American Institute of Mathematical Sciences

Advanced
March  2020, 16(2): 653-667. doi: 10.3934/jimo.2018172

Designing a hub location and pricing network in a competitive environment

Maryam Esmaeili 1,, and  Samane Sedehzade 2,

1. 

Department of Industrial Engineering, Alzahra University, Tehran, Iran
2. 

PhD Student of Industrial Engineering, Alzahra University, Tehran, Iran

* Corresponding author:esmaeili_m@alzahra.ac.ir

Received  December 2016 Revised  June 2018 Published  October 2018

This paper models a novel mixed hub location and pricing problem in a network consists of two competitive firms with different economic positions (Stackelberg-game). The flow that reflects demand of each firm directly depends on its price (Bernard's model). The flow of each firm directly depends on both firms' prices simultaneously (Bernard's model). The firm with higher position (the leader) chooses its potential hubs while the firm in lower position (the follower) may choose either its own hub locations or the other firm's existing hub locations (the competitor's hub) through two real contracts; the airlines own and the long term usage contracts. Firms have to make decision on both the location-allocation and the price determination problems through maximizing their own profits. Moreover, firms make decisions for extending hub coverage through establishing new airline bands, gates and other infrastructures by considering extra cost. In order to evaluate the proposed model, an example derived from the CAB dataset has been solved using Imperialist Competitive Algorithm (ICA) and closed expression, respectively for the hub location-allocation and pricing decisions. Finally, a sensitivity analysis of the model is conducted to show the effect of each firm's share of fixed costs on the contract type selection.

Keywords: Competitive hub location, pricing, location contracts, Stackelberg equilibrium, Imperialist Competitive Algorithm.
Mathematics Subject Classification: Primary: 90B06; Secondary: 91A12.
Citation: Maryam Esmaeili, Samane Sedehzade. Designing a hub location and pricing network in a competitive environment. Journal of Industrial & Management Optimization, 2020, 16 (2) : 653-667. doi: 10.3934/jimo.2018172
References:
[1]

S. AbbasiParizi, M. Aminnayeri and M. Bashri, Robust solution for a min-max regret hub location problem in a fuzzy stochastic environment, Journal of Industrial and Management Optimization, 14 (2018), 1271-1295.  doi: 10.3934/jimo.2018083.  Google Scholar

[2]

N. Adler and K. Smilowitz, Hub-and-spoke network alliances and mergers: Price-location competition in the airline industry, Transportation Research, 41 (2007), 394-409.  doi: 10.1016/j.trb.2006.06.005.  Google Scholar

[3]

S. Alumur and B. Y. Kara, Network hub location problems: The state of the art, European Journal of Operational Research, 190 (2008), 1-21.  doi: 10.1016/j.ejor.2007.06.008.  Google Scholar

[4]

E. Atashpas-Gargari and C. Lucas, Imperialist competitive algorithm: An algorithm for optimization inspired by imperialist competitive, Proceeding IEEE Congress on Evolutionary computation, (2007), 4661-4667.  doi: 10.1109/CEC.2007.4425083.  Google Scholar

[5]

C. Barbot, Vertical contracts between airports and airlines: Is there a trade-off between welfare and competitiveness?, Journal of Transport Economics and Policy, 45 (2011), 227-302.   Google Scholar

[6]

J. F. Campbell, Integer programming formulations of discrete hub location problems, European Journal of Operational Research, 72 (1994), 387-405.  doi: 10.1016/0377-2217(94)90318-2.  Google Scholar

[7]

J. F. Campbell and M. O'Kelly, Twenty-five years of hub location research, Transportation Science, 46 (2012), 153-295.  doi: 10.1287/trsc.1120.0410.  Google Scholar

[8]

M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options, Journal of Industrial and Management Optimization, 3 (2007), 51-69.  doi: 10.3934/jimo.2007.3.51.  Google Scholar

[9]

I. Correia, S. Nickel and F. S. Gama, A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities, Omega, 74 (2017), 122-134.  doi: 10.1016/j.omega.2017.01.011.  Google Scholar

[10]

I. Correia, S. Nickel and F. Saldanha-da-Gama, The capacitated single-allocation hub location problem revisited: A note on a classical formulation, European Journal of Operation Research, 207 (2010), 92-96.  doi: 10.1016/j.ejor.2010.04.015.  Google Scholar

[11]

G. Dobson and P. J. Lederer, Airline scheduling and routing in a hub and spoke system, Transportation Science, 27 (1993), 209-312.  doi: 10.1287/trsc.27.3.281.  Google Scholar

