|  JEI Home  |  JTAS  |  Subscription  | 

Journal of Environmental Informatics

Online ISSN 1684-8799 / Print ISSN 1726-2135

 

Guest

   Volume 19   Number 1   March  2012 = complimentary

doi:10.3808/jei.201200203 About DOIs

JEI 19(1) 2012, Pages 1-9  

© 2012 ISEIS. All rights reserved.

A Robust Two-Step Method for Solving Interval Linear Programming Problems within an Environmental Management Context

Y. R. Fan and G. H. Huang*

Institute for Energy, Environment and Sustainability Research, UR-NCEPU, North China Electric Power University, Beijing 102206, China

*Corresponding author. Tel: +86-10-61772018 Fax: +86-10-51971284 Email: huang@iseis.org

 

Abstract

In this study, a robust two-step method (RTSM) is developed to solve the interval linear programming (ILP) problem. It improved upon the two-step method (TSM) proposed by Huang et al. (1992) through incorporating additional constraints into solution procedures to avoid absolute violation. RTSM was applied to a simple case related to environmental management. The results demonstrated applicability of the developed methodology. Compare with the modified interval linear programming (MILP) method proposed by Zhou et al., (2008) and the three-step method (ThSM) developed by Cao and Huang (2011), RTSM can generate a relatively larger solution space and thus avoid significant loss of decision-related information. Besides, RTSM has simpler solution procedures than ThSM, and will not lead to great computational requirement.


Keywords: decision support, algorithm, interval number, optimization, uncertainty

 

Full Text (PDF) | Export citation to: EndNote  RefMan

Cite this paper as: Y. R. Fan and G. H. Huang, 2012. A Robust Two-Step Method for Solving Interval Linear Programming Problems within an Environmental Management Context. Journal of Environmental Informatics, 19(1), 1-9. http://dx.doi.org/10.3808/jei.201200203


