A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints

European Journal of Operational Research

Volumn 236, Issue 1, 2014, Pages 340-350

  Toyasaki, Fuminori ^a   Daniele, Patrizia ^b   Wakolbinger, Tina ^c  

^a YORK UNIVERSITY   (Canada)

^b UNIVERSITY OF CATANIA   (Italy)

^c VIENNA UNIVERSITY OF ECONOMICS AND BUSINESS   (Austria)

Author keywords

Computer electronics; Environment; Nonlinear programming; Reverse logistics; Sustainable product design; Variational inequality

Indexed keywords

CONSTRAINT QUALIFICATION; ENVIRONMENT; NON-LINEAR CONSTRAINTS; REVERSE LOGISTICS; SUSTAINABLE PRODUCT DESIGNS; TRANSPORTATION NETWORK; VARIATIONAL INEQUALITIES; VARIATIONAL INEQUALITY PROBLEMS;

NONLINEAR PROGRAMMING; PRODUCT DESIGN; SUPPLY CHAINS; SUSTAINABLE DEVELOPMENT;

VARIATIONAL TECHNIQUES;

EID: 84900568037     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2013.12.006     Document Type: Article

References (51)

1. L. Ambrosio, L. Caffarelli, and A. Maugeri Preface: A beautiful walk in the way of the understanding Discrete Discrete and Continuous Dynamical Systems 31 4 2011 I VI
2. Atasu, A.; Toktay, B.; Van Wassenhove, L. N. (2008). The impact of collection cost structure on reverse channel choice. Working paper.
3. M.S. Bazaraa, H.D. Sherali, and C.M. Shetty Nonlinear programming: Theory and algorithm 2nd ed. 1993 John Wiley & Sons Inc New York
4. G. Bigi, and M. Passacantando Gap functions and penalization for solving equilibrium problems with nonlinear constraints Computational Optimization and Applications 53 2012 323 346
5. G. Bigi, M. Castellani, M. Pappalardo, and M. Passacantando Existence and solution methods for equilibria European Journal of Operational Research 227 2013 1 11
6. J. Boon, J.A. Isaacs, and S. Gupta Economic sensitivity for end of life planning and processing of personal computers Journal of Electronics Manufacturing 11 1 2002 81 93
7. P. Daniele, A. Maugeri, and W. Oettli Variational inequalities and time-dependent traffic equilibria Comptes Rendus de l'Acadmie des Sciences - Series I - Mathematics 326 1998 1059 1062
8. P. Daniele, A. Maugeri, and W. Oettli Time-dependent traffic equilibria Journal of Optimization Theory and Applications 103 1999 543 555
9. P. Daniele Variational inequalities for static equilibrium market F. Giannessi, A. Maugeri, P. Pardalos, Lagrangean function and duality, in equilibrium problems: Nonsmooth optimization and variational inequality models 2001 Kluwer Academic Publishers 43 58
10. P. Daniele Dynamic networks and evolutionary variational inequalities 2006 Edward Elgar Publishing Cheltenham, UK
11. P. Dupuis, and A. Nagurney Dynamical systems and variational inequalities Annals of Operations Research 44 1 1993 7 42
12. Edge: Work-Group Computing Report (2000). Dell reports $ 6.8 billion in revenue, pre-share earnings of 16 cents. Continued growth in internet infrastructure sales, nonsystem revenue highlight fiscal Q4 company financial information [Accessed 25 March 2011].
13. Electronic Product Stewardship Canada (2009). Design for environment. < http://www.epsc.ca > [Accessed 5 February 2013].
14. Electronic Takeback Coalition (2013). State legislation. < http://www.electronicstakeback.com > [Accessed 27 August 2012].
15. EPA, U.S. Environmental Protection Agency, Office of Resource Conservation and Recovery (2011). Electronics waste management in the United States through 2009, May 2011, EPA 530-R-11-002.
16. F. Facchinei, and J.S. Pang Finite-dimensional variational inequalities and complementarity problems 2003 Springer Berlin
17. G. Fichera Sul problema elastico di Signorini con ambigue condizioni al contorno, Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche Matematiche e Naturali 8 3 1963 138 142
18. D. Hammond, and P. Beullens Closed-loop supply chain network equilibrium under legislation European Journal of Operational Research 183 2 2007 895 908
19. J. Jahn Introduction to the theory of nonlinear optimization 1996 Springer-Verlag Berlin
20. Kenney, B. (2007). Dell, HP meet recycling targets. Industry week, August 7, 2007.
21. D. Kinderlehrer, and G. Stampacchia An introduction to variational inequalities and their applications 1980 Academic Press New York
22. J.L. Lions, and G. Stampacchia Variational inequalities Communications on Pure and Applied Mathematics 22 1967 493 519
23. A. Maugeri, and F. Raciti On existence theorems for monotone and nonmonotone variational inequalities Journal of Convex Analysis 16 3-4 2009 899 911
