The Extension of the Spokes Model to the Streets with Unequal Length Model (Explosion Model)

Articles in Press

Document Type : Research Paper

Authors

Faculty of Economics, Urmia University, Urmia, Iran

Abstract

Locating is one of the key elements in the success and survival of industrial centers and greatly affects cost reduction of the establishment and launching of various economic activities. This study has used the streets with unequal-length model through the classic extension of the Spoke model (Lijesen and Reggiani, 2013), but with an unlimited number of streets with uneven lengths. The results show that the spoke model is a special case of the streets with unequal-length model. According to the results of this study, if the strategy of enterprises and firms is to select both price and location, there would be no balance in the game. Furthermore, the increased length of streets leads to an increased profit of enterprises, while the enterprises choose locations far from the center (the maximum differentiation) with the increased number of streets, consequently decreasing the enterprises' output. Moreover, the enterprise production rate will incline toward zero when the number of streets goes to infinity, and a complete competition outcome will be achieved.

Keywords

Main Subjects

References

Ahrens, A., & Lyons, S. (2021). Do rising rents lead to longer commutes? A gravity model of commuting flows in Ireland. Urban Studies, 58(2), 264-279. Retrived from https://www.esri.ie/system/files/publications/JA202016_0.pdf
Anderson, S. P., Goeree, J. K., & Ramer, R. (1997). Location, location, location. journal of economic theory, 77(1), 102-127. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0022053197923231
Anderson, S. P., & Neven, D. J. (1986). Spatial competition a la Cournot, charles WYPLOSZ. Retrived from https://flora.insead.edu/fichiersti_wp/Inseadwp1986/86-13.pdf
Baraklianos, I., Bouzouina, L., Bonnel, P., & Aissaoui, H. (2020). Does the accessibility measure influence the results of residential location choice modelling? Transportation, 47(3), 1147-1176. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0022053197923231
Bautista, J., & Pereira, J. (2007). A GRASP Algorithm to Solve the Unicost Set Covering Problem. Computers & Operation Research, 34 (10), 3162-3173. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S030505480500376X
Bulow, J. I., Geanakoplos, J. D., & Klemperer, P. D. (1985). Multimarket oligopoly: Strategic substitutes and complements. Journal of Political economy, 93(3), 488-511. Retrived from https://www.jstor.org/stable/1832005
Burdurlu, E., & Ejder, E. (2003). Location choice for furniture industry firms by using Analytic Hierarchy Process (AHP) method. Gazi University Journal of Science, 16(2), 369-373. Retrived from https://www.researchgate.net/publication/237658597_LOCATION_CHOICE_FOR_FURNITURE_INDUSTRY_FIRMS_BY_USING_ANALYTIC_HIERARCHY_PROCESS_AHP_METHOD
Chen, Y., & Riordan, M. H. (2007). Price and variety in the spokes model. The Economic Journal, 117(522), 897-921. Retrived from https://www.econ.queensu.ca/sites/econ.queensu.ca/files/Spokes%20Model%20Chen-Riordan.pdf
Choo, S., Lee, T., & Mokhtarian, P. L. (2007). Do transportation and communications tend to be substitutes, complements, or neither? US consumer expenditures perspective, 1984–2002. Transportation Research Record, 2010(1), 121-132. Retrived from https://www.researchgate.net/publication/46440143_Do_Transportation_and_Communications_Tend_to_Be_Substitutes_Complements_or_Neither_US_Consumer_Expenditures_Perspective_1984-2002
Mazzarol, T., & Choo, S. (2003). A study of the factors influencing the operating location decisions of small firms. Property management, 21(2), 190-208. Retrived from 225083611_A_Study_of_the_Factors_Influencing_the_Operating_Location_Decisions_of_Small_Firms
Currie, G., & Senbergs, Z. (2007, September). Exploring forced car ownership in metropolitan Melbourne. In Australasian Transport Research Forum (Vol. 200). Retrived from https://www.researchgate.net/publication/37183729_Exploring_forced_car_ownership_in_metropolitan_Melbourne
Deka, D. (2015). Relationship between Households' Housing and Transportation Expenditures: Examination from Lifestyle Perspective. Transportation Research Record, 2531(1), 26-35. Retrived from https://journals.sagepub.com/doi/abs/10.3141/2531-04
Dewita, Y., Burke, M., & Yen, B. T. (2020). The relationship between transport, housing and urban form: Affordability of transport and housing in Indonesia. Case studies on transport policy, 8(1), 252-262. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S2213624X18302256
