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The Mixed Integer Linear Bilevel Programming Problem

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  1. Lukac, Zrinka & Soric, Kristina & Rosenzweig, Visnja Vojvodic, 2008. "Production planning problem with sequence dependent setups as a bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1504-1512, June.
  2. Xiang Li & Tianyu Zhang & Liang Wang & Hongguang Ma & Xiande Zhao, 2022. "A minimax regret model for the leader–follower facility location problem," Annals of Operations Research, Springer, vol. 309(2), pages 861-882, February.
  3. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2017. "Responsive contingency planning of capacitated supply networks under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 102(C), pages 13-37.
  4. Mathur, Kanchan & Puri, M. C., 1995. "A bilevel bottleneck programming problem," European Journal of Operational Research, Elsevier, vol. 86(2), pages 337-344, October.
  5. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
  6. Zhang, Ying & Snyder, Lawrence V. & Ralphs, Ted K. & Xue, Zhaojie, 2016. "The competitive facility location problem under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 453-473.
  7. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
  8. Junlong Zhang & Osman Y. Özaltın, 2021. "Bilevel Integer Programs with Stochastic Right-Hand Sides," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1644-1660, October.
  9. Florensa, Carlos & Garcia-Herreros, Pablo & Misra, Pratik & Arslan, Erdem & Mehta, Sanjay & Grossmann, Ignacio E., 2017. "Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches," European Journal of Operational Research, Elsevier, vol. 262(2), pages 449-463.
  10. Andrea Baggio & Margarida Carvalho & Andrea Lodi & Andrea Tramontani, 2021. "Multilevel Approaches for the Critical Node Problem," Operations Research, INFORMS, vol. 69(2), pages 486-508, March.
  11. Pranjal Pragya Verma & Mohammad Reza Hesamzadeh & Steffen Rebennack & Derek Bunn & K. Shanti Swarup & Dipti Srinivasan, 2024. "Optimal investment by large consumers in an electricity market with generator market power," Computational Management Science, Springer, vol. 21(1), pages 1-56, June.
  12. Liu, Shaonan & Kong, Nan & Parikh, Pratik & Wang, Mingzheng, 2023. "Optimal trauma care network redesign with government subsidy: A bilevel integer programming approach," Omega, Elsevier, vol. 119(C).
  13. Tanınmış, Kübra & Aras, Necati & Altınel, İ. Kuban, 2022. "Improved x-space algorithm for min-max bilevel problems with an application to misinformation spread in social networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 40-52.
  14. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
  15. George Kozanidis & Eftychia Kostarelou, 2023. "An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 573-607, May.
  16. Yohan Shim & Marte Fodstad & Steven Gabriel & Asgeir Tomasgard, 2013. "A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints," Annals of Operations Research, Springer, vol. 210(1), pages 5-31, November.
  17. Tolga H. Seyhan & Lawrence V. Snyder & Ying Zhang, 2018. "A New Heuristic Formulation for a Competitive Maximal Covering Location Problem," Transportation Science, INFORMS, vol. 52(5), pages 1156-1173, October.
  18. Mintz, Yonatan & Aswani, Anil & Kaminsky, Philip & Flowers, Elena & Fukuoka, Yoshimi, 2023. "Behavioral analytics for myopic agents," European Journal of Operational Research, Elsevier, vol. 310(2), pages 793-811.
  19. Meng Xu & Guangmin Wang & Susan Grant-Muller & Ziyou Gao, 2017. "Joint road toll pricing and capacity development in discrete transport network design problem," Transportation, Springer, vol. 44(4), pages 731-752, July.
  20. Elham Ziar & Mehdi Seifbarghy & Mahdi Bashiri & Benny Tjahjono, 2023. "An efficient environmentally friendly transportation network design via dry ports: a bi-level programming approach," Annals of Operations Research, Springer, vol. 322(2), pages 1143-1166, March.
  21. Yang Zan, 1999. "Analysis of container port policy by the reaction of an equilibrium shipping market," Maritime Policy & Management, Taylor & Francis Journals, vol. 26(4), pages 369-381, October.
  22. Fischetti, Matteo & Monaci, Michele & Sinnl, Markus, 2018. "A dynamic reformulation heuristic for Generalized Interdiction Problems," European Journal of Operational Research, Elsevier, vol. 267(1), pages 40-51.
  23. Holger Heitsch & René Henrion & Thomas Kleinert & Martin Schmidt, 2022. "On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints," Journal of Global Optimization, Springer, vol. 84(3), pages 651-685, November.