References: 34

  1. Bloemhof-Ruwaard, J.M., Van Beek, P., Hordijk, L., and Van Wassenhove, L.N. (1995). Interactions between operational research and environmental management. Eur. J. Oper. Res., 85(2), 22.9-243. http://dx.doi.org/10.1016/0377-2217(94)00294-M
  2. Chang, N.B., and Lu, H.Y. (1997). A new approach for long-term planning of solid waste management system using fuzzy global criterion. J. Environ. Sci. Health. (Part A), 32(4), 1025-1047.
  3. Chang, N.-B. and Wang, S.F. (1997). A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems. Eur. J. Oper. Res., 99(2), 303-321. http://dx.doi.org/10.1016/S0377-2217(96)00024-0
  4. Chinneck, J.W., Ramada, K. (2000). Linear programming with interval coefficients. J. Oper. Res. Soc., 51(2), 209-220.
  5. Fan, Y. R., Huang, G. H., Li, Y. P., Cao M. F. and Cheng, G. H. (2009). A Fuzzy Linear Programming Approach for Municipal Solid-Waste Management under Uncertainty. Eng. Optimiz., 41(12), 1081-1101. http://dx.doi.org/10.1080/03052150902866569
  6. Fan, Y.R., Huang, G.H., Guo, P., and Yang A.L. (2012). Inexact two-stage stochastic partial programming: application to water resources management under uncertainty. Stoch. Env. Res. Risk. A., 26(2), 281-293. http://dx.doi.org/10.1007/s00477-011-0504-6
  7. Fan, Y.R., Huang, G.H., and Veawab, A. (2012). A Generalized Fuzzy Linear Programming Approach for Environmental Management Problem under Uncertainty. J. Air Waste Manage., 62(1), 72-86. http://dx.doi.org/10.1080/10473289.2011.628901
  8. Fiedler, M., Nedoma, J., Ramik, J., Rohn, J., and Zimmermann, K. (2006). Linear optimization problems with inexact data, Springer, New York.
  9. He L., Huang, G.H., Zeng, G.M., and Lu, H.W. (2008). Identifying optimal regional solid waste management strategies through an inexact integer programming model containing infinite objectives and constraints. Waste Manage., 29(1), 21-31. http://dx.doi.org/10.1016/j.wasman.2008.02.003
  10. Huang, G.H., Baetz, B.W., and Patry, G.G. (1992). A grey linear programming approach for municipal solid waste management planning under uncertainty. Civil Eng. Syst., 9(4), 319-335. http://dx.doi.org/10.1080/02630259208970657
  11. Huang, G.H., Baetz, B.W., and Patry, G.G. (1995). Grey fuzzy integer programming: An application to regional waste management planning under uncertainty. Socio Econ. Plan Sci., 29(1), 17-38. http://dx.doi.org/10.1016/0038-0121(95)98604-T
  12. Huang, G.H., and Cao, M.F., (2011). Analysis of Solution Methods for Interval Linear Programming. J. Environ. Inform., 17(2): 54-64. http://dx.doi.org/10.3808/jei.201100187
  13. Huang, G.H., and Chang, N.B. (2003). The Perspectives of Environmental Informatics and Systems Analysis. J. Environ. Inform., 1(1), 1-6. http://dx.doi.org/10.3808/jei.200300001
  14. Huang, G.H. (1998). A hybrid inexact-stochastic water management model. Eur. J. Oper. Res., 107(1), 137-158. http://dx.doi.org/10.1016/S0377-2217(97)00144-6
  15. Huang, Y.F., Baetz, B.W., Huang, G.H., and Liu, L. (2002). Violation analysis for solid waste management systems: An interval fuzzy programming approach. J. Environ. Manage., 65(4), 431-446. http://dx.doi.org/10.1006/jema.2002.0566
  16. Karmakar, S. and Mujumdar, P.P. (2006a). Grey fuzzy optimization model for water quality management of a river system. Adv. Water Resour., 29(7), 1088-1105. http://dx.doi.org/10.1016/j.advwatres.2006.04.003
  17. Karmakar, S. and Mujumdar, P.P. (2006b). An inexact optimization approach for river water quality management. J. Environ. Manage., 81(3), 233-248. http://dx.doi.org/10.1016/j.jenvman.2005.10.009
  18. Li, Y.P., Huang, G.H., and Nie, S.L. (2006). An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty. Adv. Water Resour., 29(5), 776-789. http://dx.doi.org/10.1016/j.advwatres.2005.07.008
  19. Li, Y.P., Huang, G.H., Nie, S.L., and Qin, X.S. (2007). ITCLP: An inexact two-stage chance-constrained program for planning waste management systems. Resour. Conserv. Recy., 49(3), 284-307. http://dx.doi.org/10.1016/j.resconrec.2006.03.017
  20. Li, Y.P., Huang, G.H., Nie, X.H., and Nie, S.L. (2008). A two-stage fuzzy robust integer programming approach for capacity planning of environmental management systems. Eur. J. Oper. Res., 189(2), 399-420. http://dx.doi.org/10.1016/j.ejor.2007.05.014
  21. Liu, Y., Guo, H.C., Zhou, F., Qin, X.S., Huang, K., and Yu, Y.J. (2008). Inexact Chance-Constrained Linear Programming Model for Optimal Water Pollution Management at the Watershed Scale. J. Water Res. Pl.-ASCE, 134(4), 347-356. http://dx.doi.org/10.1061/(ASCE)0733-9496(2008)134:4(347)
  22. Lv, Y., Huang, G.H., Li, Y.P., Yang, Z.F., Liu, Y., and Cheng, G.H. (2010). Planning Reginal Water Resources System Using an Interval Fuzzy Bi-liver Programming Method. J. Environ. Inform., 16(2), 43-56. http://dx.doi.org/10.3808/jei.201000177
  23. Nie, X.H., Huang, G.H., Li, Y.P., and Liu, L. (2007). IFRP: A hybrid interval-parameter fuzzy robust programming approach for waste management planning under uncertainty. J. Environ. Manage., 84(1), 1-11. http://dx.doi.org/10.1016/j.jenvman.2006.04.006
  24. Oliveira, C., and Antunes, C.H. (2007). Multiple objective linear programming models with interval coefficients - an illustrated overview. Eur. J. Oper. Res., 181(3), 1434-1463. http://dx.doi.org/10.1016/j.ejor.2005.12.042
  25. Ozdemir, M.S., and Saaty, T.L. (2006). The unknown in decision making: What to do about it. Eur. J. Oper. Res., 174(1), 349-359. http://dx.doi.org/10.1016/j.ejor.2004.12.017
  26. Ruszcyński, A. (1997). Decomposition methods in stochastic programming. Math. Program., 79(1-3), 333-353. http://dx.doi.org/10.1007/BF02614323
  27. Sengupta, A., Pal, T.K., and Chakraborty, D. (2001). Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Set. Syst., 119(1), 129-138. http://dx.doi.org/10.1016/S0165-0114(98)00407-2
  28. Sun W., and Huang, G.H. (2010). Inexact Piecewise Quadratic Programming for Waste Flow Allocation under Uncertainty and Nonlinearity. J. Environ. Inform., 16(2), 80-93. http://dx.doi.org/10.3808/jei.201000180
  29. Tong, S.C. (1994). Interval number, fuzzy number linear programming. Fuzzy Set. Syst., 66(3), 301-306. http://dx.doi.org/10.1016/0165-0114(94)90097-3
  30. van Beek, P., Fortuin, L., and Van Wassenhove, L.N. (1992). Operational Research and the Environment. Environmetal & Resource Econo., 2(6), 635-639. http://dx.doi.org/10.1007/BF00330288
  31. Yan, X.P., Ma, X.F., Huang, G.H., and Wu, C.Z. (2010). An Inexact Transportation Planning Model for Supporting Vehicle Emissions Management. J. Environ. Inform., 15(2), 87-98. http://dx.doi.org/10.3808/jei.201000169
  32. Young, R.A. (2001). Uncertainty and the Environment: Implications for Decision Making and Environmental Policy, Edward Elgar, Cheltenham, UK.
  33. Zhou, F., Guo, H.C., Huang, K., and Huang, G.H. (2008). The Interval Linear Programming: A Revisit. J. Environ. Inform., 11(1), 1-10. http://dx.doi.org/10.3808/jei.200800105
  34. Zou, R., Liu, Y., Liu, L., and Guo, H.C. (2010). REILP Approach for Uncertainty-Based Decision Making in Civil Engineering. J. Comput. Civil Eng. -ASCE, 24(4), 357-364. http://dx.doi.org/10.1061/(ASCE)CP.1943-5487.0000037

    35.  


© 2013 ISEIS - International Society for Environmental Information Sciences