Drezner, Z. (1995). Facility Location: A Survey of Applications and Methods (1st Ed). New York. Retrived from https://archive.org/details/isbn_9780387945453
Economides, N. (1986). Minimal and Maximal Product Differentiation in Hotellig’s   Duopoly, Economics Letters, 21 (1), 67-71. Retrived from https://www.sciencedirect.com/science/article/abs/pii/0165176586901242
Economides, N. (1989). Quality Variations and Maximal Variety Differentiation. Regional Science and Urban Economics, 19 (1), 21-29. Retrived from https://www.sciencedirect.com/science/article/pii/0166046289900318
Economides, N. (1989). Symmetric Equilibrium Existence and Optimality in Differentiated Product Markets. Journal of Economic Theory. 47 (1), 178 - 194. Retrived from https://www.sciencedirect.com/science/article/pii/0022053189901087
Gelormino, E., Melis, G., Marietta, C., & Costa, G. (2015). From built environment to health inequalities: An explanatory framework based on evidence. Preventive medicine reports, 2, 737-745. Retrived from https://www.sciencedirect.com/science/article/pii/S2211335515001217#:~:text=Results%3A%20The%20proposed%20explanatory%20framework,that%20these%20effects%20may%20be
Haas, P., Morse, S., Becker, S., Young, L., & Esling, P. (2013). The influence of spatial and household characteristics on household transportation costs. Research in Transportation Business & Management, 7, 14-26. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S2210539513000254
Campbell Jr, H. S. (2021). Income and cost of living: Are less equal places more costly? Social Science Quarterly, 102(6), 2689-2705. Retrived from https://ideas.repec.org/a/bla/socsci/v102y2021i6p2689-2705.html
Hotelling, H. (1929). Stability in Competition. Economic Journal, 39 (1929), 41– Retrived from https://www.math.toronto.edu/mccann/assignments/477/Hotelling29.pdf
Hsiao, C. Y., & Hansen, M. (2011). A passenger demand model for air transportation in a hub-and-spoke network. Transportation Research Part E: Logistics and Transportation Review, 47(6), 1112-1125. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S1366554511000718
Hu, L., & Wang, L. (2019). Housing location choices of the poor: does access to jobs matter?. Housing Studies, 34(10), 1721-1745. Retrived from https://www.tandfonline.com/doi/full/10.1080/02673037.2017.1364354
Jetzkowitz, J., Schneider, J., & Brunzel, S. (2007). Suburbanisation, mobility and the ‘good life in the country’: A lifestyle approach to the sociology of urban sprawl in Germany. Sociologia Ruralis, 47(2), 148-171. Retrived from https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9523.2007.00431.x
Kieron, J. M., Ernie, G., Teo, S., & Taojun, X. (2014). Socially-Optimal Locations of Duopoly Firms with Non-Uniform Consumer Densities. Theoretical Economics Letters, 4 (6), 431–445. Retrived from https://www.researchgate.net/publication/276495996_Socially-Optimal_Locations_of_Duopoly_Firms_with_Non-Uniform_Consumer_Densities
Kreps, D. M., & Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes, Bell Journal of Economics, 14 (2), 326-337. Retrived from https://www.sfu.ca/~wainwrig/Econ400/Kreps_Scheinkman.pdf
Lijesen, M., & Reggiani, C. (2013). Location Choice in the Spoke Model, EARIE Conference 2013. Casa de São Tiago.
Lijesen, M., & Reggiani, C. (2016, April). Market Competition and Firms Specialization Choices. In 56TH ERSA Congress 2016. Retrived from https://www.economia.unipd.it/sites/economia.unipd.it/files/spokes_Peter.pdf
Liu, Q., Hai, F., & Liu, G. (2010). A Model of Regional Logistics System with Multi-Level Hub-and-Spoke Network Based on Regional Economy. In ICLEM 2010: Logistics For Sustained Economic Development: Infrastructure, Information, Integration (pp. 894-899). Retrived from https://www.researchgate.net/publication/269085308_A_Model_of_Regional_Logistics_System_with_Multi-Level_Hub-and Spoke_Network_Based_on_Regional_Economy
Lu, Z., Wang, S., Li, X., Yang, L., Yang, D., & Wu, D. (2012). Online shop location optimization using a fuzzy multi-criteria decision model—Case study on Taobao. com. Knowledge-Based Systems, 32, 76-83. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0950705111001948
Mañez, J. A., & Waterson, M. (2001). Multiproduct firms and product differentiation: a survey. Retrived from https://www.researchgate.net/publication/23750401_Multiproduct_Firms_and_Product_Differentiation_A_Survey