  24. William M. Kroshl & Shahram Sarkani & Thomas A Mazzuchi, 2015. "Efficient Allocation of Resources for Defense of Spatially Distributed Networks Using Agent‐Based Simulation," Risk Analysis, John Wiley & Sons, vol. 35(9), pages 1690-1705, September.
  25. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.
  26. Böttger, T. & Grimm, V. & Kleinert, T. & Schmidt, M., 2022. "The cost of decoupling trade and transport in the European entry-exit gas market with linear physics modeling," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1095-1111.
  27. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
  28. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
  29. Alberto Caprara & Margarida Carvalho & Andrea Lodi & Gerhard J. Woeginger, 2016. "Bilevel Knapsack with Interdiction Constraints," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 319-333, May.
  30. Gerald Brown & Matthew Carlyle & Douglas Diehl & Jeffrey Kline & Kevin Wood, 2005. "A Two-Sided Optimization for Theater Ballistic Missile Defense," Operations Research, INFORMS, vol. 53(5), pages 745-763, October.
  31. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
  32. Onur Tavaslıoğlu & Oleg A. Prokopyev & Andrew J. Schaefer, 2019. "Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function," Operations Research, INFORMS, vol. 67(6), pages 1659-1677, November.
  33. Thomas Kleinert & Martin Schmidt, 2021. "Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 198-215, January.
  34. Zhao, Ning & You, Fengqi, 2019. "Dairy waste-to-energy incentive policy design using Stackelberg-game-based modeling and optimization," Applied Energy, Elsevier, vol. 254(C).
  35. Wen, U. P. & Huang, A. D., 1996. "A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 563-571, February.
  36. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
  37. van Ackooij, Wim & De Boeck, Jérôme & Detienne, Boris & Pan, Stefania & Poss, Michael, 2018. "Optimizing power generation in the presence of micro-grids," European Journal of Operational Research, Elsevier, vol. 271(2), pages 450-461.
  38. Styliani Avraamidou & Efstratios N. Pistikopoulos, 2019. "Multi-parametric global optimization approach for tri-level mixed-integer linear optimization problems," Journal of Global Optimization, Springer, vol. 74(3), pages 443-465, July.
  39. Martelli, Emanuele & Freschini, Marco & Zatti, Matteo, 2020. "Optimization of renewable energy subsidy and carbon tax for multi energy systems using bilevel programming," Applied Energy, Elsevier, vol. 267(C).
  40. Fu Lin & Sven Leyffer & Todd Munson, 2016. "A two-level approach to large mixed-integer programs with application to cogeneration in energy-efficient buildings," Computational Optimization and Applications, Springer, vol. 65(1), pages 1-46, September.
  41. Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
  42. Paola Cappanera & Maria Paola Scaparra, 2011. "Optimal Allocation of Protective Resources in Shortest-Path Networks," Transportation Science, INFORMS, vol. 45(1), pages 64-80, February.
  43. Deniz Aksen & Nuray Piyade & Necati Aras, 2010. "The budget constrained r-interdiction median problem with capacity expansion," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 269-291, September.
  44. Chaya Losada & M. Scaparra & Richard Church & Mark Daskin, 2012. "The stochastic interdiction median problem with disruption intensity levels," Annals of Operations Research, Springer, vol. 201(1), pages 345-365, December.
  45. Liu, Shaonan & Wang, Mingzheng & Kong, Nan & Hu, Xiangpei, 2021. "An enhanced branch-and-bound algorithm for bilevel integer linear programming," European Journal of Operational Research, Elsevier, vol. 291(2), pages 661-679.
  46. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
  47. Dempe, Stephan & Kalashnikov, Vyacheslav & Rios-Mercado, Roger Z., 2005. "Discrete bilevel programming: Application to a natural gas cash-out problem," European Journal of Operational Research, Elsevier, vol. 166(2), pages 469-488, October.
  48. Richard Oberdieck & Nikolaos A. Diangelakis & Styliani Avraamidou & Efstratios N. Pistikopoulos, 2017. "On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory," Journal of Global Optimization, Springer, vol. 69(3), pages 587-606, November.
  49. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
  50. Jonathan F. Bard & James T. Moore, 1992. "An algorithm for the discrete bilevel programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 419-435, April.
