American Institute of Mathematical Sciences

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

Designing a hub location and pricing network in a competitive environment

 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.

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
Flowchart of the imperialist competitive algorithm
Continuous solution encoding for HLP
Links of firms 1 and 2 on CAB dataset for different Beta
Firm 1's profit during two contracts for different Beta
Firm 2's profit during two contracts for different Beta
Value and distribution of input parameters
 Value & Distribution Fk(hundred  $) Kij hundred ($ ) C ${\rm{\tilde U}}$(100, 1000) ${\rm{\tilde U}}$(10, 50) $0.01 \times d$ Q (hundred  $) R (K.M)$\beta$50 600 0.5  Value & Distribution Fk(hundred$ ) Kij hundred ( $) C${\rm{\tilde U}}$(100, 1000)${\rm{\tilde U}}$(10, 50)$0.01 \times d$Q (hundred$ ) R (K.M) $\beta$ 50 600 0.5
The optimal rout between nodes (1-10) and nodes (8-25)
 Route Cost Price Q Contract 1 - Beta 0.5 Example 1 (1-10) Firm 1 1-5-5-10 12.53 57.16 24.18 Firm 2 1-20-20-10 16.52 51.48 34.96 Example 2 (8-25) Firm 1 8-5-5-25 14.80 55.76 24.29 Firm 2 8-20-20-25 14.96 50.08 35.12 Contract 1 - Beta 1 Example 1 (1-10) Firm 1 1-5-5-10 12.53 75.93 22.63 Firm 2 1-22-22-10 37.91 70.62 32.72 Example 2 (8-25) Firm 1 8-5-5-25 14.80 56.33 24.24 Firm 2 8-22-5-25 15.59 50.64 35.08 Contract 1 - Beta 1.5 Example 1 (1-10) Firm 1 1-5-5-10 12.53 78.44 22.42 Firm 2 1-23-23-10 40.76 73.17 32.42 Example 2 (8-25) Firm 1 8-5-5-25 14.80 72.03 22.95 Firm 2 8-23-23-25 33.46 66.65 33.18 Contract 2 Example 1 (1-10) Firm 1 1-6-6-10 16.64 73.31 22.84 Firm 2 1-23-6-10 34.92 67.95 33.08 Example 2 (8-25) Firm 1 8-6-6-25 15.16 73.03 22.95 Firm 2 8-23-23-25 33.46 66.65 33.18
 Route Cost Price Q Contract 1 - Beta 0.5 Example 1 (1-10) Firm 1 1-5-5-10 12.53 57.16 24.18 Firm 2 1-20-20-10 16.52 51.48 34.96 Example 2 (8-25) Firm 1 8-5-5-25 14.80 55.76 24.29 Firm 2 8-20-20-25 14.96 50.08 35.12 Contract 1 - Beta 1 Example 1 (1-10) Firm 1 1-5-5-10 12.53 75.93 22.63 Firm 2 1-22-22-10 37.91 70.62 32.72 Example 2 (8-25) Firm 1 8-5-5-25 14.80 56.33 24.24 Firm 2 8-22-5-25 15.59 50.64 35.08 Contract 1 - Beta 1.5 Example 1 (1-10) Firm 1 1-5-5-10 12.53 78.44 22.42 Firm 2 1-23-23-10 40.76 73.17 32.42 Example 2 (8-25) Firm 1 8-5-5-25 14.80 72.03 22.95 Firm 2 8-23-23-25 33.46 66.65 33.18 Contract 2 Example 1 (1-10) Firm 1 1-6-6-10 16.64 73.31 22.84 Firm 2 1-23-6-10 34.92 67.95 33.08 Example 2 (8-25) Firm 1 8-6-6-25 15.16 73.03 22.95 Firm 2 8-23-23-25 33.46 66.65 33.18
Result of CAB data set for the proposed model
 Contract 1 Contract 2 Beta = 0.5 Beta = 1 Beta = 1.5 Firm 1 #Hub 3 1 1 1 Hubs 5, 20, 21 5 5 6 Increase Cover radius 1436, 0,181 1436 1436 1565 Cost 328185 340926 341911 343243 Income 676086 791716 794212 778227 Profit 347901 450790 452301 434984 Firm 2 459283 #Hub 1 2 2 2 Hubs 20 5, 22 21, 23 6, 23 Increase Cover radius 0 0, 0 0, 0 1565, 0 Cost 1680 92644 428533 346233 Income 635061 656739 656096 656286 Profit 633381 564095 227562 310053
 Contract 1 Contract 2 Beta = 0.5 Beta = 1 Beta = 1.5 Firm 1 #Hub 3 1 1 1 Hubs 5, 20, 21 5 5 6 Increase Cover radius 1436, 0,181 1436 1436 1565 Cost 328185 340926 341911 343243 Income 676086 791716 794212 778227 Profit 347901 450790 452301 434984 Firm 2 459283 #Hub 1 2 2 2 Hubs 20 5, 22 21, 23 6, 23 Increase Cover radius 0 0, 0 0, 0 1565, 0 Cost 1680 92644 428533 346233 Income 635061 656739 656096 656286 Profit 633381 564095 227562 310053