[12]

H. A. Eiselt and V. Marianov, A conditional p-hub location problem with attraction functions, Computers & Operations Research, 36 (2009), 3128-3135.  doi: 10.1016/j.cor.2008.11.014.  Google Scholar

[13]

M. Esmaeili, M. Aryanezhad and P. Zeephongsekul, A game theory approach in seller-buyer supply chain, European Journal of Operational Research, 195 (2009), 442-448.  doi: 10.1016/j.ejor.2008.02.026.  Google Scholar

[14]

J. M. Faulhaber, J. J. Schulthess, A. C. Eastmond, C., P. Lewis and R. W. Block, Airport/Airline Agreements Practices and Characteristics, Transportation Research Board, 2010. Google Scholar

[15]

S. Gelareh, S. Nickel and D. Pisinger, Liner shipping hub network design in a competitive environment, Transportation Research Part E, 46 (2010), 991-1004.  doi: 10.1016/j.tre.2010.05.005.  Google Scholar

[16]

A. Lüer-Villagra and V. Marianov, A competitive hub location and pricing problem, European Journal of Operational Research, 231 (2013), 734-744.  doi: 10.1016/j.ejor.2013.06.006.  Google Scholar

[17]

A. E. Mahmutogullari and B. Y. Kara, Hub location under competition, European Journal of Operational Research, 250 (2016), 214-225.  doi: 10.1016/j.ejor.2015.09.008.  Google Scholar

[18]

V. Marianov, D. Serra and C. ReVelle, Location of hubs in a competitive environment, European Journal of Operational Research, 114 (1999), 363-371.   Google Scholar

[19]

M. Mohammadi, R. Tavakkoli-Moghaddam, A. Siadat and Y. Rahimi, A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem, Engineering Applications of Artificial Intelligence, 50 (2016), 1-19.  doi: 10.1016/j.engappai.2015.12.009.  Google Scholar

[20]

A. Niknamfar, S. T. Akhavan Niaki and S. A. Akhavan Niaki, Opposition-based learning for competitive hub location: A Bi-objective biogeography-based optimization algorithm, Knowledge-Based Systems, 128 (2017), 1-19.  doi: 10.1016/j.knosys.2017.04.017.  Google Scholar

[21]

M. E. O'Kelly, The location of interacting hub facilities, Transportation Science, 20 (1986), 65-141.  doi: 10.1287/trsc.20.2.92.  Google Scholar

[22]

M. E. O'Kelly, A quadratic integer program for the location of interacting hub facilities, European Journal of Operational Research, 32 (1987), 393-404.  doi: 10.1016/S0377-2217(87)80007-3.  Google Scholar

[23]

T. H. Oum and X. Fu, Impacts of airports on airline competition: Focus on airport performance and airport-airline vertical relations, JTRC Discussion paper, (2008), 2008-2017.   Google Scholar

[24]

M. Sasaki and M. Fukushima, Stackelberg hub location problem, Journal of the Operations Research Society of Japan, 44 (2001), 390-402.  doi: 10.15807/jorsj.44.390.  Google Scholar

[25]

S. Sedehzadeh, R. Tavakkoli-Moghaddam, A. Baboli and M. Mohammadi, Optimization of a multi-modal tree hub location network with transportation energy consumption: A fuzzy approach, Journal of Intelligent & Fuzzy Systems, 30 (2016), 43-60.  doi: 10.3233/IFS-151709.  Google Scholar

[26]

S. Sedehzadeh, R. Tavakkoli-Moghaddam and F. Jolai, New Multi-Mode and Multi-Product Hub Covering Problem: A Priority M/M/c Queue Approach, International Journal of Industrial Mathematics, 72 (2015), 139-148.   Google Scholar

[27]

A. S. Ta, L. T. An, D. Khadraoui and P. D. Tao, Solving Partitioning-Hub Location-Routing Problem using DCA, Journal of Industrial and Management Optimization, 8 (2012), 87-102.  doi: 10.3934/jimo.2012.8.87.  Google Scholar

[28]

B. Wagner, Model formulations for hub covering problems, The Journal of the Operational Research Society, 59 (2008), 932-938.  doi: 10.1057/palgrave.jors.2602424.  Google Scholar

[29]

B. Wagner, A note on "Location of hubs in a competitive environment", European Journal of Operational Research, 184 (2008), 57-62.  doi: 10.1016/j.ejor.2006.10.057.  Google Scholar

