Models and algorithms for competitive facility location problems with different customer behavior

Abstract

Competitive facility location problems arise in the context of two noncooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For this bi-level optimization problem we consider six different customer behavior scenarios from the literature: binary, proportional and partially binary, each combined with essential and unessential demand. The decision making for the leader and the follower depends on these scenarios. In this work we present mixed integer linear programming models for the follower problem of each scenario and use them in combination with an evolutionary algorithm to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them efficiently into similar, not yet considered ones. We present numerical results of our algorithm and compare them to so far state-of-the-art approaches from the literature. Our method shows good performance in all customer behavior scenarios and is able to outperform previous solution procedures on many occasions.

A Genetic Algorithm in Combination with a Solution Archive for Solving the Generalized Vehicle Routing Problem with Stochastic Demands

“…Several applications to different kinds of combinatorial optimization problems showed that especially for problems that have a costly solution evaluation and a compact representation, which we are exactly facing with the GVRPSD, such a complete solution archive is frequently able to boost the performance of a pure genetic algorithm significantly. Examples of such problems where solution archives have already been successfully applied are benchmark problems like NK landscapes and Royal Road functions (Raidl and Hu 2010) but also more practical relevant problems like the generalized minimum spanning tree problem (Hu and Raidl 2012a,b), the rooted delay-constrained minimum spanning tree problem (Ruthmair and Raidl 2012) and several variants of competitive facility location problems (Biesinger et al 2015a(Biesinger et al , 2014a.…”

Competitive location: a state-of-art review

“…The archive was used to store and convert already visited solutions in order to avoid costly unnecessary re-evaluations. The authors in another work considered six different customer behavior scenarios for the discrete leaderfollower problem (Biesinger et al, 2014c). They presented mixed integer linear programming models for the follower problem of each scenario and used them in combination with an evolutionary algorithm to optimize the location selection for the leader.…”

Robust Model of Discrete Competitive Facility Location Problem with Partially Proportional Rule

“…e partially binary rule is usually studied together with the binary rule and/or the proportional rule. For example, Suárez-Vega et al [21] and Biesinger et al [23] studied the competitive facility location problems in the network space and the discrete space, respectively. Six scenarios have been considered in both papers, they are combinations of two service types (essential and unessential) and three customer behavior rules (binary, proportional, and partially binary).…”