 [1] Robert Stephen Cantrell, King-Yeung Lam. Competitive exclusion in phytoplankton communities in a eutrophic water column. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020361 [2] Shahede Omidi, Jafar Fathali. Inverse single facility location problem on a tree with balancing on the distance of server to clients. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021017 [3] Ömer Arslan, Selçuk Kürşat İşleyen. A model and two heuristic methods for The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021002 [4] Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest, Stefan W. Pickl. A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure. Journal of Industrial & Management Optimization, 2021, 17 (2) : 669-686. doi: 10.3934/jimo.2019128 [5] Manuel Friedrich, Martin Kružík, Ulisse Stefanelli. Equilibrium of immersed hyperelastic solids. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021003 [6] Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020047 [7] Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103 [8] Wolfgang Riedl, Robert Baier, Matthias Gerdts. Optimization-based subdivision algorithm for reachable sets. Journal of Computational Dynamics, 2021, 8 (1) : 99-130. doi: 10.3934/jcd.2021005 [9] Musen Xue, Guowei Zhu. Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items. Journal of Industrial & Management Optimization, 2021, 17 (2) : 633-648. doi: 10.3934/jimo.2019126 [10] Evelyn Sander, Thomas Wanner. Equilibrium validation in models for pattern formation based on Sobolev embeddings. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 603-632. doi: 10.3934/dcdsb.2020260 [11] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065 [12] Shasha Hu, Yihong Xu, Yuhan Zhang. Second-Order characterizations for set-valued equilibrium problems with variable ordering structures. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020164 [13] Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084 [14] Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1305-1335. doi: 10.3934/dcdsb.2020164 [15] Jingjing Wang, Zaiyun Peng, Zhi Lin, Daqiong Zhou. On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set. Journal of Industrial & Management Optimization, 2021, 17 (2) : 869-887. doi: 10.3934/jimo.2020002 [16] Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 [17] Mohammed Abdulrazaq Kahya, Suhaib Abduljabbar Altamir, Zakariya Yahya Algamal. Improving whale optimization algorithm for feature selection with a time-varying transfer function. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 87-98. doi: 10.3934/naco.2020017 [18] Cheng Peng, Zhaohui Tang, Weihua Gui, Qing Chen, Jing He. A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size. Journal of Industrial & Management Optimization, 2021, 17 (1) : 205-220. doi: 10.3934/jimo.2019107 [19] Editorial Office. Retraction: Honggang Yu, An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 901-901. doi: 10.3934/dcdss.2019060 [20] Editorial Office. Retraction: Xiaohong Zhu, Zili Yang and Tabharit Zoubir, Research on the matching algorithm for heterologous image after deformation in the same scene. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1281-1281. doi: 10.3934/dcdss.2019088

2019 Impact Factor: 1.366

Metrics

• PDF downloads (287)
• HTML views (1254)
• Cited by (0)

Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]