Abstract
This paper deals with the problem of waste treatment pricing in the waste-to-energy (WtE) plants' network. The correct and stable estimate of gate fees should ensure efficient and financially sustainable waste energy recovery. The main contribution is a new price-setting approach, combining bilevel optimization techniques and game theory. The proposed approach dwells on two challenging steps. The first step is to solve the bilevel program, where the WtE plant on the upper level maximizes its income by setting the optimal gate fee, whereas waste producers on the lower level minimize the sum of their waste treatment costs. This optimization problem considers cities' waste production amounts, WtE plants' capacities, and locations. The novel heuristic algorithm, which can handle this bilevel program time-efficiently, is presented. It is based on the reformulations of bilevel problems of highway networks and pricing. The functionality of the heuristic has been validated using artificial waste management network scenarios. The second step is to establish the stable gate fee outcome in the waste management network, where numerous WtE plants are presented. This task is reformulated as a search for the Nash equilibrium in a normal-form game. The best-response dynamics algorithm enables establishing the game's equilibrium with numerous WtE plants and continuous strategy sets. The potential application of the proposed approach is demonstrated in the exemplary problem motivated by the Czech Republic. The found stable gate fee outcome is then used to estimate the optimal capacity of the prepared WtE facility project and ensure its financial viability in the existing waste management network.
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References
Amasuomo E, Bair J (2016) The concept of waste and waste management. J Manag Sustain 6(4):88–96. https://doi.org/10.5539/jms.v6n4p88
Anjos MF, Brtcorne L, Gomez-Herrera JA (2021) Optimal setting of time-and-level-of-use prices for an electricity supplier. Energy 225:120517. https://doi.org/10.1016/j.energy.2021.120517
Ban X, Shu L, Ferris M, Liu HX (2009) Risk averse second best toll pricing. In: William HKL, Wong SC, Lo HK (eds) Transportation and Traffic Theory 2009: Golden Jubilee: Papers selected for presentation at ISTTT18, a peer reviewed series since 1959. Springer US, Boston, MA, pp 197–218. https://doi.org/10.1007/978-1-4419-0820-9_10
Barbosa-Póvoa AP, da Silva C, Carvalho A (2018) Opportunities and challenges in sustainable supply chain: an operations research perspective. Eur J Oper Res 268(2):399–431. https://doi.org/10.1016/j.ejor.2017.10.036
Besançon M, Anjos MA, Brotcorne L, Gómez-Herrera JA (2020) A bilevel approach for optimal price-setting of time-and-level-of-use tariffs. IEEE Trans Smart Grid 11(6):5462–5465. https://doi.org/10.1109/TSG.2020.3000651
Bouhtou M, Grigoriev A, van Hoesel S, van der Kraaij AF, Spieksma FCR, Uetz M (2007) Pricing bridges to cross a river. Nav Res Logist 54(4):41–420. https://doi.org/10.1002/nav.20216
Brotcorne L, Marcotte P, Savard G (2008) Bilevel programming: the montreal school. INFOR Inform Syst Op Resarch 46(4):231–246. https://doi.org/10.3138/infor.46.4.231
Brotcorne L, Cirinei F, Marcotte P, Savard G (2011) An exact algorithm for the network pricing problem. Discret Optim 8(2):246–258. https://doi.org/10.1016/j.disopt.2010.09.003
Budnitzki A (2014) Computation of the optimal tolls on the traffic network. Eur J Oper Res 235(1):247–251. https://doi.org/10.1016/j.ejor.2013.10.059
Castelli L, Labbé M, Violin A (2013) A network pricing formulation for the revenue maximization of European air navigation service providers. Transp Res Part C Emerg Technol 33:214–226. https://doi.org/10.1016/j.trc.2012.04.013
Chen M, Bernstein DH (2004) Solving the toll design problem with multiple user groups. Transp Res Part B Methodol 38(1):61–79
Consonni S, Giugliano M, Grosso M (2005) Alternative strategies for energy recovery from municipal solid waste: Part B: Emission and cost estimates. Waste Manag 25(2):137–148. https://doi.org/10.1016/j.wasman.2004.09.006
Dempe S (2002) Foundations of bilevel programming. Springer, New York
Directive (EU) 2018/850 of the European Parliament and of the Council of 30 May 2018 amending Directive 1999/31/EC on the landfill of waste.