Marwal, A., & Silva, E. A. (2023). City affordability and residential location choice: A demonstration using agent based model. Habitat International, 136, 102816. Retrived from https://www.sciencedirect.com/science/article/pii/S0197397523000760
Melaniphy, J. (1999). Food courts–the food operator's perspective. Retrieved from http://www.melaniphy.com/ARTIC3.htm
Michael, J. H., Teitel, J., & Granskog, J. E. (1998). Production facility site selection factors for Texas value-added wood producers. Forest Products Journal Vol. 48 (7/8) pp. 27-32. Retrived from https://research.fs.usda.gov/treesearch/20671
Neven, D. J. (1986). On Hotelling's competition with non-uniform customer distributions. Economics Letters, 21(2), 121-126. Retrived from https://www.sciencedirect.com/science/article/abs/pii/0165176586900492
O'Kelly, M. E., & Bryan, D. L. (1998). Hub Location with Flow Economies of Scale. Transportation Research Part B: Methodological, 32(8), 605–616. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0191261598000216
Redondo, J. L., Fernández, J., García, I., & Ortigosa, P. M. (2008). Parallel algorithms for continuous competitive location problems. Optimisation Methods & Software, 23(5), 779-791. Retrived from https://www.tandfonline.com/doi/abs/10.1080/10556780802402564
Reggiani, C. (2009). Optimal differentiation and spatial competition: The spoke model with product delivery. Discussion Papers in Economics, (13). Retrived from https://ideas.repec.org/p/yor/yorken/09-13.html
Rhim, H., Ho, T. H., & Karmarkar, U. S. (2003). Competitive location, production, and market selection. European journal of operational Research, 149(1), 211-228. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0377221702004459
Salimian, S., Shahbazi, K., & NAZAR, M. M. B. (2023). Locating The Sale Agents In Spoke Model Through Uniform Distribution Of Consumers. Journal of Economic Sciences: Theory & Practice, 80(1).  Retrived from https://www.ecosciences.edu.az/view.php?lang=en&menu=journal&id=436
Shahbazi, K., & Salimian, S. (2017). The Expansion of Location Theories of Firms and Products’ Consistency Using Triangular Distribution Approach. Iranian Economic Review, 21(3), 497-518. Retrived from https://ier.ut.ac.ir/article_62937.html
Shaked, A., & Sutton, J. (1982). Relaxing price competition through product differentiation. The review of economic studies, 49(1), 3-13. Retrived from https://www.jstor.org/stable/2297136
Shy, O. (1996). Industrial Economics: Theory and Applications. Retrived from https://pdfcoffee.com/oz-shy-industrial-organization-theory-and-applications-pdf-free.html
Tartavulea, R. I. (2015). Model for determining the optimum location for performance improvement in supply-chain strategies. European journal of interdisciplinary studies, 7(1), 39. Retrived from https://ejist.ro/files/pdf/392.pdf
Vandenbosch, M. B., & Weinberg, C. B. (1995). Product and price competition in a two-dimensional vertical differentiation model. Marketing science, 14(2), 224-249. Retrived from https://pubsonline.informs.org/doi/10.1287/mksc.14.2.224
Viggers, H., & Howden-Chapman, P. (2011). Urban form, public transport and mortgagee sales. Growth misconduct? Avoiding sprawl and improving urban intensification in New Zealand, 159-177. Retrived from https://www.researchgate.net/publication/313199643_Urban_form_public_transport_and_mortgagee_sales
Vinay.  S., & Chakra, V. (2005). Industrial Location and Spatial in Equal IML Theory and Evidence from India. Review of Development Economics, 9(1), 47–65. Retrived from https://www.researchgate.net/publication/4995273_Industrial_Location_and_Spatial_Inequality_Theory_and_Evidence_from_India
Yang, J., & Lee, H. (1997). An AHP decision model for facility location selection. Facilities, 15(9/10), 241-254. Retrived from https://www.emerald.com/f/article-abstract/15/9-10/241/242122/An-AHP-decision-model-for-facility-location?redirectedFrom=fulltext
Wongsak, S. (2011). Logistics Strategy for Agricultural Products in Thailand; Case Study: Hub and Spoke System Applied within the Shrimp Industry. Cuvillier Verlag. Retrived from https://books.google.com/books/about/Logistics_Strategy_for_Agricultural_Prod.html?id=P9_-DwAAQBAJ
Zhao, C., Nielsen, T. A. S., Olafsson, A. S., Carstensen, T. A., & Meng, X. (2018).  Urban form, demographic and socio-economic correlates of walking, cycling, and e-biking: Evidence from eight neighborhoods in Beijing. Transport Policy, 64, 102-112. Retrived from https://www.sciencedirect.com/science/article/abs/pii/S0967070X17300392
Iranian Economic Review

Articles in Press, Accepted Manuscript
Available Online from 01 September 2025

Files

Share

How to cite

Statistics