[30]

R. Zanjirani Farahani and M. Hekmatfar, Facility Location Concepts, Models, Algorithms and Case Studies, Chapter 11, 2009. Google Scholar

[31]

R. Zanjirani Farahani, M. Hekmatfar, A. Boloori Arabani and E. Nikbakhsh, Hub location problems: A review of models, classification, techniques and application, Computers & Industrial Engineering, 64 (2013), 1096-1109.  doi: 10.1016/j.cie.2013.01.012.  Google Scholar

[32]

M. Zhalechian, R. Tavakkoli-Moghaddam, Y. Rahimi and F. Jolai, An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design, Applied Soft Computing, 52 (2017), 699-713.  doi: 10.1016/j.asoc.2016.10.002.  Google Scholar

show all references

References:
[1]

S. AbbasiParizi, M. Aminnayeri and M. Bashri, Robust solution for a min-max regret hub location problem in a fuzzy stochastic environment, Journal of Industrial and Management Optimization, 14 (2018), 1271-1295.  doi: 10.3934/jimo.2018083.  Google Scholar

[2]

N. Adler and K. Smilowitz, Hub-and-spoke network alliances and mergers: Price-location competition in the airline industry, Transportation Research, 41 (2007), 394-409.  doi: 10.1016/j.trb.2006.06.005.  Google Scholar

[3]

S. Alumur and B. Y. Kara, Network hub location problems: The state of the art, European Journal of Operational Research, 190 (2008), 1-21.  doi: 10.1016/j.ejor.2007.06.008.  Google Scholar

[4]

E. Atashpas-Gargari and C. Lucas, Imperialist competitive algorithm: An algorithm for optimization inspired by imperialist competitive, Proceeding IEEE Congress on Evolutionary computation, (2007), 4661-4667.  doi: 10.1109/CEC.2007.4425083.  Google Scholar

[5]

C. Barbot, Vertical contracts between airports and airlines: Is there a trade-off between welfare and competitiveness?, Journal of Transport Economics and Policy, 45 (2011), 227-302.   Google Scholar

[6]

J. F. Campbell, Integer programming formulations of discrete hub location problems, European Journal of Operational Research, 72 (1994), 387-405.  doi: 10.1016/0377-2217(94)90318-2.  Google Scholar

[7]

J. F. Campbell and M. O'Kelly, Twenty-five years of hub location research, Transportation Science, 46 (2012), 153-295.  doi: 10.1287/trsc.1120.0410.  Google Scholar

[8]

M. L. F. Cheong, R. Bhatnagar and S. C. Graves, Logistics network design with supplier consolidation hubs and multiple shipment options, Journal of Industrial and Management Optimization, 3 (2007), 51-69.  doi: 10.3934/jimo.2007.3.51.  Google Scholar

[9]

I. Correia, S. Nickel and F. S. Gama, A stochastic multi-period capacitated multiple allocation hub location problem: Formulation and inequalities, Omega, 74 (2017), 122-134.  doi: 10.1016/j.omega.2017.01.011.  Google Scholar

[10]

I. Correia, S. Nickel and F. Saldanha-da-Gama, The capacitated single-allocation hub location problem revisited: A note on a classical formulation, European Journal of Operation Research, 207 (2010), 92-96.  doi: 10.1016/j.ejor.2010.04.015.  Google Scholar

[11]

G. Dobson and P. J. Lederer, Airline scheduling and routing in a hub and spoke system, Transportation Science, 27 (1993), 209-312.  doi: 10.1287/trsc.27.3.281.  Google Scholar

[12]

H. A. Eiselt and V. Marianov, A conditional p-hub location problem with attraction functions, Computers & Operations Research, 36 (2009), 3128-3135.  doi: 10.1016/j.cor.2008.11.014.  Google Scholar

[13]

M. Esmaeili, M. Aryanezhad and P. Zeephongsekul, A game theory approach in seller-buyer supply chain, European Journal of Operational Research, 195 (2009), 442-448.  doi: 10.1016/j.ejor.2008.02.026.  Google Scholar

[14]

J. M. Faulhaber, J. J. Schulthess, A. C. Eastmond, C., P. Lewis and R. W. Block, Airport/Airline Agreements Practices and Characteristics, Transportation Research Board, 2010. Google Scholar

[15]

S. Gelareh, S. Nickel and D. Pisinger, Liner shipping hub network design in a competitive environment, Transportation Research Part E, 46 (2010), 991-1004.  doi: 10.1016/j.tre.2010.05.005.  Google Scholar

