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Linear Programming with Interval Data: A Two-Level Programming Approach

In: Optimization, Simulation, and Control

Author

Listed:
  • Chiang Kao

    (National Cheng Kung University)

  • Shiang-Tai Liu

    (Vanung University)

Abstract

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.

Suggested Citation

  • Chiang Kao & Shiang-Tai Liu, 2013. "Linear Programming with Interval Data: A Two-Level Programming Approach," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 63-77, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-5131-0_5
    DOI: 10.1007/978-1-4614-5131-0_5
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