Eryganov I, Šomplák R, Nevrlý V, Smejkalová V, Hrabec D, Haugen KK (2020) Application of cooperative game theory in waste management. Chem Eng Trans 81:877–882. https://doi.org/10.3303/CET2081147
Farm A (2019) Pricing in practice in consumer markets. J Post Keynesian Econ 43(1):61–75. https://doi.org/10.1080/01603477.2019.1616562
Farm A (2020) Pricing in practice in consumer markets. J Post Keynesian Econ 43(1):61–75. https://doi.org/10.1080/01603477.2019.1616562
Feng C, Li Z, Shahidehpour M, Wen F, Li Q (2020) Stackelberg game based transactive pricing for optimal demand response in power distribution systems. Int J Electr Power Energy Syst 118:105764. https://doi.org/10.1016/j.ijepes.2019.105764
Fernandes CG, Ferreira CE, Franco ÁJP, Schouery RCS (2016) The envy-free pricing problem, unit-demand markets and connections with the network pricing problem. Discrete Optim 22:141–161. https://doi.org/10.1016/j.disopt.2015.09.003
Fernández-Bianco R, Arroyo JM, Alguacil N, Guan X (2016) Incorporating price-responsive demand in energy scheduling based on consumer payment minimization. IEEE Trans Smart Grid 7(2):817–826. https://doi.org/10.1109/TSG.2015.2427584
Geissdoerfer M, Savaget P, Bocken NMP, Hultink EJ (2017) The circular economy – A new sustainability paradigm? J Clean Prod 143:757–768. https://doi.org/10.1016/j.jclepro.2016.12.048
Grimm V, Orlinskaya G, Schewe L, Schmidt M, Zottl G (2021) Optimal design of retailer-prosumer electricity tariffs using bilevel optimization. Omega 102:102327. https://doi.org/10.1016/j.omega.2020.102327
Heilporn G, Labbé M, Marcotte P, Savard G (2009) A polyhedral study of the network pricing problem with connected toll arcs. Networks 55(3):234–246. https://doi.org/10.1002/net.20368
Heilporn G, Labbé M, Marcotte P, Savard G (2010) A parallel between two classes of pricing problems in transportation and marketing. J Rev Pric Manag 9:110–125. https://doi.org/10.1057/rpm.2009.39
Hrabec D, Šomplák R, Nevrlý V, Viktorin A, Pluháček M, Popela P (2020) Sustainable waste-to-energy facility location: influence of demand on energy sales. Energy 207:118257. https://doi.org/10.1016/j.energy.2020.118257
Hughes R (2017) The EU circular economy package – Life cycle thinking to life cycle law? Procedia CIRP 61:10–16. https://doi.org/10.1016/j.procir.2016.12.006
Inayati S, Endrayanto I (2016) Optimization of the toll charges by using an effective algorithm: The case in Semarang traffic network. AIP Conf Proc 1746(1):020048. https://doi.org/10.1063/1.4953973
Jammeli H, Argoubi M, Masri H (2021) A Bi-objective stochastic programming model for the household waste collection and transportation problem: case of the city of Sousse. Oper Res Int J 21:1613–1639. https://doi.org/10.1007/s12351-019-00538-5
Kalashnikov VV, Vallejo JFC, Askin R, Kalashnykova NI (2010) Comparison of algorithms for solving a bi-level toll setting problem. Int J Innov Comput Inform Control IJICIC 6(8):3529–3549
