A leader-follower model for discrete competitive facility location problem under the partially proportional rule with a threshold
Autoři:
Wuyang Yu aff001
Působiště autorů:
School of Management, Hangzhou Dianzi University, Zhejiang, China
aff001
Vyšlo v časopise:
PLoS ONE 14(12)
Kategorie:
Research Article
prolekare.web.journal.doi_sk:
https://doi.org/10.1371/journal.pone.0225693
Souhrn
When consumers are faced with the choice of competitive chain facilities that offer exclusive services, current rules do not properly describe the behavior pattern of these consumers. To eliminate the gap between the current rules and this kind of customers behavior pattern, the partially proportional rule with a threshold is proposed in this paper. A leader-follower model for discrete competitive facility location problem is established under the partially proportional rule with a threshold. Combining with the greedy strategy and the 2-opt strategy, a heuristical algorithm (GFA) is designed to solve the follower’s problem. By embedding the algorithm (GFA), an improved ranking-based algorithm (IRGA) is proposed to solve the leader-follower model. Numerical tests show that the algorithm proposed in this paper can solve the leader-follower model for discrete competitive facility location problem effectively. The effects of different parameters on the market share captured by the leader firm and the follower firm are analyzed in detail using a quasi-real example. An interesting finding is that in some cases the leader firm does not have a first-mover advantage.
Klíčová slova:
Algorithms – Decision making – Florida – Pennsylvania – Ranking algorithms – Mississippi – New York – Louisiana
Zdroje
1. Santos-Peñate DR, Suárez-Vega R, Dorta-González P. The leader-follower location model. Networks & Spatial Economics. 2007 Mar;7(1):45–61. doi: 10.1007/s11067-006-9007-2
2. Floudas CA, Pardalos PM. Encyclopedia of optimization. Berlin, Heidelberg and New York: Springer-Verlag.; 2009.
3. ReVelle CS, Eiselt HA, Daskin MS. A bibliography for some fundamental problem categories in discrete location science. European Journal of Operational Research. 2008 Feb;184(3):817–848. doi: 10.1016/j.ejor.2006.12.044
4. Plastria F. Static competitive facility location: An overview of optimisation approaches. European Journal of Operational Research. 2001 Mar;129(3):461–470. doi: 10.1016/S0377-2217(00)00169-7
5. Ashtiani MG, Makui A, Ramezanian R. A robust model for a leader-follower competitive facility location problem in a discrete space. Applied Mathematical Modelling. 2013 Jan;37(1-2):62–71. doi: 10.1016/j.apm.2011.12.013
6. Drezner T, Drezner Z. Finding the optimal solution to the Huff based competitive location model. Computational Management Science. 2004 July;1(2):193–208. doi: 10.1007/s10287-004-0009-6
7. Drezner T, Drezner Z, Zerom D. Competitive facility location with random attractiveness. Operations Research Letters. 2018 May;46(3):312–317. doi: 10.1016/j.orl.2018.02.008
8. Campos CM, Santos-Peñate DR, Moreno JA. An exact procedure and LP formulations for the leader-follower location problem. TOP. 2010 July;18(1):97–121. doi: 10.1007/s11750-009-0117-0
9. Bilir C, Ekici SO, Ulengin F. An integrated multi-objective supply chain network and competitive facility location model. Computers & Industrial Engineering. 2017 June;108:136–148. doi: 10.1016/j.cie.2017.04.020
10. Suárez-Vega R, Santos-Peñate DR, Dorta-González P. The follower location problem with attraction thresholds. Papers in Regional Science. 2007 Mar;86(1):123–137. doi: 10.1111/j.1435-5957.2007.00104.x
11. Grohmann S, Urošević D, Carrizosa E, Mladenović N. Solving multifacility huff location models on networks using metaheuristic and exact approaches. Computers & Operations Research. 2017 Feb;78:537–546. doi: 10.1016/j.cor.2016.03.005
12. Shiode S, Yeh KY, Hsia HC. Optimal location policy for three competitive facilities. Computers & Industrial Engineering. 2012 Apr;62(3):703–707. doi: 10.1016/j.cie.2011.12.019
13. Shiode S, Drezner Z. A competitive facility location problem on a tree network with stochastic weights. European Journal of Operational Research. 2013 Aug;149(1):47–52. doi: 10.1016/S0377-2217(02)00459-9
14. Fernández J, G.-Tóth B, Redondo JL, Ortigosa PM. A planar single-facility competitive location and design problem under the multi-deterministic choice rule. Computers & Operations Research. 2017 Feb;78:305–315. doi: 10.1016/j.cor.2016.09.019
15. Fernández J, G.-Tóth B, Redondo JL, Ortigosa PM. The probabilistic customer’s choice rule with a threshold attraction value: effect on the location of competitive facilities in the plane. Computers & Operations Research. 2019 Jan;101:234–249. doi: 10.1016/j.cor.2018.08.001
16. Gilbride TJ, Allenby GM. A choice model with conjunctive, disjunctive, and compensatory screening rules. Marketing Science. 2004 June;23(3):391–406. doi: 10.1287/mksc.1030.0032
17. Hotelling H. Stability in competition. The Economic Journal. 1929 Mar;39(153):41–57. doi: 10.2307/2224214
18. Huff D. Defining and estimating a trade area. Journal of Marketing. 1964 July;28(3):34–38. doi: 10.2307/1249154
19. Hakimi SL. Location with spatial interactions, competitive locations. In Mirchandani PB, Francis RL, editors. Discrete location theory. John Wiley & Sons, New York: 1990.
