Çok Aşamalı Yer Seçim Modelleriyle Satış Mağazası Yerinin Belirlenmesi: Konya Örneği

Abstract

İşletmeler için tedarik zinciri ve lojistik ağ mekanizmasının etkin ve dinamik biçimde tasarlanması en önemli faaliyet kriterlerinden biridir. Bu kapsamda kurulacak tesis yerinin doğru biçimde seçilmesi hızlı, kolay ve düşük maliyetli ulaşım imkânı sağlaması açısından kritik bir optimizasyon modeli olarak ortaya çıkmaktadır. Çünkü talep ve/veya nüfusun yoğun olduğu bölgelerde açılacak tesis sayısı ve tesis kapsamının daha büyük olması beklenirken düşük talepli merkezlerde ise kurulacak tesis sayısının daha az olması beklenmektedir. Ayrıca, hizmet alacak bölgeler ve kurulacak tesis yerleri arasındaki mesafenin de küçüklenmesi gerekmektedir. Bu çalışmada, bir gıda işletmesine ait doğrudan satış mağazası yerlerinin optimum biçimde belirlenebilmesi için yer seçim modelleriyle-küme kapsama modeli, en büyük kapsama modeli ve p medyan modelleriyle- araştırma yapılmıştır. Öncelikle kurulacak en az sayıdaki tesisin belirlenmesi amaçlanmıştır. Ardından mesafe bazlı kapsanacak sahalar belirlenmektedir. Daha sonra belirli sayıdaki tesislerin talep ağırlıklı en küçük mesafe amacına göre konumları belirlenmektedir. Elde edilen sonuçlar birbiriyle karşılaştırılarak en uygun modelin hangisi olduğu tespit edilmiştir. Ayrıca senaryo analizleri ile ortaya çıkabilecek farklı durumlar için geliştirilen modeller sunulmuştur.

Keywords

• Optimizasyon
• yer seçim modeli
• küme kapsama
• en büyük kapsama
• p medyan modeli

Determination of Sales Store Location with Multi-Stage Location Selection Models: The Case of Konya

Abstract

Effectively and dynamically designing of the supply chain and logistics network mechanism for companies is one of the most important operation criteria. In this context, choosing the proper facility location to be established is a critical optimization model in terms of providing quick, easy and low-cost access. Because, while the number of facilities and the scope of facilities to be opened are expected to be higher in regions with high demand and/or population ratio, the number of facilities to be established in centers with low demand is expected to be lower. In addition, the distance between the regions that will receive service and the facilities to be established should be minimized. In this study, site selection models - set covering model, maximum coverage model and p-median models- were investigated to determine the optimal location of direct sales stores of a food company. First of all, it is aimed to determine the minimum number of facilities to be established. Then, the areas to be covered are determined according to the distance levels. Then, the locations of a certain number of facilities are defined according to the demand-weighted minimum distance objective function. The obtained results were compared with each other, and the most suitable model was determined. In addition, various models developed for different situations were presented and tested with scenario analysis.

Keywords

• Optimization
• site selection model
• set-covering model
• maximum-coverage model
• p-median model
• Optimization, site selection model, set-covering model, maximum-coverage model, p-median model

References

1. Avella, P. and Sassano, A. (2001) ‘On the p-Median polytope’, Mathematical Programming 2000 89:3, 89(3), pp. 395–411. doi: 10.1007/PL00011405.
2. Basti, M. (2012) ‘P-medyan Tesis Yeri Seçim Problemi ve Çözüm Yaklaşımları The P-median Facility Location Problem and Solution Approaches’, Online Academic Journal of Information Technology, 3(7), p. 7. doi: 10.5824/1309-1581.2012.2.004.x.
3. Beasley, J. E. (1993) ‘Lagrangean heuristics for location problems’, European Journal of Operational Research, 65(3), pp. 383–399. doi: 10.1016/0377-2217(93)90118-7.
4. Church, R. and ReVelle, C. (1974) ‘The maximal covering location problem’, Papers of the Regional Science Association 1974 32:1, 32(1), pp. 101–118. doi: 10.1007/BF01942293.
5. Current, J., Daskin, M. and Schiling, D. (2001) ‘Facility Location: Applications and Theory’, in Z. Drezner and H.W. Hamacher (ed.) Discrete Network Location Model, pp. 83–120. Available at: https://edisciplinas.usp.br/pluginfile.php/2455195/mod_resource/content/1/Daskin-discrete_location_models.pdf (Accessed: 3 March 2022).
6. Daskin, M. S. (1995) ‘Network and discrete location : models, algorithms, and applications’, p. 498.
7. Elloumi, S. (2008) ‘A tighter formulation of the p-median problem’, Journal of Combinatorial Optimization 2008 19:1, 19(1), pp. 69–83. doi: 10.1007/S10878-008-9162-0.
8. Fo, A. R. de A. V. and Iara da Silva Mota (2012) ‘Optimization models in the location of healthcare facilities: a real case in Brazil’, in Journal of Applied Operational Research, pp. 37–50. Available at: https://books.google.com.tr/books?hl=tr&lr=&id=bOU_EAAAQBAJ&oi=fnd&pg=PA37&dq=Fo+ve+Silva+Mota+(2012)+p+median&ots=phFqbA_3Bu&sig=JyRB8ua1NVgxhfYRtDJqxdulL2U&redir_esc=y#v=onepage&q=Fo ve Silva Mota (2012) p median&f=false (Accessed: 4 March 2022).

