A firefly algorithm for solving competitive location-design problem: a case study

This paper aims at determining the optimal number of new facilities besides specifying both the optimal location and design level of them under the budget constraint in a competitive environment by a novel hybrid continuous and discrete firefly algorithm. A real-world application of locating new chain stores in the city of Tehran, Iran, is used and the results are analyzed. In addition, several examples have been solved to evaluate the efficiency of the proposed model and algorithm. The results demonstrate that the performed method provides good-quality results for the test problems.

[1]  Zvi Drezner,et al.  Strategic competitive location: improving existing and establishing new facilities , 2012, J. Oper. Res. Soc..

[2]  Yanfeng Ouyang,et al.  A Continuum Approximation Approach to Competitive Facility Location Design Under Facility Disruption Risks , 2013 .

[3]  M. Sayadi,et al.  A discrete firefly meta-heuristic with local search for makespan minimization in permutation flow shop scheduling problems , 2010 .

[4]  Oded Berman,et al.  Efficient solution approaches for a discrete multi-facility competitive interaction model , 2009, Ann. Oper. Res..

[5]  I. K. Altinel,et al.  Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution , 2011, Eur. J. Oper. Res..

[6]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[7]  M. Gorji Ashtiani,et al.  SEQUENTIAL COMPETITIVE FACILITY LOCATION PROBLEM IN A DISCRETE PLANAR SPACE , 2011 .

[8]  Blas Pelegrín,et al.  Solving a Huff-like competitive location and design model for profit maximization in the plane , 2007, Eur. J. Oper. Res..

[9]  Zvi Drezner,et al.  Finding the optimal solution to the Huff based competitive location model , 2004, Comput. Manag. Sci..

[10]  Feng Chu,et al.  Competitive facility location and design with reactions of competitors already in the market , 2012, Eur. J. Oper. Res..

[11]  T. Drezner,et al.  Competitive supply chain network design: An overview of classifications, models, solution techniques and applications , 2014 .

[12]  Ahmad Makui,et al.  A robust model for a leader–follower competitive facility location problem in a discrete space , 2013 .

[13]  David L. Huff,et al.  Defining and Estimating a Trading Area , 1964 .

[14]  Ahmad Makui,et al.  Huff-type competitive facility location model with foresight in a discrete space , 2011 .

[15]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[16]  Oded Berman,et al.  Competitive facility location and design problem , 2007, Eur. J. Oper. Res..

[17]  Slawomir Zak,et al.  Firefly Algorithm for Continuous Constrained Optimization Tasks , 2009, ICCCI.

[18]  Blas Pelegrín,et al.  On Nash equilibria of a competitive location-design problem , 2011, Eur. J. Oper. Res..

[19]  Amir Hossein Gandomi,et al.  Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect , 2012, Appl. Soft Comput..

[20]  José Fernández,et al.  A two-level evolutionary algorithm for solving the facility location and design (1|1)-centroid problem on the plane with variable demand , 2013, J. Glob. Optim..

[21]  José Fernández,et al.  Sensitivity analysis of a continuous multifacility competitive location and design problem , 2008 .

[22]  Xin-She Yang,et al.  Cuckoo Search and Firefly Algorithm: Theory and Applications , 2013 .

[23]  Zvi Drezner,et al.  Retail facility location under changing market conditions , 2002 .

[24]  Inmaculada García,et al.  Solving the facility location and design (1∣1)-centroid problem via parallel algorithms , 2011, The Journal of Supercomputing.

[25]  Xin-She Yang,et al.  Firefly Algorithms for Multimodal Optimization , 2009, SAGA.

[26]  A. Volgenant,et al.  Facility location: a survey of applications and methods , 1996 .

[27]  A. Gandomi,et al.  Mixed variable structural optimization using Firefly Algorithm , 2011 .

[28]  Blas Pelegrín,et al.  On the impact of spatial pattern, aggregation, and model parameters in planar Huff-type competitive location and design problems , 2009, OR Spectr..

[29]  Stefano Benati,et al.  An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem , 2003, Ann. Oper. Res..

[30]  Milad Gorji Ashtiani,et al.  Competitive location: a state-of-art review , 2016 .

[31]  Frank Plastria,et al.  Optimal location and design of a competitive facility , 2004, Math. Program..

[32]  Frank Plastria,et al.  Static competitive facility location: An overview of optimisation approaches , 2001, Eur. J. Oper. Res..

[33]  Xin-She Yang,et al.  Firefly Algorithm: Recent Advances and Applications , 2013, ArXiv.

[34]  I. K. Altinel,et al.  A leader-follower game in competitive facility location , 2012, Comput. Oper. Res..

[35]  H. Hotelling.  Stability in Competition , 1929 .