Shades of grey: A critical review of grey-number optimization

Engineering Optimization

Volumn 41, Issue 6, 2009, Pages 573-592

  Rosenberg, David E ^a  

^a Utah State University   (United States)

Author keywords

Interval number; Linear program; Optimization with uncertainty; Stochastic program with recourse

Indexed keywords

CASE ANALYSIS; CRITICAL REVIEW; DECISION SPACE; DECISION VARIABLES; GREY MODEL; GREY NUMBER; INTERVAL NUMBER; LINEAR PROGRAM; LOWER AND UPPER BOUNDS; NEW SOLUTIONS; OBJECTIVE FUNCTIONS; POOR PERFORMANCE; SOLUTION ALGORITHMS; STOCHASTIC PROGRAM WITH RECOURSE; STOCHASTIC PROGRAMMING WITH RECOURSE; WORST-CASE ANALYSIS;

OPTIMIZATION; STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

RISK ANALYSIS;

EID: 70449595783     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/03052150902718125     Document Type: Article

References (23)

1. Huang, G., 1996. IPWM: An interval parameter water quality management model. Engineering Optimization, 26 (2), 79-103.
2. Huang, G.H., 1998. A hybrid inexact-stochastic water management model. European Journal of Operational Research, 107 (1), 137-158.
3. Huang, G.H. and Baetz, B.W., 1995. Grey quadratic-programming and its application to municipal solid-waste management planning under uncertainty. Engineering Optimization, 23 (3), 201-223.
4. Huang, G.H., Baetz, B.W., and Patry, G.G., 1992. A gray linear-programming approach for municipal solid-waste management planning under uncertainty. Civil Engineering Systems, 9 (4), 319-335.
5. Huang, G.H., Baetz, B.W., and Patry, G.G., 1995. Grey integer programming - an application to waste management planning under uncertainty. European Journal of Operational Research, 83 (3), 594-620.
6. Huang, G.H. and Loucks, D.P., 2000.Aninexact two-stage stochastic programming model forwater resources management under uncertainty. Civil Engineering and Environmental Systems, 17 (2), 95-118.
7. Huang, G.H. and Moore, R.D., 1993. Graylinear-programming, its solving approach, and its application. International Journal of Systems Science, 24 (1), 159-172.
8. Ishibuchi, H. and Tanaka, H., 1990. Multiobjective programming in optimization of the interval objective function. European Journal of Operational Research, 48 (2), 219-225.
9. Li, Y.P. and Huang, G.H., 2006. An inexact two-stage mixed integer linear programming method for solid waste management in the City of Regina. Journal of Environmental Management, 81(3), 188-209.
10. Li, Y.P. and Huang, G.H., 2007. Fuzzy two-stage quadratic programming for planning solid waste management under uncertainty. International Journal of Systems Science, 38 (3), 219-233.
11. Li, Y.P., Huang, G.H., and Baetz, B.W., 2006a. Environmental management under uncertainty - an internal-parameter two-stage chance-constrained mixed integer linear programming method. Environmental Engineering Science, 23 (5), 761-779.
12. Li,Y.P., Huang, G.H., and Nie, S.L., 2006b. An interval-parameter multi-stage stochastic programming model for water resources management under uncertainty. Advances in Water Resources, 29 (5), 776-789.
13. Li, Y.P., Huang, G.H., and Nie, S.L., 2007. Mixed interval-fuzzy two-stage integer programming and its application to flood-diversion planning. Engineering Optimization, 39 (2), 163-183.
14. Li,Y.P., Huang, G.H., Nie, S.L., and Huang,Y.F., 2006c. IFTSIP: Interval fuzzy two-stage stochastic mixed-integer linear programming: A case study for environmental management and planning. Civil Engineering and Environmental Systems, 23 (2), 73-99.
15. Li, Y.P., Huang, G.H., Nie, S.L., Nie, X.H., and Maqsood, I., 2006d. An interval-parameter two-stage stochastic integer programming model for environmental systems planning under uncertainty. Engineering Optimization, 38 (4), 461-483.
16. Maqsood, I., Huang, G.H., Huang,Y.F., and Chen, B., 2005a. ITOM:An interval-parameter two-stage optimization model for stochastic planning of water resources systems. Stochastic Environmental Research and Risk Assessment, 19 (2), 125-133.
17. Maqsood, I., Huang, G.H., and Zeng, G.M., 2004. An inexact two-stage mixed integer linear programming model for waste management under uncertainty. Civil Engineering and Environmental Systems, 21 (3), 187-206.
18. Maqsood, M. and Huang, G.H., 2003. A two-stage interval-stochastic programming model for waste management under uncertainty. Journal of the Air & Waste Management Association, 53 (5), 540-552.
19. Maqsood, M., Huang, G.H., and Yeomans, J.S., 2005b. An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty. European Journal of Operational Research, 167 (1), 208-225.
20. Rosenberg, D.E. and Lund, J.R., 2009. Modeling integrated water utility decisions with recourse and uncertainties.Water Resources Management, 23 (1), 85-115.
21. Sahinidis, N.V., 2004. Optimization under uncertainty: State-of-the-art and opportunities. Computers & Chemical Engineering, 28 (6/7), 971-983.
22. Tong, S.C., 1994. Interval number and fuzzy number linear programmings. Fuzzy Sets and Systems, 66 (3), 301-306.
23. Yeh, S.-C., 1996. Grey programming and its applications towater resources management. Thesis (PhD). Cornell University, Ithaca, NY.