[16]

A. Lüer-Villagra and V. Marianov, A competitive hub location and pricing problem, European Journal of Operational Research, 231 (2013), 734-744.  doi: 10.1016/j.ejor.2013.06.006.  Google Scholar

[17]

A. E. Mahmutogullari and B. Y. Kara, Hub location under competition, European Journal of Operational Research, 250 (2016), 214-225.  doi: 10.1016/j.ejor.2015.09.008.  Google Scholar

[18]

V. Marianov, D. Serra and C. ReVelle, Location of hubs in a competitive environment, European Journal of Operational Research, 114 (1999), 363-371.   Google Scholar

[19]

M. Mohammadi, R. Tavakkoli-Moghaddam, A. Siadat and Y. Rahimi, A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem, Engineering Applications of Artificial Intelligence, 50 (2016), 1-19.  doi: 10.1016/j.engappai.2015.12.009.  Google Scholar

[20]

A. Niknamfar, S. T. Akhavan Niaki and S. A. Akhavan Niaki, Opposition-based learning for competitive hub location: A Bi-objective biogeography-based optimization algorithm, Knowledge-Based Systems, 128 (2017), 1-19.  doi: 10.1016/j.knosys.2017.04.017.  Google Scholar

[21]

M. E. O'Kelly, The location of interacting hub facilities, Transportation Science, 20 (1986), 65-141.  doi: 10.1287/trsc.20.2.92.  Google Scholar

[22]

M. E. O'Kelly, A quadratic integer program for the location of interacting hub facilities, European Journal of Operational Research, 32 (1987), 393-404.  doi: 10.1016/S0377-2217(87)80007-3.  Google Scholar

[23]

T. H. Oum and X. Fu, Impacts of airports on airline competition: Focus on airport performance and airport-airline vertical relations, JTRC Discussion paper, (2008), 2008-2017.   Google Scholar

[24]

M. Sasaki and M. Fukushima, Stackelberg hub location problem, Journal of the Operations Research Society of Japan, 44 (2001), 390-402.  doi: 10.15807/jorsj.44.390.  Google Scholar

[25]

S. Sedehzadeh, R. Tavakkoli-Moghaddam, A. Baboli and M. Mohammadi, Optimization of a multi-modal tree hub location network with transportation energy consumption: A fuzzy approach, Journal of Intelligent & Fuzzy Systems, 30 (2016), 43-60.  doi: 10.3233/IFS-151709.  Google Scholar

[26]

S. Sedehzadeh, R. Tavakkoli-Moghaddam and F. Jolai, New Multi-Mode and Multi-Product Hub Covering Problem: A Priority M/M/c Queue Approach, International Journal of Industrial Mathematics, 72 (2015), 139-148.   Google Scholar

[27]

A. S. Ta, L. T. An, D. Khadraoui and P. D. Tao, Solving Partitioning-Hub Location-Routing Problem using DCA, Journal of Industrial and Management Optimization, 8 (2012), 87-102.  doi: 10.3934/jimo.2012.8.87.  Google Scholar

[28]

B. Wagner, Model formulations for hub covering problems, The Journal of the Operational Research Society, 59 (2008), 932-938.  doi: 10.1057/palgrave.jors.2602424.  Google Scholar

[29]

B. Wagner, A note on "Location of hubs in a competitive environment", European Journal of Operational Research, 184 (2008), 57-62.  doi: 10.1016/j.ejor.2006.10.057.  Google Scholar

[30]

R. Zanjirani Farahani and M. Hekmatfar, Facility Location Concepts, Models, Algorithms and Case Studies, Chapter 11, 2009. Google Scholar

[31]

R. Zanjirani Farahani, M. Hekmatfar, A. Boloori Arabani and E. Nikbakhsh, Hub location problems: A review of models, classification, techniques and application, Computers & Industrial Engineering, 64 (2013), 1096-1109.  doi: 10.1016/j.cie.2013.01.012.  Google Scholar

[32]

M. Zhalechian, R. Tavakkoli-Moghaddam, Y. Rahimi and F. Jolai, An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design, Applied Soft Computing, 52 (2017), 699-713.  doi: 10.1016/j.asoc.2016.10.002.  Google Scholar

