Enhanced-interval linear programming

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A±, B± and C±) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to that of interval linear programming (ILP), which helps to achieve insight into the expected-value-oriented trade-off between system benefits and risks of constraint violations. The degree of uncertainty of its enhanced-interval objective function (EIOF) would be lower than that of ILP model when the solution space is absolutely feasible, and the EIOF's expected value could be used as a criterion for generating the appropriate alternatives, which help decision-makers obtain non-extreme decisions. Moreover, because it can be decomposed into two submodels, EILP's computational requirement is lower than that of stochastic and fuzzy LP models. The results of a numeric example further indicated the feasibility and effectiveness of EILP model. In addition, EI nonlinear programming models, hybrid stochastic or fuzzy EILP models as well as risk-based trade-off analysis for EI uncertainty within decision process can be further developed to improve its applicability.

[1]  Tong Shaocheng,et al.  Interval number and fuzzy number linear programmings , 1994 .

[2]  Baoding Liu,et al.  Modelling stochastic decision systems using dependent-chance programming , 1997 .

[3]  Carlos Henggeler Antunes,et al.  Multiple objective linear programming models with interval coefficients - an illustrated overview , 2007, Eur. J. Oper. Res..

[4]  C. Hwang,et al.  Interactive fuzzy linear programming , 1992 .

[5]  G. Huang,et al.  Grey integer programming: An application to waste management planning under uncertainty , 1995 .

[6]  Guohe Huang,et al.  Grey linear programming, its solving approach, and its application , 1993 .

[7]  John W. Chinneck,et al.  Linear programming with interval coefficients , 2000, J. Oper. Res. Soc..

[8]  Gordon H. Huang,et al.  IPWM: AN INTERVAL PARAMETER WATER QUALITY MANAGEMENT MODEL , 1996 .

[9]  G. H. Huang,et al.  A hybrid inexact-stochastic water management model , 1998, Eur. J. Oper. Res..

[10]  M. K. Luhandjula.  Fuzzy stochastic linear programming: Survey and future research directions , 2006, Eur. J. Oper. Res..

[11]  Ralph E. Steuer.  Algorithms for Linear Programming Problems with Interval Objective Function Coefficients , 1981, Math. Oper. Res..

[12]  Efstratios N. Pistikopoulos,et al.  Stochastic optimization based algorithms for process synthesis under uncertainty , 1998 .

[13]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[14]  Peter Kall,et al.  Stochastic Linear Programming , 1975 .

[15]  Ching-Pin Tung,et al.  Interval number fuzzy linear programming for climate change impact assessments of reservoir active storage , 2009, Paddy and Water Environment.

[16]  Masahiro Inuiguchi,et al.  Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem , 2000, Fuzzy Sets Syst..

[17]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[18]  Ni-Bin Chang,et al.  A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems , 1997 .

[19]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[20]  Guo H. Huang,et al.  An interval-parameter fuzzy two-stage stochastic program for water resources management under uncertainty , 2005, Eur. J. Oper. Res..

[21]  Debjani Chakraborty,et al.  Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming , 2001, Fuzzy Sets Syst..

[22]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[23]  Kenneth Lange,et al.  Applied Probability , 2003 .

[24]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[25]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[26]  Arthur M. Geoffrion,et al.  Exceptional Paper—Parametric and Postoptimality Analysis in Integer Linear Programming , 1977 .

[27]  George B. Dantzig,et al.  Linear Programming Under Uncertainty , 2004, Manag. Sci..

[28]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[29]  H. Rommelfanger,et al.  Linear programming with fuzzy objectives , 1989 .

[30]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[31]  Guohe Huang,et al.  AN INEXACT TWO-STAGE STOCHASTIC PROGRAMMING MODEL FOR WATER RESOURCES MANAGEMENT UNDER UNCERTAINTY , 2000 .

[32]  Milan Vlach,et al.  Satisficing solutions and duality in interval and fuzzy linear programming , 2003, Fuzzy Sets Syst..

[33]  Nikolaos V. Sahinidis,et al.  Optimization under uncertainty: state-of-the-art and opportunities , 2004, Comput. Chem. Eng..

[34]  K. Asai,et al.  Fuzzy linear programming problems with fuzzy numbers , 1984 .

[35]  Masahiro Inuiguchi,et al.  Minimax regret solution to linear programming problems with an interval objective function , 1995 .

[36]  Adi Ben-Israel,et al.  A Decomposition Method for Interval Linear Programming , 1970 .

[37]  Weldon A. Lodwick,et al.  Special issue: interfaces between fuzzy set theory and interval analysis , 2003, Fuzzy Sets Syst..

[38]  A. Charnes,et al.  Chance-Constrained Programming , 1959 .