Kalashnikov VV, Herrera-Maldonado RC, Vallejo JFC, Kalashnykova NI (2016) A heuristic algorithm solving bilevel toll optimization problems. Int J Logist Manag 27(1):31–51. https://doi.org/10.1108/IJLM-06-2013-0072
Kalashnikov VV, Kalashnykova NI, Flores-Muñiz JG (2019) Toll optimization problems with quadratic costs. In: 2018 international conference on unconventional modelling, simulation and optimization - soft computing and meta heuristics – UMSO. https://doi.org/10.1109/UMSO.2018.8637246
Kleinert T, Labbé M, Ljubić I, Schmidt M (2021) A survey on mixed-integer programming techniques in bilevel optimization. EURO J Comput Optim 9:100007. https://doi.org/10.1016/j.ejco.2021.100007
Korhonen J, Honkasalo A, Seppälä J (2018) Circular economy: the concept and its limitation. Ecol Econ 143:37–46. https://doi.org/10.1016/j.ecolecon.2017.06.041
Labbé M, Violin A (2016) Bilevel programming and price setting problems. Ann Oper Res 240(1):141–169. https://doi.org/10.1007/s10479-015-2016-0
Labbé M, Marcotte P, Savard G (1998) A bilevel model of taxation and its application to optimal highway pricing. Manag Sci 44(12):1608–1622. https://doi.org/10.1287/mnsc.44.12.1608
Leal M, Ponce D, Puerto J (2020) Portfolio problems with two levels decision-makers: optimal portfolio selection with pricing decisions on transaction costs. Eur J Oper Res 284(2):712–727. https://doi.org/10.1016/j.ejor.2019.12.039
Liu J, Fan Y, Chen Z, Zheng Y (2018) Pessimistic bilevel optimization: a survey. Int J Comput Intell Syst 11(1):725–736. https://doi.org/10.2991/ijcis.11.1.56
Lubkert T, Venzke M, Vo N-V, Turau V (2018) Understanding price functions to control domestic electric water heaters for demand response. Comput Sci Res Dev 33:81–92. https://doi.org/10.1007/s00450-017-0349-4
Maravillo H, Camacho-Vallejo J-F, Puerto J, Labbé M (2020) A market regulation bilevel problem: a case study of the Mexican petrochemical industry. Omega 97:102105. https://doi.org/10.1016/j.omega.2019.08.012
Matsui A (1992) Best response dynamics and socially stable strategies. J Econ Theory 57(2):343–362. https://doi.org/10.1016/0022-0531(92)90040-O
Migdalas A (2002) Applications of game theory in finance and managerial accounting. Oper Res Int J 2:209–241. https://doi.org/10.1007/BF02936328
Mitropoulos P, Giannikos I, Mitropoulos I (2009) Exact and heuristic approaches for the locational planning of an integrated solid waste management system. Oper Res Int Jurnal 9:329–347. https://doi.org/10.1007/s12351-009-0052-8
Myklebust TGJ, Sharpe MA, Tunçel L (2016) Efficient heuristic algorithms for maximum utility product pricing problems. Comput Oper Res 69:25–39. https://doi.org/10.1016/j.cor.2015.11.013
Osička O (2016) Game theory in waste management. Master thesis, Brno University of Technology.
