Advertisement

Operational Research

, Volume 17, Issue 3, pp 901–919 | Cite as

Subsidy rate decisions for the printer recycling industry by bi-level optimization techniques

Original Paper
  • 125 Downloads

Abstract

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the ROC Government (in Taiwan), by using a subsidy rate decision for domestic printer recyclers. The hierarchical and interactive relation between the two parties is modeled by bi-level programming, where the RFMB serves as the upper-level decision unit, recyclers are the lower-level counterpart, and the consumer’s action is embedded in the constraints of the lower level problem. The problem is solved by the Karush–Kuhn–Tucker transformation approach. Practical data including sales of printers per year, a survey of recycling intention, recycler cost structure, and resource recycling value are used to solve the problem. The resulting solution discovers the inefficiency of the current operations of RFMB, and suggests an appropriate recycling fee and subsidy rate that balance the interests of printer manufacturers, recyclers, and the RFMB.

Keywords

Bi-level programming problem Printer recyclers Subsidy rate Recycling rate KKT approach 

Notes

Acknowledgements

The authors are grateful to Dr. Lih-Chyi Wen at Chung-Hua Institution for Economic Research, Taiwan, and Mr. Chipwu Cheng at the Recycling Fund Management Board, Environmental Protection Administration, ROC (Taiwan), for their valuable help.

