TY - CHAP
T1 - Linear programming with interval data
T2 - A two-level programming approach
AU - Kao, Chiang
AU - Liu, Shiang Tai
N1 - Funding Information:
This research is supported by the National Science Council of the Republic of China (Taiwan) under Contract NSC 89-2418-H-006-001.
Publisher Copyright:
© Springer Science+Business Media New York 2013.
PY - 2013
Y1 - 2013
N2 - Linear programming has been widely applied to solving real world problems. The conventional linear programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This chapter discusses the general interval linear programming problems where all the parameters, including the cost coefficients, requirement coefficients, and technological coefficients, are represented by interval data. Since the parameters are interval-valued, the objective value is interval-valued as well. A pair of two-level mathematical programs is formulated to calculate the lower bound and upper bound of the objective values of the interval linear program. The two-level mathematical programs are then transformed into one-level nonlinear programs. Solving the pair of nonlinear programs produces the interval of the objective values of the problem. An example illustrates the whole idea and sheds some light on interval linear programming.
AB - Linear programming has been widely applied to solving real world problems. The conventional linear programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This chapter discusses the general interval linear programming problems where all the parameters, including the cost coefficients, requirement coefficients, and technological coefficients, are represented by interval data. Since the parameters are interval-valued, the objective value is interval-valued as well. A pair of two-level mathematical programs is formulated to calculate the lower bound and upper bound of the objective values of the interval linear program. The two-level mathematical programs are then transformed into one-level nonlinear programs. Solving the pair of nonlinear programs produces the interval of the objective values of the problem. An example illustrates the whole idea and sheds some light on interval linear programming.
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U2 - 10.1007/978-1-4614-5131-0_5
DO - 10.1007/978-1-4614-5131-0_5
M3 - Chapter
AN - SCOPUS:84978796167
T3 - Springer Optimization and Its Applications
SP - 63
EP - 77
BT - Springer Optimization and Its Applications
PB - Springer International Publishing
ER -