20. Suárez-Vega R, Santos-Peñate D, Dorta-González P. Discretization and resolution of the (r|Xp)-medianoid problem involving quality criteria. TOP. 2004 June;12(1):111–133. doi: 10.1007/BF02578927
21. Peeters PH, Plastria F. Discretization results for the huff and pareto-huff competitive location models on networks. TOP. 1998 Dec;6(2):247–260. doi: 10.1007/BF02564790
22. Serra D, Colomé R. Consumer choice and optimal location models formulations and heuristics. Papers in Regional Science. 2001 Oct;80(4):439–464. doi: 10.1111/j.1435-5597.2001.tb01213.x
23. Beresnev V. Branch-and-bound algorithm for a competitive facility location problem. Computers & Operations Research. 2013 Aug;40(8):2062–2070. doi: 10.1016/j.cor.2013.02.023
24. Fernández J, Hendrix EM. Recent insights in Huff-like competitive facility location and design. European Journal of Operational Research. 2013 June;227(3):581–584. doi: 10.1016/j.ejor.2012.12.032
25. Fernández J, Salhi S, Tóth BG. Location equilibria for a continuous competitive facility location problem under delivered pricing. Computers & Operations Research. 2014 Jan;41:185–195. doi: 10.1016/j.cor.2013.08.004
26. Biesinger B, Hu B, Raidl G. Models and algorithms for competitive faciltity location problems with different customer behaviour. Annals of Mathematics and Artificial Intelligence. 2016 Feb;76(1-2):93–119. doi: 10.1007/s10472-014-9448-0
27. Fernández P, Pelegrín B, Lačinskas A, Žilinskas J. New heuristic algorithms for discrete competitive location problems with binary and partially binary customer behavior. Computers & Operations Research. 2017 Mar;79:12–18. doi: 10.1016/j.cor.2016.10.002
28. Qi M, Xia M, Zhang Y, Miao L. Competitive facility location problem with foresight considering service distance limitations. Computers & Industrial Engineering. 2017 Oct;112:483–491. doi: 10.1016/j.cie.2017.04.024
29. Ashtiani MG. Competitive locaiton: a state-of-art review. International Journal of Industrial Engineering Computations. 2016 Sep;7(1):1–18. doi: 10.5267/j.ijiec.2015.8.002
30. Wang X, Ouyang Y. Acontinuum approximation approach to competitive facility location design under facility disruption risks. Transportation Research Part B. 2013 Apr;50:90–103. doi: 10.1016/j.trb.2012.12.004
31. Nasiri M, Mahmoodian V, Rahbari A, Farahmand S. A modified genetic algorithm for the capacitated competitive facility location problem with the partial demand satisfaction. Computers & Industrial Engineering. 2018 Aug;124(1):435–448. doi: 10.1016/j.cie.2018.07.045
32. Kung LC, Liao WH. An approximation algorithm for a competitive facility location problem with network effects. European Journal of Operational Research. 2018 May;267(1):176–186. doi: 10.1016/j.ejor.2017.11.037
33. Casas-Ramírez M, Camacho-Vallejo J, Martínez-Salazar I. Approximating solutions to a bilevel capatitated facility location problem with customer’s patronization toward a list of preferences. Applied Mathematics and Computation. 2018 Feb;319:369–386. doi: 10.1016/j.amc.2017.03.051
34. Zhang Y, Snyder LV, Ralphs TK, Xue Z. The competitive facility location problem under disruption risks. The Transportation Research Part E. 2016 Sep;93:453–473. doi: 10.1016/j.tre.2016.07.002
35. Hansen P, Jaumard B, Savard G. New branch-and-bound rules for linear bilevel programming. SIAM Journal of Scientific and Statistical Computing. 1992 Sep;13(5):1194–1217. doi: 10.1137/0913069
36. Mirzaei E, Bashiri M, Shemirani HS. Exact algorithms for solving a bi-level location-allocation problem considering customer preferences. Journal of Industrial Engineering International. 2019 Sep;15(3):423–433. doi: 10.1007/s40092-018-0302-6
37. Alekseeva E, Kochetova N, Kochetov Y, Alexandr P. Heruistic and exact methods for the discrete (r|p)-centroid problem. Evolutionary Computation in Combinatorial Optimization. New York: Springer, 2010.
38. Daskin MS. Network and discrete location: models, algorithms, and applications. New York: Wiley, 1995.
Článok vyšiel v časopise
PLOS One
2019 Číslo 12
- Metamizol jako analgetikum první volby: kdy, pro koho, jak a proč?
- Nejasný stín na plicích – kazuistika
- Masturbační chování žen v ČR − dotazníková studie
- Úspěšná resuscitativní thorakotomie v přednemocniční neodkladné péči
- Fixní kombinace paracetamol/kodein nabízí synergické analgetické účinky
Najčítanejšie v tomto čísle
- Methylsulfonylmethane increases osteogenesis and regulates the mineralization of the matrix by transglutaminase 2 in SHED cells
- Oregano powder reduces Streptococcus and increases SCFA concentration in a mixed bacterial culture assay
- The characteristic of patulous eustachian tube patients diagnosed by the JOS diagnostic criteria
- Parametric CAD modeling for open source scientific hardware: Comparing OpenSCAD and FreeCAD Python scripts