  51. Küçükaydin, Hande & Aras, Necati & Kuban AltInel, I., 2011. "Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution," European Journal of Operational Research, Elsevier, vol. 208(3), pages 206-220, February.
  52. O'Hanley, Jesse R. & Church, Richard L., 2011. "Designing robust coverage networks to hedge against worst-case facility losses," European Journal of Operational Research, Elsevier, vol. 209(1), pages 23-36, February.
  53. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
  54. Soares, Inês & Alves, Maria João & Henggeler Antunes, Carlos, 2021. "A deterministic bounding procedure for the global optimization of a bi-level mixed-integer problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 52-66.
  55. Ambrosius, Mirjam & Grimm, Veronika & Kleinert, Thomas & Liers, Frauke & Schmidt, Martin & Zöttl, Gregor, 2020. "Endogenous price zones and investment incentives in electricity markets: An application of multilevel optimization with graph partitioning," Energy Economics, Elsevier, vol. 92(C).
  56. Steven Gabriel & Sauleh Siddiqui & Antonio Conejo & Carlos Ruiz, 2013. "Solving Discretely-Constrained Nash–Cournot Games with an Application to Power Markets," Networks and Spatial Economics, Springer, vol. 13(3), pages 307-326, September.
  57. Ghavamifar, Ali & Makui, Ahmad & Taleizadeh, Ata Allah, 2018. "Designing a resilient competitive supply chain network under disruption risks: A real-world application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 87-109.
  58. Matthias Köppe & Christopher Thomas Ryan & Maurice Queyranne, 2011. "Rational Generating Functions and Integer Programming Games," Operations Research, INFORMS, vol. 59(6), pages 1445-1460, December.
  59. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
  60. Caballero, William N. & Lunday, Brian J. & Meissner, Finn, 2024. "Regulating the rebound effect in the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 660-677.
  61. Juan S. Borrero & Leonardo Lozano, 2021. "Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1570-1589, October.
  62. Blom, Danny & Smeulders, Bart & Spieksma, Frits, 2024. "Rejection-proof mechanisms for multi-agent kidney exchange," Games and Economic Behavior, Elsevier, vol. 143(C), pages 25-50.
  63. H. I. Calvete & C. Galé, 1998. "On the Quasiconcave Bilevel Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 613-622, September.
  64. Thomas Byrne, 2022. "The Stackelberg Game: responses to regular strategies," Papers 2211.06472, arXiv.org.
  65. Fakhry, Ramy & Hassini, Elkafi & Ezzeldin, Mohamed & El-Dakhakhni, Wael, 2022. "Tri-level mixed-binary linear programming: Solution approaches and application in defending critical infrastructure," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1114-1131.
  66. Hatim Djelassi & Moll Glass & Alexander Mitsos, 2019. "Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints," Journal of Global Optimization, Springer, vol. 75(2), pages 341-392, October.
  67. Bhuiyan, Tanveer Hossain & Medal, Hugh R. & Nandi, Apurba K. & Halappanavar, Mahantesh, 2021. "Risk-averse bi-level stochastic network interdiction model for cyber-security risk management," International Journal of Critical Infrastructure Protection, Elsevier, vol. 32(C).
  68. Karabulut, Ezgi & Aras, Necati & Kuban Altınel, İ., 2017. "Optimal sensor deployment to increase the security of the maximal breach path in border surveillance," European Journal of Operational Research, Elsevier, vol. 259(1), pages 19-36.
  69. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2019. "Interdiction Games and Monotonicity, with Application to Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 390-410, April.
  70. Milička, P. & Šůcha, P. & Vanhoucke, M. & Maenhout, B., 2022. "The bilevel optimisation of a multi-agent project scheduling and staffing problem," European Journal of Operational Research, Elsevier, vol. 296(1), pages 72-86.
  71. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2021. "The impact of congestion on protection decisions in supply networks under disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
  72. Losada, Chaya & Scaparra, M. Paola & O’Hanley, Jesse R., 2012. "Optimizing system resilience: A facility protection model with recovery time," European Journal of Operational Research, Elsevier, vol. 217(3), pages 519-530.
  73. Dajun Yue & Jiyao Gao & Bo Zeng & Fengqi You, 2019. "A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs," Journal of Global Optimization, Springer, vol. 73(1), pages 27-57, January.
  74. Moon, Kyungduk & Lee, Kangbok & Chopra, Sunil & Kwon, Steve, 2022. "Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy," European Journal of Operational Research, Elsevier, vol. 300(2), pages 743-754.
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