References

  1. Aiyoshi E, Shimizu K (1984) A solution method for the static constrained stackelberg problem via penalty method. IEEE Trans Autom Control 29:1111–1114CrossRefGoogle Scholar
  2. Allende GB, Still G (2013) Solving bilevel programs with the KKT-approach. Math Program 138:309–332CrossRefGoogle Scholar
  3. Amendola A, Wilkinson DR (2000) Risk assessment and environmental policy making. J Hazard Mater 78:9–14CrossRefGoogle Scholar
  4. Anandalingam G (1988) A mathematical programming model of decentralized multi-level systems. J Oper Res Soc 39:1021–1033CrossRefGoogle Scholar
  5. Ashenmiller B (2009) Cash recycling, waste disposal costs, and the incomes of the working poor: evidence from California. Land Econ 85:539–551CrossRefGoogle Scholar
  6. Bard JF (1984) Optimality conditions for the bilevel programming problem. Naval Res Logist Q 31:13–26CrossRefGoogle Scholar
  7. Bard JF, Falk JE (1982) An explicit solution to the multi-level programming problem. Comput Oper Res 9:77–100CrossRefGoogle Scholar
  8. Bartl A (2014) Ways and entanglements of the waste hierarchy. Waste Manag 34:1–2CrossRefGoogle Scholar
  9. Becker GS (1968) Crime and punishment: an economic approach. J Polit Econ 76:169–217CrossRefGoogle Scholar
  10. Ben-Ayed O, Blair CE (1990) Computational difficulties of bilevel linear programming. Oper Res 38:556–560CrossRefGoogle Scholar
  11. Bialas WF, Karwan MH (1982) On two-level optimization. IEEE Trans Autom Control 27:211–214CrossRefGoogle Scholar
  12. Bialas WF, Karwan MH (1984) Two-level linear programming. Manag Sci 30:1004–1020CrossRefGoogle Scholar
  13. Bor YJ, Chien YL, Hsu E (2004) The market-incentive recycling system for waste packaging containers in Taiwan. Environ Sci Policy 7:509–523CrossRefGoogle Scholar
  14. Caulkins JP (1993) Local drug markets’ response to focused police enforcement. Oper Res 41:848–863CrossRefGoogle Scholar
  15. Chang N-B (2008) Economic and policy instrument analyses in support of the scrap tire recycling program in Taiwan. J Environ Manag 86:435–450CrossRefGoogle Scholar
  16. Chen Y, Florian M (1995) The non-linear bi-level programming problem: formulations, regularity and optimality conditions. Optimization 32:193–209CrossRefGoogle Scholar
  17. Dempe S, Kalashnikov V, Pérez-Valdés G-A, Kalashnykova N (2015) Bilevel programming problems: theory, algorithms and applications to energy networks. Springer, GermanyCrossRefGoogle Scholar
  18. Enhanced Online News (2011) Worldwide Hardcopy Peripherals Market Continues Positive Trend with 7.2% Year-Over-Year Growth in First Quarter, According to IDC, June 14. http://eon.businesswire.com/news/eon/20110614005761/en/hardcopy-peripherals/Samsung/inkjet-printers, accessed June 2016
  19. Fan K-S, Lin C-H, Chang T-C (2005) Management and performance of Taiwan’s waste recycling fund. J Air Waste Manag Assoc 55:574–582CrossRefGoogle Scholar
  20. Feichtinger G (1999) Dynamic economic models of optimal law enforcement. In: Leopold-Wildburger U et al (eds) Modelling and decisions in economics. Springer, Berlin, pp 269–293CrossRefGoogle Scholar
  21. Feichtinger G (2001) Environmental policy design and the economics of crime: some analogies in intertemporal optimization. In: Kischka P et al (eds) Models, methods and decision support for management. Springer, Berlin, pp 23–47CrossRefGoogle Scholar
  22. Fliege J, Vicente LN (2006) Multicriteria approach to bilevel optimization. J Optim Theory Appl 131:209–225CrossRefGoogle Scholar
  23. Fortuny-Amat J, McCarl B (1981) A representation and economic interpretation of a two-level programming problem. J Oper Res Soc 32:783–792CrossRefGoogle Scholar
  24. Goicoechea A, Hanson DR, Duckstein L (1982) Multiobjective decision analysis with engineering and business applications. Wiley, New YorkGoogle Scholar
  25. Kinnaman TC, Fullerton D (2000) Garbage and recycling with endogenous local policy. J Urban Econ 48:419–442CrossRefGoogle Scholar
  26. Koh A (2007) Solving transportation bi-level programs with differential evolution. In: IEEE Congress on Evolutionary Computation, pp 2243–2250Google Scholar
  27. Kohn RE (1995) Convex combinations of recycling incentives. Math Comput Model 21:13–21CrossRefGoogle Scholar
  28. Lai Y-J (1996) Hierarchical optimization: a satisfactory solution. Fuzzy Seta Syst 77:321–335CrossRefGoogle Scholar
  29. Lee S-H (2010) Standard formulation of energy saving products: printers as an example. Technical Report, Green Energy and Environment Research Laboratories (in Chinese) Google Scholar
  30. Legillon F, Liefooghe A, Talbi E-G (2012) Cobra: a cooperative covolutonary algorithm for bi-level optimization. In: IEEE CEC 2012 Congress on Evolutionary Computation, Brisbane, AustraliaGoogle Scholar
  31. Li X, Tian P, Min X (2006) A hierarchical particle swarm optimization for solving bilevel programming problems. In: ICAISC 2006, LNCS (LNAI), 4029. Springer, Berlin, pp 1169-1178Google Scholar
  32. Oduguwa V, Roy R (2002) Bi-level optimization using genetic algorithm. In: IEEE international conference on artificial intelligence systems, pp 322–327Google Scholar
  33. Onal H (1993) A modified simplex approach for solving bilevel linear programming problem. Eur J Oper Res 67:126–135CrossRefGoogle Scholar
  34. Roelfsema H (2007) Strategic delegation of environmental policy making. J Environ Econ Manag 53:270–275CrossRefGoogle Scholar
  35. Shih H-S, Cheng CB, Wen UP, Huang Y-C, Peng MY (2012) Determining a subsidy rate for Taiwan’s recycling glass industry: an application of bi-level programming. J Oper Soc 63:28–37CrossRefGoogle Scholar
  36. Sidique SF, Joshi SV, Lupi F (2010) Factors influencing the rate of recycling: an analysis of Minnesota counties. Resour Conserv Recycl 54:242–249CrossRefGoogle Scholar
  37. Sinha S, Sinha SB (2002) KKT transformation approach for multi-objective multi-level linear programming problems. Eur J Oper Res 143:19–31CrossRefGoogle Scholar
  38. Stephens B (2010) The decline of inkjet printer life expectancy, http://www.asapinkjets.com/article-printer-life-expectancy.html, accessed July 2013
  39. Talbi E-G (2013) Metaheuristics for bi-level optimization. Springer, BerlinCrossRefGoogle Scholar
  40. Wen L-C (2008) Analysis and planning of the waste electronic and information products recycling system. In: Environmental protection administration, Taiwan. Unpublished report (in Chinese) Google Scholar
  41. Yang Y (2012) Environmental policy for chemical pollution in Taiwan: the An-Shun plant case. In: Deflem M (ed) ) Disasters, hazards and law. Emerald Group Publishing, UKGoogle Scholar
  42. Yang H-L, Innes R (2007) Economic incentives and residential waste management in Taiwan: an empirical investigation. Environ Resour Econ 37:489–519CrossRefGoogle Scholar
  43. Zeleny M (1973) Compromise programming. In: Cochrane JL, Zeleny M (eds) Multiple criteria decision making. University of South Carolina Press, Columbia, pp 262–301Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Information ManagementTamkang UniversityTamsui, New TaipeiTaiwan, ROC
  2. 2.Department of Management SciencesTamkang UniversityTamsui, New TaipeiTaiwan, ROC

Personalised recommendations