9. Francis, R. L., Lowe, T. J. and Tamir, A. (2000) ‘Aggregation error bounds for a class of location models’, Operations Research, 48(2), pp. 294–307. doi: 10.1287/OPRE.48.2.294.12382.
10. García, S., Labbé, M. and Marín, A. (2010) ‘Solving Large p-Median Problems with a Radius Formulation’, https://doi.org/10.1287/ijoc.1100.0418, 23(4), pp. 546–556. doi: 10.1287/IJOC.1100.0418.
11. Garfinkel, R. S., Neebe, A. W. and Rao, M. R. (1974) ‘An Algorithm for the M-Median Plant Location Problem’, https://doi.org/10.1287/trsc.8.3.217, 8(3), pp. 217–236. doi: 10.1287/TRSC.8.3.217.
12. Goetzinger, M., Brandt, T. and Neumann, D. (2012) ‘Green Facility Location – A Case Study’, AMCIS 2012 Proceedings. Available at: https://aisel.aisnet.org/amcis2012/proceedings/GreenIS/1 (Accessed: 4 March 2022).
13. Güden, H. (2021) ‘New complexity results for the p-hub median problem’, Annals of Operations Research, 298(1–2), pp. 229–247. doi: 10.1007/S10479-018-2824-0.
14. Güden, H. and Süral, H. (2019) ‘The dynamic p-median problem with mobile facilities’, Computers & Industrial Engineering, 135, pp. 615–627. doi: 10.1016/J.CIE.2019.06.024.
15. Hakimi, S. L. (1964) ‘Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph’, Operations Research, 12(3), pp. 450–459. doi: 10.1287/opre.12.3.450.
16. Hribar, M. and Daskin, M. S. (1997) ‘A dynamic programming heuristic for the P-median problem’, European Journal of Operational Research, 101(3), pp. 499–508. doi: 10.1016/S0377-2217(96)00218-4.
17. Kariv, O. and Hakimi, S. L. (1979) ‘ALGORITHM APPROACH TO NETWORK LOCATION PROBLEMS - 2. THE p-MEDIANS.’, SIAM Journal on Applied Mathematics, 37(3), pp. 539–560. doi: 10.1137/0137041.
18. Kim, J. H. and Soh, S. (2012) ‘Designing Hub-and-Spoke School Bus Transportation Network: A Case Study of Wonkwang University’, Promet - Traffic&Transportation, 24(5), pp. 389–394. doi: 10.7307/PTT.V24I5.1174.
19. Liu, C., Chen, Z. H. and Gong, Y. Y. (2013) ‘Site selection of emergency material warehouse under fuzzy environment’, Journal of Central South University 2013 20:6, 20(6), pp. 1610–1615. doi: 10.1007/S11771-013-1653-1.
20. Mohammadi, M., Torabi, S. A. and Tavakkoli-Moghaddam, R. (2014) ‘Sustainable hub location under mixed uncertainty’, Transportation Research Part E: Logistics and Transportation Review, 62, pp. 89–115. doi: 10.1016/J.TRE.2013.12.005.
21. Ndiaye, F., Ndiaye, B. M. and Ly, I. (2012) ‘Application of the p-Median Problem in School Allocation’, American Journal of Operations Research, 2012(02), pp. 253–259. doi: 10.4236/AJOR.2012.22030.
22. Panteli, A., Boutsinas, B. and Giannikos, I. (2021) ‘On solving the multiple p-median problem based on biclustering’, Operational Research, 21(1), pp. 775–799. doi: 10.1007/S12351-019-00461-9/TABLES/3.
23. Rath, S. and Gutjahr, W. J. (2014) ‘A math-heuristic for the warehouse location–routing problem in disaster relief’, Computers & Operations Research, 42, pp. 25–39. doi: 10.1016/J.COR.2011.07.016.
24. ReVelle, C. S. and Swain, R. W. (1970) ‘Central Facilities Location’, Geographical Analysis, 2(1), pp. 30–42. doi: 10.1111/J.1538-4632.1970.TB00142.X.
25. Rosing, K. E., Revelle, C. S. and Rosing-Vogelaar, H. (2017) ‘The p-Median and its Linear Programming Relaxation: An Approach to Large Problems’, https://doi.org/10.1057/jors.1979.192, 30(9), pp. 815–823. doi: 10.1057/JORS.1979.192.
26. Sule, D. R. (2001) ‘Logistics of Facility Location and Allocation’, Logistics of Facility Location and Allocation. doi: 10.1201/9780203910405.
27. Whitaker, R. A. (1984) ‘ERrata: A Fast Algorithm For The Greedy Interchange For Large-Scale Clustering And Median Location Problems’, INFOR: Information Systems and Operational Research, 22(1), pp. 70–71. doi: 10.1080/03155986.1984.11731914.
28. Zaferanieh, M., Abareshi, M. and Fathali, J. (2021) ‘The minimum information approach to the uncapacitated p-median facility location problem’, https://doi.org/10.1080/19427867.2020.1864595. doi: 10.1080/19427867.2020.1864595.