24. D. Matsypura, A. Nagurney, and Z. Liu Modeling of electric power supply chain networks with fuel suppliers via variational inequalities International Journal of Emerging Electric Power Systems 8 1 2007 Article 5
25. M. Yu, and A. Nagurney Competitive food supply chain networks with application to fresh produce European Journal of Operational Research 227 2013 273 282
26. A. Nagurney Network economics - A variational inequality approach 1993 Kluwer Academic Publishers.
27. A. Nagurney Sustainable transportation networks 2000 Edward Elgar Publishing, Inc
28. A. Nagurney Innovations in financial and economic networks 2003 Edward Elgar Publishing, Inc.
29. A. Nagurney Network economics: A variational inequality approach 2nd and revised ed. 1999 Kluwer Academic Publishers Dordrecht, The Netherlands
30. A. Nagurney, and D. Zhang Projected dynamical systems and variational inequalities with applications 1996 Kluwer Academic Publishers
31. A. Nagurney, and S. Siokos Financial networks: Statics and dynamics Advances in spatial science 1997 Springer
32. A. Nagurney, and F. Toyasaki Reverse supply chain management and electronic waste recycling: a multitiered network equilibrium framework for e-cycling Transportation Research Part E 41 1 2005 1 28
33. A. Nagurney, Z. Liu, M.G. Cojocaru, and P. Daniele Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation Transportation Research Part E 43 2007 624 646
34. A. Nagurney, D. Parkes, and P. Daniele The internet, evolutionary variational inequalities, and the time-dependent braess paradox Computational Management Science 4 2007 355 375
35. J.F. Nash Noncooperative games Annals of Mathematics 54 1951 286 298
36. Ontario Electronic Stewardship (2008). Final waste electrical & electronic equipment (WEEE) program plan. < http://www.ene.gov.on.ca > [Accessed 31 July 2012].
37. PC 3R Promotion Association (2011). Present state analysis of PC manufacturers' recycling and their efforts for rare metal recycling. < http://www.env.go.jp/council/03haiki/y0326-01/mat07.pdf > [Accessed 21 January 2013].
38. Q. Qiang, K. Ke, T. Anderson, and J. Dong The closed-loop supply chain network with competition, distribution channel investment, and uncertainties Omega 41 2 2013 186 194
39. M.S. Sodhi, and B. Reimer Models for recycling electronics end-of-life products OR Spectrum 23 1 2001 97 115
40. Souma, T. (2009). Sharp introduced new facilities for recycling rare metals from liquid crystal television. Nikkei ecology, May 12 (in Japanese).
41. Savage, M. (2006). Implementation of the waste electric and electronic equipment directive in EU. Institute for Prospective Technological Studies. < http://ftp.jrc.es/EURdoc/eur22231en.pdf > [Accessed 2 February 2012].
42. G. Stampacchia Formes bilineaires coercitives sur les ensembles convexes Comptes Rendus de l'Acadmie des Sciences - Series I - Mathematics 258 1964 4413 4416
43. Stampacchia, G. (1969). Variational inequalities, theory and applications of monotone operators. In Proceedings of the N.A.T.O. Advanced Study Institute, Venice 1968 Ed. Oderisi, Gubbio (pp. 101-192).
44. K. Taji, and M. Fukushima A new merit function and a successive quadratic program- ming algorithm for variational inequality problems SIAM Journal on Optimization 6 1996 704 713
45. F. Toyasaki, T. Wakolbinger, and W. Kettinger The value of information systems for product recovery management International Journal of Production Research 51 4 2013 1214 1235
46. The Japan Machinery Federation and Manufacturing and Science Technology Center (2008). A research report about environmentally-friendly product designs for resources recycling in the global marketplace (in Japanese).
47. The Nikkei American Edition (2010). Recycling system for rare metals (in Japanese). December 11, 2010.
48. The Nikkei American Edition (2011). Rising price for rare earth: reasons for instable procurement (in Japanese). June 17, 2011.
49. The Nikkei American Edition (2012). Hitachi eliminates the use of rare earth for industrial motors (in Japanese). April 12, 2012.
50. T. Wakolbinger, and A. Nagurney Dynamic supernetworks for the integration of social networks and supply chains with electronic commerce: modeling and analysis of buyer-seller relationships with computations Netnomics 6 2004 153 185
51. Wakolbinger, T.; Toyasaki, F.; Nowak, T.; Nagurney, A. (2013). When and for whom would e-waste be a treasure trove: Insights from a network equilibrium model of e-waste flows. Working paper.