Owen G (2013) Game theory, 4th edn. Emerald Publishing, Bingley
Pfadt-Trilling AR, Volk TA, Fortier M-OP (2021) Climate change impacts of electricity generated at a Waste-to-Energy facility. Environ Sci Technol 55(3):1436–1445. https://doi.org/10.1021/acs.est.0c03477
Reisi M, Gabriel SA, Fahimnia B (2019) Supply chain competition on shelf space and pricing for soft drinks: a bilevel optimization approach. Int J Prod Econ 211:237–250. https://doi.org/10.1016/j.ijpe.2018.12.018
Shioda R, Tunçel L, Myklebust TGJ (2009) Maximum utility product pricing models and algorithms based on reservation price. Comput Optim Appl 48:157–198. https://doi.org/10.1007/s10589-009-9254-5
Sinha A, Malo P, Deb K (2018) A review on bilevel optimization: from classical to evolutionary approaches and applications. IEEE Trans Evol Comput 22(2):276–295. https://doi.org/10.1109/TEVC.2017.2712906
Su Y, Geunes J (2013) Multi-period price promotions in a single-supplier, multi-retailer supply chain under asymmetric demand information. Ann Oper Res 211:447–472. https://doi.org/10.1007/s10479-013-1485-2
Tanaka M, Chen Y, Siddiqui AS (2022) Regulatory jurisdiction and policy coordination: a bi-level modeling approach for performance-based environmental policy. J Oper Res Soc 73:509–524. https://doi.org/10.1080/01605682.2020.1843980
Tao L, Gao Y, Liu Y, Zhu H (2020) A rolling penalty function algorithm of real-time pricing for smart microgrids based on bilevel programming. Eng Optim 52(8):1295–1312. https://doi.org/10.1080/0305215X.2019.1642882
Tawfik C, Limbourg S (2015) Bilevel optimization in the context of intermodal pricing: state of art. Transp Proced 10:636–643. https://doi.org/10.1016/j.trpro.2015.09.017
Trachanas GP, Forouli A, Gkonis N, Doukas H (2020) Hedging uncertainty in energy efficiency strategies: a minimax regret analysis. Oper Res Int J 20:2229–2244. https://doi.org/10.1007/s12351-018-0409-y
van Hoesel S (2008) An overview of Stackelberg pricing in networks. Eur J Oper Res 189(3):1393–1402. https://doi.org/10.1016/j.ejor.2006.08.064
Velarde JLG, Vallejo JFC, Serrano GP (2015) A scatter search algorithm for solving a bilevel optimization model for determining highway tolls. Comput Sist 19(1):5–16. https://doi.org/10.13053/CyS-19-1-1916
Wang JYT, Ehrgott M, Dirks KN, Gupta A (2014) A bilevel multi-objective road pricing model for economic, environmental and health sustainability. Transp Res Proced 3:393–402. https://doi.org/10.1016/j.trpro.2014.10.020
Xu C, Zhu D (2021) On conflicts between pharmaceutical patent protection and the right to life and health based on a stackelberg game. Int J Environ Res Public Health 18:1119. https://doi.org/10.3390/ijerph18031119
Yaman C, Anil I, Alagha O (2020) Potential for greenhouse gas reduction and energy recovery from MSW through different waste management technologies. J Clean Prod 264:121432. https://doi.org/10.1016/j.jclepro.2020.121432
Yue D, You F (2015a) Bilevel programming approach for manufacturing facility investment optimization with non-cooperative suppliers and customers. In: 2015a American control conference (ACC). https://doi.org/10.1109/ACC.2015.7171942
Yue D, You F (2015b) Bilevel optimization for design and operations of non-cooperative biofuel supply chains. Chem Eng Trans 43:1309–1314. https://doi.org/10.3303/CET1543219
Zhang L, Hu Y, Cai L, Kung C-C (2021) A review of economic and environmental consequences from waste-based power generation: evidence from Taiwan. Energy Explor Exploit 39(2):571–589. https://doi.org/10.1177/0144598719900283
Zheng Y, Zhang G, Han J, Lu J (2016) Pessimistic bilevel optimization model for risk-averse production-distribution planning. Inf Sci 372:677–689. https://doi.org/10.1016/j.ins.2016.08.033
Acknowledgements
The authors gratefully acknowledge the financial support provided by the Technology Agency of the Czech Republic, Grant No. SS02030008 “Center of Environmental Research: Waste management, circular economy and environmental security”. This work was supported by FME BUT within the research project No. FSI-S-20-6187, by Grant No. GA 20-00091Y “Development of Sustainable Waste Management: Methods and Operations Research Perspectives” of the Czech Science Foundation and by the by the Tomas Bata University under project no. FSR FORD 5-6/2022-23/FLKŘ/001 Sustainability in Transport: Modern Trends and their Impact on the Environment.
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Eryganov, I., Šomplák, R., Hrabec, D. et al. Bilevel programming methods in waste-to-energy plants' price-setting game. Oper Res Int J 23, 32 (2023). https://doi.org/10.1007/s12351-023-00775-9
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DOI: https://doi.org/10.1007/s12351-023-00775-9