Figure 1.  Flowchart of the imperialist competitive algorithm
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Continuous solution encoding for HLP
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Links of firms 1 and 2 on CAB dataset for different Beta
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Firm 1's profit during two contracts for different Beta
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Firm 2's profit during two contracts for different Beta
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Value and distribution of input parameters
Value & DistributionFk(hundred $ $ $)Kij hundred ($ $ $)C
${\rm{\tilde U}}$(100, 1000) ${\rm{\tilde U}}$(10, 50) $0.01 \times d$
Q (hundred $ $ $)R (K.M) $\beta$
506000.5
Table Options

Download as excel

Value & DistributionFk(hundred $ $ $)Kij hundred ($ $ $)C
${\rm{\tilde U}}$(100, 1000) ${\rm{\tilde U}}$(10, 50) $0.01 \times d$
Q (hundred $ $ $)R (K.M) $\beta$
506000.5
Table 2.  The optimal rout between nodes (1-10) and nodes (8-25)
RouteCostPriceQ
Contract 1 - Beta
0.5
Example 1 (1-10)
Firm 11-5-5-1012.5357.1624.18
Firm 21-20-20-1016.5251.4834.96
Example 2 (8-25)
Firm 18-5-5-2514.8055.7624.29
Firm 28-20-20-2514.9650.0835.12
Contract 1 - Beta 1
Example 1 (1-10)
Firm 11-5-5-1012.5375.9322.63
Firm 21-22-22-1037.9170.6232.72
Example 2 (8-25)
Firm 18-5-5-2514.8056.3324.24
Firm 28-22-5-2515.5950.6435.08
Contract 1 - Beta 1.5
Example 1 (1-10)
Firm 11-5-5-1012.5378.4422.42
Firm 21-23-23-1040.7673.1732.42
Example 2 (8-25)
Firm 18-5-5-2514.8072.0322.95
Firm 28-23-23-2533.4666.6533.18
Contract 2
Example 1 (1-10)
Firm 11-6-6-1016.6473.3122.84
Firm 21-23-6-1034.9267.9533.08
Example 2 (8-25)
Firm 18-6-6-2515.1673.0322.95
Firm 28-23-23-2533.4666.6533.18
Table Options

Download as excel

RouteCostPriceQ
Contract 1 - Beta
0.5
Example 1 (1-10)
Firm 11-5-5-1012.5357.1624.18
Firm 21-20-20-1016.5251.4834.96
Example 2 (8-25)
Firm 18-5-5-2514.8055.7624.29
Firm 28-20-20-2514.9650.0835.12
Contract 1 - Beta 1
Example 1 (1-10)
Firm 11-5-5-1012.5375.9322.63
Firm 21-22-22-1037.9170.6232.72
Example 2 (8-25)
Firm 18-5-5-2514.8056.3324.24
Firm 28-22-5-2515.5950.6435.08
Contract 1 - Beta 1.5
Example 1 (1-10)
Firm 11-5-5-1012.5378.4422.42
Firm 21-23-23-1040.7673.1732.42
Example 2 (8-25)
Firm 18-5-5-2514.8072.0322.95
Firm 28-23-23-2533.4666.6533.18
Contract 2
Example 1 (1-10)
Firm 11-6-6-1016.6473.3122.84
Firm 21-23-6-1034.9267.9533.08
Example 2 (8-25)
Firm 18-6-6-2515.1673.0322.95
Firm 28-23-23-2533.4666.6533.18
Table 3.  Result of CAB data set for the proposed model
Contract 1Contract 2
Beta = 0.5Beta = 1Beta = 1.5
Firm 1
#Hub3111
Hubs5, 20, 21556
Increase Cover radius1436, 0,181143614361565
Cost328185340926341911343243
Income676086791716794212778227
Profit347901450790452301434984
Firm 2459283
#Hub1222
Hubs205, 2221, 236, 23
Increase Cover radius00, 00, 01565, 0
Cost168092644428533346233
Income635061656739656096656286
Profit633381564095227562310053
Table Options

Download as excel

Contract 1Contract 2
Beta = 0.5Beta = 1Beta = 1.5
Firm 1
#Hub3111
Hubs5, 20, 21556
Increase Cover radius1436, 0,181143614361565
Cost328185340926341911343243
Income676086791716794212778227
Profit347901450790452301434984
Firm 2459283
#Hub1222
Hubs205, 2221, 236, 23
Increase Cover radius00, 00, 01565, 0
Cost168092644428533346233
Income635061656739656096656286
Profit633381564095227562310053
[1]

Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817
[2]

Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027
[3]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[4]

J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008
[5]

Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (317)
  • HTML views (1256)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences