problem ◽

Computing Time ◽

Competitive Location ◽

Content Type ◽

Multiple Markets ◽

Computational Resources ◽

Special Case ◽

New Facilities

Purpose – The purpose of this paper is to investigate a competitive location problem to determine how to allocate a budget to expand company’s chain by either adding new facilities, expanding existing facilities, or a combination of both actions. Solving large problems may exceed the computational resources currently available. The authors treat a special case when the market can be divided into mutually exclusive sub-markets. These can be markets in cities around the globe or markets far enough from each other so that it can be assumed that customers in one market do not patronize retail facilities in another market, or that cross-patronizing is negligible. The company has a given budget to invest in these markets. Three objectives are considered: maximizing profit, maximizing return on investment (ROI), and maximizing profit subject to a minimum ROI. An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Design/methodology/approach – Since the market can be partitioned into disjoint sub-markets, the profit at each market by investing any budget in this sub-market can be calculated. The best allocation of the budget among the sub-markets can be done by either solving an integer linear program or by dynamic programming. This way, intractabole large competitive location problems can be optimally solved. Findings – An illustrative example problem of 20 sub-markets with a total of 400 facilities, 4,800 potential locations for new facilities, and 5,000 demand points is optimally solved in less than two hours of computing time. Such a problem cannot be optimally solved by existing methods. Originality/value – This model is new and was not done in previous papers.

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